Abstract We show how to use passive automata learning to infer models of attacker-defender interactions in cybersecurity. By treating system event logs as words in a formal language, we can apply algorithms such as RPNI to infer compact deterministic finite automata from observed traces. We evaluate this approach through a case study on the Cyber Operations Research Gymnasium (CybORG), a widely-used simulation framework for training defensive agents using machine learning. We analyze the structural properties of the inferred automata and assess their empirical fidelity with respect to the semantics of CybORG. Our results show that accurate formal models can be learned from a relatively small number of traces, suggesting a promising path toward more automated and data-driven approaches to cybersecurity.

This paper introduces NEST (Network Enforced Session Types), a runtime verification framework that moves application-level protocol monitoring into the network fabric. Unlike prior work that instruments or wraps application code, we synthesise packet-level monitors that enforce protocols directly in the data plane. We develop algorithms to generate network-level monitors from session types and extend them to handle packet loss and reordering. We implement NEST in P4 and evaluate it on applications including microservice and network-function models, showing that network-level monitors can enforce realistic non-trivial protocols.

We introduce weighted NetKAT, a domain-specific language for modeling and verifying quantitative network properties. The language is parametric on a semiring, enabling the treatment of a wide range of quantities in a uniform way. We provide a denotational semantics and an equivalent operational semantics, the latter based on a novel model of weighted NetKAT automata (WNKA) capturing the stateful behavior of our language. With WNKA, we obtain a class of generic decision procedures for reasoning about quantitative safety and reachability in a fully automatic way, even in the presence of possibly unbounded iteration. We demonstrate the applicability of our framework in a case study using Internet2's Abilene network as the underlying topology.

Hypervisors are an essential part of our computing infrastructure, yet ensuring their correctness remains a significant challenge for the community. While several hypervisors have been formally verified using traditional methods, they have typically required a huge effort and significant input from verification experts. With the increasing diversity of hypervisors, driven by open hardware and custom ISAs, there is a growing need for more accessible approaches that can be used by non-experts.

We develop StacKAT, a network verification language featuring loops, finite state variables, nondeterminism, and—most importantly—access to a stack with accompanying push and pop operations. By viewing the variables and stack as the (parsed) headers and (to-be-parsed) contents of a network packet, StacKAT can express a wide range of network behaviors including parsing, source routing, and telemetry. These behaviors are difficult or impossible to model using existing languages like NetKAT . We develop a decision procedure for StacKAT program equivalence, based on finite automata. This decision procedure provides the theoretical basis for verifying network-wide properties and is able to provide counterexamples for inequivalent programs. Finally, we provide an axiomatization of StacKAT equivalence and establish its completeness.

NetKAT is a domain-specific programming language and logic that has been successfully used to specify and verify the behavior of packet-switched networks. This paper develops techniques for automatically learning NetKAT models of unknown networks using active learning. Prior work has explored active learning for a wide range of automata (e.g., deterministic, register, Büchi, timed etc.) and also developed applications, such as validating implementations of network protocols. We present algorithms for learning different types of NetKAT automata, including symbolic automata proposed in recent work. We prove the soundness of these algorithms, build a prototype implementation, and evaluate it on a standard benchmark. Our results highlight the applicability of symbolic NetKAT learning for realistic network configurations and topologies.

The quest to build scalable data center networks has driven much of the innovation in the networking community in recent decades. But the one-size-fits-all service model offered by these networks does not meet the needs of every application. In response, cloud providers have started to design custom clusters to support the specialized workloads used in finance, AI, high-performance computing, and other areas.

Verifying network programs is challenging because of how they divide labor: the control plane computes high level routes through the network and compiles them to device configurations, while the data plane uses these configurations to realize the desired forwarding behavior. In practice, the correctness of the data plane often assumes that the configurations generated by the control plane will satisfy complex specifications. Consequently, validation tools such as program verifiers, runtime monitors, fuzzers, and test-case generators must be aware of these control interface specifications (ci-specs) to avoid raising false alarms. In this paper, we propose the first algorithm for computing precise ci-specs for network data planes. Our specifications are designed to be efficiently monitorable —concretely, checking that a fixed configuration satisfies a ci-spec can be done in polynomial time. Our algorithm, based on modular program instrumentation, quantifier elimination, and a path-based analysis, is more expressive than prior work, and is applicable to practical network programs. We describe an implementation and show that ci-specs computed by our tool are useful for finding real bugs in real-world data plane programs.

