Online services are commonly implemented with a scalable microservice architecture, where isomorphic workers process client requests, recording persistent state in a backend data store. To maintain service, modifications to service functionality must be made on the fly - i.e., as the service continues to process client requests - but doing so is challenging. The central difficulty is that of avoiding inconsistencies from mixed-mode operation, caused by workers of current and new versions interacting via the data store. Some update methods avoid mixed-mode altogether, but only at the cost of substantial inefficiency - by doubling resources (memory and compute), or by halving throughput. The alternative is an uncontrolled “rolling” update, which runs the risk of serious service failures arising from inconsistent mixed-mode behavior. Ideally, it should appear to every client that a service update takes effect atomically; this ensures that a client is not exposed to inconsistent mixed-mode behavior. In this paper, we introduce a framework that formalizes this intuition and develop foundational theory for reasoning about update consistency. We apply this theory to derive the first algorithms that guarantee consistency for mixed-mode updates. The algorithms rely on semantic properties of service actions, such as commutativity. We show that this is unavoidable, by proving that any semantically oblivious mixed-mode update method must allow inconsistencies.

Global protocols specify distributed, message-passing protocols from a birds-eye view, and are used as a specification for synthesizing local implementations. Implementability asks whether a given global protocol admits a distributed implementation. We present the first comprehensive investigation of global protocol implementability modulo network architectures. We propose a set of network-parametric Coherence Conditions, and exhibit sufficient assumptions under which it precisely characterizes implementability. We further reduce these assumptions to a minimal set of operational axioms describing insert and remove behavior of individual message buffers. Our reduction immediately establishes that five commonly studied asynchronous network architectures, namely peer-to-peer FIFO, mailbox, senderbox, monobox and bag, are instances of our network-parametric result. We use our characterization to derive optimal complexity results for implementability modulo networks, relationships between classes of implementable global protocols, and symbolic algorithms for deciding implementability modulo networks. We implement the latter in the first network-parametric tool Sprout(A), and show that it achieves network generality without sacrificing performance and modularity.

Abstract This paper presents , a new intermediate verification language and deductive verification tool that provides inbuilt support for concurrency reasoning. ’s meta-theory is based on the higher-order concurrent separation logic Iris, incorporating core features such as user-definable ghost state and thread-modular reasoning via shared-state invariants. To achieve better accessibility and enable proof automation via SMT solvers, restricts Iris to its first-order fragment. The entailed loss of expressivity is mitigated by a higher-order module system that enables proof modularization and reuse. We provide an overview of the language and describe key aspects of the supported proof automation. We evaluate on a benchmark suite of verification tasks comprising linearizability and memory safety proofs for common concurrent data structures and clients as well as one larger case study. Our evaluation shows that improves over existing proof automation tools for Iris in terms of verification times and usability. Moreover, the tool significantly reduces the proof overhead compared to proofs constructed using the Iris/Rocq proof mode.

Abstract We present Sprout , the first sound and complete implementability checker for symbolic multiparty protocols. Sprout supports protocols with dependent refinements on message values, loop memory, and multiparty communication with generalized, sender-driven choice. Sprout checks implementability via an optimized, sound and complete reduction to the fixpoint logic $$\mu $$ μ CLP, and uses MuVal as a backend solver for $$\mu $$ μ CLP instances. We evaluate Sprout on an extended benchmark suite of implementable and non-implementable examples, and show that Sprout outperforms its competititors in terms of expressivity and precision, and provides competitive runtime performance. Sprout additionally provides support for verifying custom functional correctness properties beyond implementability.

Abstract Memory safety is a fundamental correctness property of software. For programs that manipulate linked, heap-allocated data structures, ensuring memory safety requires analyzing their possible shapes. Despite significant advances in shape analysis, existing techniques rely on hand-crafted domains tailored to specific data structures, making them difficult to generalize and extend. This paper presents a novel approach that reduces memory-safety proofs to the verification of heap-less imperative programs, enabling the use of off-the-shelf software verification tools. We achieve this reduction through two complementary program instrumentation techniques: space invariants, which enable symbolic reasoning about unbounded heaps, and flow abstraction, which encodes global heap properties as local flow equations. The approach effectively verifies memory safety across a broad range of programs, including concurrent lists and trees that lie beyond the reach of existing shape analysis tools.