We develop new data structures and algorithms for checking verification queries in NetKAT, a domain-specific language for specifying the behavior of network data planes. Our results extend the techniques obtained in prior work on symbolic automata and provide a framework for building efficient and scalable verification tools. We present KATch, an implementation of these ideas in Scala, featuring an extended set of NetKAT operators that are useful for expressing network-wide specifications, and a verification engine that constructs a bisimulation or generates a counter-example showing that none exists. We evaluate the performance of our implementation on real-world and synthetic benchmarks, verifying properties such as reachability and slice isolation, typically returning a result in well under a second, which is orders of magnitude faster than previous approaches. Our advancements underscore NetKAT’s potential as a practical, declarative language for network specification and verification.

P4Cub is a new intermediate representation (IR) for the P4 programming language. It has been designed with the goal of facilitating development of certified tools. To achieve this, P4Cub is organized around a small set of core constructs and avoids side effects in expressions, which avoids mutual recursion between the semantics of expressions and statements. Still, it retains the essential domain-specific features of P4 itself. P4Cub has a front-end based on Petr4, and has been fully mechanized in Coq including big-step and small-step semantics and a type system. As case studies, we have engineered several certified tools with P4Cub including proofs of type soundness, a verified compilation pass, and an automated verification tool.

It is notoriously difficult to verify that a network is behaving as intended, especially at scale. This paper presents Hydra, a system that uses ideas from runtime verification to check that every packet is correctly processed with respect to a specification in real time. We propose a domain-specific language for writing properties, called Indus, and we develop a compiler that turns properties thus specified into executable P4 code that runs alongside the forwarding code at line rate. To evaluate our approach, we used Indus to model a range of properties, showing that it is expressive enough to capture examples studied in prior work. We also deployed Hydra checkers for validating paths in source routing and for enforcing slice isolation in Aether, an open-source cellular platform. We confirmed a subtle bug in Aether's 5G mobile core that would have been hard to detect using static techniques. We also evaluated the overheads of Hydra on hardware, finding that it does not significantly increase latency and often does not require additional pipeline stages.

We present P4Testgen, a test oracle for the P416 language. P4Testgen supports automatic test generation for any P4 target and is designed to be extensible to many P4 targets. It models the complete semantics of the target's packet-processing pipeline including the P4 language, architectures and externs, and target-specific extensions. To handle non-deterministic behaviors and complex externs (e.g., checksums and hash functions), P4Testgen uses taint tracking and concolic execution. It also provides path selection strategies that reduce the number of tests required to achieve full coverage.

Early programming models for software-defined networking (SDN) focused on basic features for controlling network-wide forwarding paths, but more recent work has considered richer features, such as packet scheduling and queueing, that affect performance. In particular,PIFO trees, proposed by Sivaraman et al., offer a flexible and efficient primitive forprogrammablepacket scheduling. Prior work has shown that PIFO trees can express a wide range of practical algorithms including strict priority, weighted fair queueing, and hierarchical schemes. However, the semantic properties of PIFO trees are not well understood. This paper studies PIFO trees from a programming language perspective. We formalize the syntax and semantics of PIFO trees in an operational model that decouples the scheduling policy running on a tree from the topology of the tree. Building on this formalization, we develop compilation algorithms that allow the behavior of a PIFO tree written against one topology to be realized using a tree with a different topology. Such a compiler could be used to optimize an implementation of PIFO trees, or realize a logical PIFO tree on a target with a fixed topology baked into the hardware. To support experimentation, we develop a software simulator for PIFO trees, and we present case studies illustrating its behavior on standard and custom algorithms.

Abstract We introduce Concurrent (), an extension of with operators for specifying and reasoning about concurrency in scenarios where multiple packets interact through state. We provide a model of the language based on partially-ordered multisets (pomsets), which are a well-established mathematical structure for defining the denotational semantics of concurrent languages. We provide a sound and complete axiomatization of this model, and we illustrate the use of through examples. More generally, can be understood as an algebraic framework for reasoning about programs with both local state (in packets) and global state (in a global store).

We present Leapfrog, a Coq-based framework for verifying equivalence of network protocol parsers. Our approach is based on an automata model of P4 parsers, and an algorithm for symbolically computing a compact representation of a bisimulation, using "leaps." Proofs are powered by a certified compilation chain from first-order entailments to low-level bitvector verification conditions, which are discharged using off-the-shelf SMT solvers. As a result, parser equivalence proofs in Leapfrog are fully automatic and push-button.

Programming languages like P4 enable specifying the behavior of network data planes in software. However, with increasingly powerful and complex applications running in the network, the risk of faults also increases. Hence, there is growing recognition of the need for methods and tools to statically verify the correctness of P4 code, especially as the language lacks basic safety guarantees. Type systems are a lightweight and compositional way to establish program properties, but there is a significant gap between the kinds of properties that can be proved using simple type systems (e.g., SafeP4) and those that can be obtained using full-blown verification tools (e.g., p4v). In this paper, we close this gap by developing Π4, a dependently-typed version of P4 based on decidable refinements. We motivate the design of Π4, prove the soundness of its type system, develop an SMT-based implementation, and present case studies that illustrate its applicability to a variety of data plane programs.

In this paper, we explore how programmable data planes can naturally provide a higher-level of service to user applications via a new abstraction called packet subscriptions. Packet subscriptions generalize forwarding rules, and can be used to express both traditional routing and more esoteric, content-based approaches. We present strategies for routing with packet subscriptions in which a centralized controller has a global view of the network, and the network topology has a hierarchical or general structure. We also describe a compiler for packet subscriptions that uses a novel BDD-based algorithm to efficiently translate predicates into P4 tables that can support O(100K) expressions. Using our system, we have built eight diverse applications. We show that these applications can be deployed in brownfield networks while performing line-rate message processing, using the full switch bandwidth of 6.5Tbps.

P4 is a domain-specific language for programming and specifying packet-processing systems. It is based on an elegant design with high-level abstractions like parsers and match-action pipelines that can be compiled to efficient implementations in software or hardware. Unfortunately, like many industrial languages, P4 has developed without a formal foundation. The P4 Language Specification is a 160-page document with a mixture of informal prose, graphical diagrams, and pseudocode, leaving many aspects of the language semantics up to individual compilation targets. The P4 reference implementation is a complex system, running to over 40KLoC of C++ code, with support for only a few targets. Clearly neither of these artifacts is suitable for formal reasoning about P4 in general. This paper presents a new framework, called Petr4, that puts P4 on a solid foundation. Petr4 consists of a clean-slate definitional interpreter and a core calculus that models a fragment of P4. Petr4 is not tied to any particular target: the interpreter is parameterized over an interface that collects features delegated to targets in one place, while the core calculus overapproximates target-specific behaviors using non-determinism. We have validated the interpreter against a suite of over 750 tests from the P4 reference implementation, exercising our target interface with tests for different targets. We validated the core calculus with a proof of type-preserving termination. While developing Petr4, we reported dozens of bugs in the language specification and the reference implementation, many of which have been fixed.

In this paper, we explore how programmable data planes can naturally provide a higher-level of service to user applications via a new abstraction called packet subscriptions. Packet subscriptions generalize forwarding rules, and can be used to express both traditional routing and more esoteric, content-based approaches. We present strategies for routing with packet subscriptions in which a centralized controller has a global view of the network, and the network topology is organized as a hierarchical structure. We also describe a compiler for packet subscriptions that uses a novel BDD-based algorithm to efficiently translate predicates into P4 tables that can support O(100K) expressions. Using our system, we have built three diverse applications. We show that these applications can be deployed in brownfield networks while performing line-rate message processing, using the full switch bandwidth of 6.5Tbps.

Dataplane languages like P4 enable flexible and efficient packet-processing using domain-specific primitives such as programmable parsers and match-action tables. Unfortunately, P4 programs tend to be monolithic and tightly coupled to the hardware architecture, which makes it hard to write programs in a portable and modular way---e.g., by composing reusable libraries of standard protocols.

Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebra with Tests (KAT) that arises by restricting the union (+) and iteration (*) operations from KAT to predicate-guarded versions. We develop the (co)algebraic theory of GKAT and show how it can be efficiently used to reason about imperative programs. In contrast to KAT, whose equational theory is PSPACE-complete, we show that the equational theory of GKAT is (almost) linear time. We also provide a full Kleene theorem and prove completeness for an analogue of Salomaa’s axiomatization of Kleene Algebra.

Computer networks often serve as the first line of defense against malicious attacks. Although there are a growing number of tools for defining and enforcing security policies in software-defined networks (SDNs), most assume a single point of control and are unable to handle the challenges that arise in networks with multiple administrative domains. For example, consumers may want want to allow their home IoT networks to be configured by device vendors, which raises security and privacy concerns. In this paper we propose a framework called Proof-Carrying Network Code (PCNC) for specifying and enforcing security in SDNs with interacting administrative domains. Like Proof-Carrying Authorization (PCA), PCNC provides methods for managing authorization domains, and like Proof-Carrying Code (PCC), PCNC provides methods for enforcing behavioral properties of network programs. We develop theoretical foundations for PCNC and evaluate it in simulated and real network settings, including a case study that considers security in IoT networks for home health monitoring.

The P4 programming language offers high-level, declarative abstractions that bring the flexibility of software to the domain of networking. Unfortunately, the main abstraction used to represent packet data in P4, namely header types, lacks basic safety guarantees. Over the last few years, experience with an increasing number of programs has shown the risks of the unsafe approach, which often leads to subtle software bugs. This paper proposes SafeP4, a domain-specific language for programmable data planes in which all packet data is guaranteed to have a well-defined meaning and satisfy essential safety guarantees. We equip SafeP4 with a formal semantics and a static type system that statically guarantees header validity---a common source of safety bugs according to our analysis of real-world P4 programs. Statically ensuring header validity is challenging because the set of valid headers can be modified at runtime, making it a dynamic program property. Our type system achieves static safety by using a form of path-sensitive reasoning that tracks dynamic information from conditional statements, routing tables, and the control plane. Our evaluation shows that SafeP4's type system can effectively eliminate common failures in many real-world programs.

To achieve good performance, modern applications often partition their state across multiple geographically distributed nodes. While this approach reduces latency in the common case, it can be challenging for programmers to use correctly, especially in applications that require strong consistency. We introduce predictive treaties, a mechanism that can significantly reduce distributed coordination without losing strong consistency. The central insight behind our approach is that many computations can be expressed in terms of predicates over distributed state that can be partitioned and enforced locally. Predictive treaties improve on previous work by allowing the locally enforced predicates to depend on time. Intuitively, by predicting the evolution of system state, coordination can be significantly reduced compared to static approaches. We implemented predictive treaties in a distributed system that exposes them in an intuitive programming model. We evaluate performance on several benchmarks, including TPC-C, showing that predictive treaties can significantly increase performance by orders of magnitude and can even outperform customized algorithms.

This paper presents McNetKAT, a scalable tool for verifying probabilistic network programs. McNetKAT is based on a new semantics for the guarded and history-free fragment of Probabilistic NetKAT in terms of finite-state, absorbing Markov chains. This view allows the semantics of all programs to be computed exactly, enabling construction of an automatic verification tool. Domain-specific optimizations and a parallelizing backend enable McNetKAT to analyze networks with thousands of nodes, automatically reasoning about general properties such as probabilistic program equivalence and refinement, as well as networking properties such as resilience to failures. We evaluate McNetKAT's scalability using real-world topologies, compare its performance against state-of-the-art tools, and develop an extended case study on a recently proposed data center network design.

Network virtualization stacks are the linchpins of public clouds. A key goal is to provide performance isolation so that workloads on one Virtual Machine (VM) do not adversely impact the network experience of another VM. Using data from a major public cloud provider, we systematically characterize how performance isolation can break in current virtualization stacks and find a fundamental tradeoff between isolation and resource multiplexing for efficiency. In order to provide predictable performance, we propose a new system called PicNIC that shares resources efficiently in the common case while rapidly reacting to ensure isolation. PicNIC builds on three constructs to quickly detect isolation breakdown and to enforce it when necessary: CPU-fair weighted fair queues at receivers, receiver-driven congestion control for backpressure, and sender-side admission control with shaping. Based on an extensive evaluation, we show that this combination ensures isolation for VMs at sub-millisecond timescales with negligible overhead.

In this paper, we explore how programmable data planes can provide a higher-level of service to user applications via a new abstraction called packet subscriptions. Packet subscriptions generalize forwarding rules, and can be used to express both traditional routing and more esoteric, content-based approaches. We describe a compiler for packet subscriptions that uses a novel BDD-based algorithm to efficiently translate predicates into P4 tables that can support O(100K) expressions. Using our compiler, we've built a proof-of-concept pub/sub financial application for splitting market feeds (e.g., Nasdaq's ITCH protocol) with line-rate message processing, using the full switch bandwidth of 6.5Tbps.

We present the design and implementation of p4v, a practical tool for verifying data planes described using the P4 programming language. The design of p4v is based on classic verification techniques but adds several key innovations including a novel mechanism for incorporating assumptions about the control plane and domain-specific optimizations which are needed to scale to large programs. We present case studies showing that p4v verifies important properties and finds bugs in real-world programs. We conduct experiments to quantify the scalability of p4v on a wide range of additional examples. We show that with just a few hundred lines of control-plane annotations, p4v is able to verify critical safety properties for switch.p4, a program that implements the functionality of on a modern data center switch, in under three minutes.

Current frameworks for network programming assume that the network contains a collection of homogenous devices that can be rapidly reconfigured in response to changing policies and network conditions. Unfortunately, these assumptions are incompatible with the realities of modern networks, which contain legacy devices that offer diverse functionality and can only be reconfigured slowly. Additionally, network service providers need to walk a fine line between providing flexibility to users, and maintaining the integrity and reliability of their core networks. These issues are particularly evident in optical networks which are used by ISPs and WANs and provide high bandwidth at the cost of limited flexibility and long reconfiguration times. This paper presents a different approach to implementing high-level policies, by pushing functionality to the edge and using the core merely for transit. Building on the NetKAT framework and leveraging linear programming problem solvers, we develop techniques for analyzing and transforming policies into configurations that can be installed at the edge of the network. Furthermore, our approach is extensible to include constraints crucial to optical networks such as path constraints and fault tolerance. We develop a working implementation using off-the-shelf solvers and evaluate our approach on a set of large-scale optical topologies.

ProbNetKAT is a probabilistic extension of NetKAT with a denotational semantics based on Markov kernels. The language is expressive enough to generate continuous distributions, which raises the question of how to compute effectively in the language. This paper gives an new characterization of ProbNetKAT’s semantics using domain theory, which provides the foundation needed to build a practical implementation. We show how to use the semantics to approximate the behavior of arbitrary ProbNetKAT programs using distributions with finite support. We develop a prototype implementation and show how to use it to solve a variety of problems including characterizing the expected congestion induced by different routing schemes and reasoning probabilistically about reachability in a network.

We present NetCache, a new key-value store architecture that leverages the power and flexibility of new-generation programmable switches to handle queries on hot items and balance the load across storage nodes. NetCache provides high aggregate throughput and low latency even under highly-skewed and rapidly-changing workloads. The core of NetCache is a packet-processing pipeline that exploits the capabilities of modern programmable switch ASICs to efficiently detect, index, cache and serve hot key-value items in the switch data plane. Additionally, our solution guarantees cache coherence with minimal overhead. We implement a NetCache prototype on Barefoot Tofino switches and commodity servers and demonstrate that a single switch can process 2+ billion queries per second for 64K items with 16-byte keys and 128-byte values, while only consuming a small portion of its hardware resources. To the best of our knowledge, this is the first time that a sophisticated application-level functionality, such as in-network caching, has been shown to run at line rate on programmable switches. Furthermore, we show that NetCache improves the throughput by 3-10x and reduces the latency of up to 40% of queries by 50%, for high-performance, in-memory key-value stores.

Specification and verification of computer networks has become a reality in recent years, with the emergence of domain-specific programming languages and automated reasoning tools. But the design of these frameworks has been largely ad hoc, driven more by the needs of applications and the capabilities of hardware than by any foundational principles. This talk will present NetKAT, a language for programming networks based on a well-studied mathematical foundation: regular languages and finite automata. The talk will describe the design of the language, discuss its semantic underpinnings, and present highlights from ongoing work extending the language with stateful and probabilistic features.

Automatic program repair modifies a faulty program to make it correct with respect to a specification. Previous approaches have typically been restricted to specific programming languages and a fixed set of syntactical mutation techniques-e.g., changing the conditions of if statements. We present a more general technique based on repairing sets of unsolvable Horn clauses. Working with Horn clauses enables repairing programs from many different source languages, but also introduces challenges, such as navigating the large space of possible repairs. We propose a conservative semantic repair technique that only removes incorrect behaviors and does not introduce new behaviors. Our proposed framework allows the user to request the best repairs-it constructs an optimization lattice representing the space of possible repairs, and uses a novel local search technique that exploits heuristics to avoid searching through sub-lattices with no feasible repairs. To illustrate the applicability of our approach, we apply it to problems in software-defined networking (SDN), and illustrate how it is able to help network operators fix buggy configurations by properly filtering undesired traffic. We show that interval and Boolean lattices are effective choices of optimization lattices in this domain, and we enable optimization objectives such as modifying the minimal number of switches. We have implemented a prototype repair tool, and present preliminary experimental results on several benchmarks using real topologies and realistic repair scenarios in data centers and congested networks.

File systems are often used to store persistent application data, but manipulating file systems using standard APIs can be difficult for programmers. Forest is a domain-specific language that bridges the gap between the on-disk and in-memory representations of file system data. Given a high-level specification of the structure, contents, and properties of a collection of directories, files, and symbolic links, the Forest compiler generates tools for loading, storing, and validating that data. Unfortunately, the initial implementation of Forest offered few mechanisms for controlling cost-e.g., the run-time system could load gigabytes of data, even if only a few bytes were needed. This paper introduces Incremental Forest (iForest), an extension to Forest with an explicit delay construct that programmers can use to precisely control costs. We describe the design of iForest using a series of running examples, present a formal semantics in a core calculus, and define a simple cost model that accurately characterizes the resources needed to use a given specification. We propose skins, which allow programmers to modify the delay structure of a specification in a compositional way, and develop a static type system for ensuring compatibility between specifications and skins. We prove the soundness and completeness of the type system and a variety of algebraic properties of skins. We describe an OCaml implementation and evaluate its performance on applications developed in collaboration with watershed hydrologists.

Software-defined networking (SDN) programs must simultaneously describe static forwarding behavior and dynamic updates in response to events. Event-driven updates are critical to get right, but difficult to implement correctly due to the high degree of concurrency in networks. Existing SDN platforms offer weak guarantees that can break application invariants, leading to problems such as dropped packets, degraded performance, security violations, etc. This paper introduces EVENT-DRIVEN CONSISTENT UPDATES that are guaranteed to preserve well-defined behaviors when transitioning between configurations in response to events. We propose NETWORK EVENT STRUCTURES (NESs) to model constraints on updates, such as which events can be enabled simultaneously and causal dependencies between events. We define an extension of the NetKAT language with mutable state, give semantics to stateful programs using NESs, and discuss provably-correct strategies for implementing NESs in SDNs. Finally, we evaluate our approach empirically, demonstrating that it gives well-defined consistency guarantees while avoiding expensive synchronization and packet buffering.

High-level programming languages play a key role in a growing number of networking platforms, streamlining application development and enabling precise formal reasoning about network behavior. Unfortunately, current compilers only handle "local" programs that specify behavior in terms of hop-by-hop forwarding behavior, or modest extensions such as simple paths. To encode richer "global" behaviors, programmers must add extra state -- something that is tricky to get right and makes programs harder to write and maintain. Making matters worse, existing compilers can take tens of minutes to generate the forwarding state for the network, even on relatively small inputs. This forces programmers to waste time working around performance issues or even revert to using hardware-level APIs. This paper presents a new compiler for the NetKAT language that handles rich features including regular paths and virtual networks, and yet is several orders of magnitude faster than previous compilers. The compiler uses symbolic automata to calculate the extra state needed to implement "global" programs, and an intermediate representation based on binary decision diagrams to dramatically improve performance. We describe the design and implementation of three essential compiler stages: from virtual programs (which specify behavior in terms of virtual topologies) to global programs (which specify network-wide behavior in terms of physical topologies), from global programs to local programs (which specify behavior in terms of single-switch behavior), and from local programs to hardware-level forwarding tables. We present results from experiments on real-world benchmarks that quantify performance in terms of compilation time and forwarding table size.

Software-defined networking (SDN) is revolutionizing the networking industry, but current SDN programming platforms do not provide automated mechanisms for updating global configurations on the fly. Implementing updates by hand is challenging for SDN programmers because networks are distributed systems with hundreds or thousands of interacting nodes. Even if initial and final configurations are correct, naively updating individual nodes can lead to incorrect transient behaviors, including loops, black holes, and access control violations. This paper presents an approach for automatically synthesizing updates that are guaranteed to preserve specified properties. We formalize network updates as a distributed programming problem and develop a synthesis algorithm based on counterexample-guided search and incremental model checking. We describe a prototype implementation, and present results from experiments on real-world topologies and properties demonstrating that our tool scales to updates involving over one-thousand nodes.

NetKAT is a domain-specific language and logic for specifying and verifying network packet-processing functions. It consists of Kleene algebra with tests (KAT) augmented with primitives for testing and modifying packet headers and encoding network topologies. Previous work developed the design of the language and its standard semantics, proved the soundness and completeness of the logic, defined a PSPACE algorithm for deciding equivalence, and presented several practical applications.

Datastores today rely on distribution and replication to achieve improved performance and fault-tolerance. But correctness of many applications depends on strong consistency properties--something that can impose substantial overheads, since it requires coordinating the behavior of multiple nodes. This paper describes a new approach to achieving strong consistency in distributed systems while minimizing communication between nodes. The key insight is to allow the state of the system to be inconsistent during execution, as long as this inconsistency is bounded and does not affect transaction correctness. In contrast to previous work, our approach uses program analysis to extract semantic information about permissible levels of inconsistency and is fully automated. We then employ a novel homeostasis protocol to allow sites to operate independently, without communicating, as long as any inconsistency is governed by appropriate treaties between the nodes. We discuss mechanisms for optimizing treaties based on workload characteristics to minimize communication, as well as a prototype implementation and experiments that demonstrate the benefits of our approach on common transactional benchmarks.

This paper presents Merlin, a new framework for managing resources in software-defined networks. With Merlin, administrators express high-level policies using programs in a declarative language. The language includes logical predicates to identify sets of packets, regular expressions to encode forwarding paths, and arithmetic formulas to specify bandwidth constraints. The Merlin compiler maps these policies into a constraint problem that determines bandwidth allocations using parameterizable heuristics. It then generates code that can be executed on the network elements to enforce the policies. To allow network tenants to dynamically adapt policies to their needs, Merlin provides mechanisms for delegating control of sub-policies and for verifying that modifications made to sub-policies do not violate global constraints. Experiments demonstrate the expressiveness and effectiveness of Merlin on real-world topologies and applications. Overall, Merlin simplifies network administration by providing high-level abstractions for specifying network policies that provision network resources.

Recent years have seen growing interest in high-level languages for programming networks. But the design of these languages has been largely ad hoc, driven more by the needs of applications and the capabilities of network hardware than by foundational principles. The lack of a semantic foundation has left language designers with little guidance in determining how to incorporate new features, and programmers without a means to reason precisely about their code.

In this tutorial, we will show participants how to program software defined networks (SDN) in a modular way, using Frenetic's abstractions. We will build several realistic network applications from the ground up, and also learn to use more sophisticated modules, such as NAT and MAC-learning, which are part of the Frenetic standard library. We will also look under the hood to see how the Frenetic compiler and runtime system work.

This paper presents the Merlin network management framework. With Merlin, administrators express network policy using programs in a declarative language based on logical predicates and regular expressions. The Merlin compiler automatically partitions these programs into components that can be placed on a variety of devices including switches, middleboxes, and end hosts. It uses a constraint solver and parameterizable heuristics to allocate resources such as paths and bandwidth. To ease the administration of federated networks, Merlin provides mechanisms for delegating management of sub-policies to tenants, along with tools for verifying that delegated sub-policies do not violate global constraints. Overall, Merlin simplifies the task of network administration by providing high-level abstractions for directly specifying network policy.

In many areas of computing, techniques ranging from testing to formal modeling to full-blown verification have been successfully used to help programmers build reliable systems. But although networks are critical infrastructure, they have largely resisted analysis using formal techniques. Software-defined networking (SDN) is a new network architecture that has the potential to provide a foundation for network reasoning, by standardizing the interfaces used to express network programs and giving them a precise semantics.

Software-defined networks (SDNs) are a new kind of network architecture in which a controller machine manages a distributed collection of switches by instructing them to install or uninstall packet-forwarding rules and report traffic statistics. The recently formed Open Networking Consortium, whose members include Google, Facebook, Microsoft, Verizon, and others, hopes to use this architecture to transform the way that enterprise and data center networks are implemented.

Configuration changes are a common source of instability in networks, leading to outages, performance disruptions, and security vulnerabilities. Even when the initial and final configurations are correct, the update process itself often steps through intermediate configurations that exhibit incorrect behaviors. This paper introduces the notion of consistent network updates---updates that are guaranteed to preserve well-defined behaviors when transitioning mbetween configurations. We identify two distinct consistency levels, per-packet and per-flow, and we present general mechanisms for implementing them in Software-Defined Networks using switch APIs like OpenFlow. We develop a formal model of OpenFlow networks, and prove that consistent updates preserve a large class of properties. We describe our prototype implementation, including several optimizations that reduce the overhead required to perform consistent updates. We present a verification tool that leverages consistent updates to significantly reduce the complexity of checking the correctness of network control software. Finally, we describe the results of some simple experiments demonstrating the effectiveness of these optimizations on example applications.

Configuration changes are a common source of instability in networks, leading to broken connectivity, forwarding loops, and access control violations. Even when the initial and final states of the network are correct, the update process often steps through intermediate states with incorrect behaviors. These problems have been recognized in the context of specific protocols, leading to a number of point solutions. However, a piecemeal attack on this fundamental problem, while pragmatic in the short term, is unlikely to lead to significant long-term progress.

A filestore is a structured collection of data files housed in a conventional hierarchical file system. Many applications use filestores as a poor-man's database, and the correct execution of these applications requires that the collection of files, directories, and symbolic links stored on disk satisfy a variety of precise invariants. Moreover, all of these structures must have acceptable ownership, permission, and timestamp attributes. Unfortunately, current programming languages do not provide support for documenting assumptions about filestores, detecting errors in them, or safely loading from and storing to them.

Modern networks provide a variety of interrelated services including routing, traffic monitoring, load balancing, and access control. Unfortunately, the languages used to program today's networks lack modern features - they are usually defined at the low level of abstraction supplied by the underlying hardware and they fail to provide even rudimentary support for modular programming. As a result, network programs tend to be complicated, error-prone, and difficult to maintain.

Bidirectional programming languages are a practical approach to the view update problem. Programs in these languages, called lenses, define both a view and an update policy - i.e., every program can be read as a function mapping sources to views as well as one mapping updated views back to updated sources.

Security views are a flexible and effective mechanism for controlling access to confidential information. Rather than allowing untrusted users to access source data directly, they are instead provided with are restricted view, from which all confidential information has been removed. The program that generates the view effectively embodies a confidentiality policy for the underlying source data. However, this approach has a significant drawback: it prevents users from updating the data in the view.To address the "view update problem" in general, a number of bidirectional languages have been proposed. Programs in these languages---often called lenses---can be run in two directions: read from left to right, they map sources to views; from right to left,they map updated views back to updated sources. However, existing bidirectional languages do not deal adequately with security. In particular, they do not provide a way to ensure the integrity of source data as it is manipulated by untrusted users of the view.We propose a novel framework of secure lenses that addresses these shortcomings. We enrich the types of basic lenses with equivalence relations capturing notions of confidentiality and integrity, and formulate the essential security conditions as non-interference properties. We then instantiate this framework in the domain of string transformations, developing syntax for bidirectional string combinators with security-annotated regular expressions as their types.

There are now a number of BIDIRECTIONAL PROGRAMMING LANGUAGES, where every program can be read both as a forward transformation mapping one data structure to another and as a reverse transformation mapping an edited output back to a correspondingly edited input. Besides parsimony - the two related transformations are described by just one expression - such languages are attractive because they promise strong behavioral laws about how the two transformations fit together - e.g., their composition is the identity function. It has repeatedly been observed, however, that such laws are actually a bit too strong: in practice, we do not want them "on the nose," but only up to some equivalence, allowing inessential details, such as whitespace, to be modified after a round trip. Some bidirectional languages loosen their laws in this way, but only for specific, baked-in equivalences.

We present a formal framework for capturing the provenance of data appearing in XQuery views of XML. Building on previous work on relations and their (positive) query languages, we decorate unordered XML with annotations from commutative semirings and show that these annotations suffice for a large positive fragment of XQuery applied to this data. In addition to tracking provenance metadata, the framework can be used to represent and process XML with repetitions, incomplete XML, and probabilistic XML, and provides a basis for enforcing access control policies in security applications.

A lens is a bidirectional program. When read from left toright, it denotes an ordinary function that maps inputs to outputs. When read from right to left, it denotes an ''update translator'' that takes an input together with an updated output and produces a new input that reflects the update. Many variants of this idea have been explored in the literature, but none deal fully with ordered data. If, for example, an update changes the order of a list in theoutput, the items in the output list and the chunks of the input that generated them can be misaligned, leading to lost or corrupted data.

We propose a novel approach to the view-update problem for tree-structured data: a domain-specific programming language in which all expressions denote bidirectional transformations on trees. In one direction, these transformations---dubbed lenses ---map a concrete tree into a simplified abstract view; in the other, they map a modified abstract view, together with the original concrete tree, to a correspondingly modified concrete tree. Our design emphasizes both robustness and ease of use, guaranteeing strong well-behavedness and totality properties for well-typed lenses. We begin by identifying a natural space of well-behaved bidirectional transformations over arbitrary structures, studying definedness and continuity in this setting. We then instantiate this semantic framework in the form of a collection of lens combinators that can be assembled to describe bidirectional transformations on trees. These combinators include familiar constructs from functional programming (composition, mapping, projection, conditionals, recursion) together with some novel primitives for manipulating trees (splitting, pruning, merging, etc.). We illustrate the expressiveness of these combinators by developing a number of bidirectional list-processing transformations as derived forms. An extended example shows how our combinators can be used to define a lens that translates between a native HTML representation of browser bookmarks and a generic abstract bookmark format.

We propose a novel approach to the well-known view update problem for the case of tree-structured data: a domain-specific programming language in which all expressions denote bi-directional transformations on trees. In one direction, these transformations---dubbed lenses---map a "concrete" tree into a simplified "abstract view"; in the other, they map a modified abstract view, together with the original concrete tree, to a correspondingly modified concrete tree. Our design emphasizes both robustness and ease of use, guaranteeing strong well-behavedness and totality properties for well-typed lenses.We identify a natural space of well-behaved bi-directional transformations over arbitrary structures, study definedness and continuity in this setting, and state a precise connection with the classical theory of "update translation under a constant complement" from databases. We then instantiate this semantic framework in the form of a collection of lens combinators that can be assembled to describe transformations on trees. These combinators include familiar constructs from functional programming (composition, mapping, projection, conditionals, recursion) together with some novel primitives for manipulating trees (splitting, pruning, copying, merging, etc.). We illustrate the expressiveness of these combinators by developing a number of bi-directional list-processing transformations as derived forms.