Privacy policies dictate how systems handle user data, yet engineers struggle to verify compliance because policies use intentionally vague legal language. Current automated analyzers extract data practices using NLP but fail when policies say things like "share data for legitimate purposes" - terms that have no computational definition. This mismatch between legal flexibility and formal verification creates a fundamental barrier to automated compliance checking. We identify four systematic challenges: vague terms, evolving terminology, exception patterns that appear contradictory, and external legal dependencies. We propose an approach that preserves this ambiguity, where we use LLMs to extract structured parameters and convert them to first-order logic while keeping vague conditions as explicit placeholders for human interpretation. Our system can extract hundreds of data practices and reveals hidden complexities in TikTok and Meta policies, though the resulting formulas remain too complex for SMT solvers. This demonstrates the promise and fundamental limits of formalizing the legal text.

We study the implementability problem for an expressive class of symbolic communication protocols involving multiple participants. Our symbolic protocols describe infinite states and data values using dependent refinement predicates. Implementability asks whether a global protocol specification admits a distributed, asynchronous implementation, namely one for each participant, that is deadlock-free and exhibits the same behavior as the specification. We provide a unified explanation of seemingly disparate sources of non-implementability through a precise semantic characterization of implementability for infinite protocols. Our characterization reduces the problem of implementability to (co)reachability in the global protocol restricted to each participant. This compositional reduction yields the first sound and relatively complete algorithm for checking implementability of symbolic protocols. We use our characterization to show that for finite protocols, implementability is co-NP-complete for explicit representations and PSPACE-complete for symbolic representations. The finite, explicit fragment subsumes a previously studied fragment of multiparty session types for which our characterization yields a co-NP decision procedure, tightening a prior PSPACE upper bound.

This paper describes a new abstract interpretation -based approach to verify temporal safety properties of recursive, higher-order programs. While prior works have provided theoretical impact and some automation, they have had limited scalability. We begin with a new automata-based “abstract effect domain” for summarizing context-sensitive dependent effects, capable of abstracting relations between the program environment and the automaton control state. Our analysis includes a new transformer for abstracting event prefixes to automatically computed context-sensitive effect summaries, and is instantiated in a type-and-effect system grounded in abstract interpretation. Since the analysis is parametric on the automaton, we next instantiate it to a broader class of history/register (or “accumulator”) automata, beyond finite state automata to express some context-free properties, input-dependency, event summation, resource usage, cost, equal event magnitude, etc. We implemented a prototype ev Drift that computes dependent effect summaries (and validates assertions) for OCaml-like recursive higher-order programs. As a basis of comparison, we describe reductions to assertion checking for higher-order but effect-free programs, and demonstrate that our approach outperforms prior tools Drift , RCaml / Spacer , MoCHi , and ReTHFL . Overall, across a set of 23 benchmarks, Drift verified 12 benchmarks, RCaml/Spacer verified 6, MoCHi verified 11, ReTHFL verified 18, and ev Drift verified 21; ev Drift also achieved a 6.3×, 5.3×, 16.8×, and 6.4× speedup over Drift , RCami/Spacer , MoCHi , and ReTHFL , respectively, on those benchmarks that both tools could solve.

We present and verify template algorithms for lock-free concurrent search structures that cover a broad range of existing implementations based on lists and skiplists. Our linearizability proofs are fully mechanized in the concurrent separation logic Iris. The proofs are modular and cover the broader design space of the underlying algorithms by parameterizing the verification over aspects such as the low-level representation of nodes and the style of data structure maintenance. As a further technical contribution, we present a mechanization of a recently proposed method for reasoning about future-dependent linearization points using hindsight arguments. The mechanization builds on Iris' support for prophecy reasoning and user-defined ghost resources. We demonstrate that the method can help to reduce the proof effort compared to direct prophecy-based proofs.

Abstract Multiparty session types (MSTs) are a type-based approach to verifying communication protocols, represented as global types in the framework. We present a precise subtyping relation for asynchronous MSTs with communicating state machines (CSMs) as implementation model. We address two problems: when can a local implementation safely substitute another, and when does an arbitrary CSM implement a global type? We define safety with respect to a given global type, in terms of subprotocol fidelity and deadlock freedom. Our implementation model subsumes existing work which considers local types with restricted choice. We exploit the connection between MST subtyping and refinement to formulate concise conditions that are directly checkable on the candidate implementations, and use them to show that both problems are decidable in polynomial time.

Abstract Multiparty session types (MSTs) are a type-based approach to verifying communication protocols. Central to MSTs is a projection operator: a partial function that maps protocols represented as global types to correct-by-construction implementations for each participant, represented as a communicating state machine. Existing projection operators are syntactic in nature, and trade efficiency for completeness. We present the first projection operator that is sound, complete, and efficient. Our projection separates synthesis from checking implementability. For synthesis, we use a simple automata-theoretic construction; for checking implementability, we present succinct conditions that summarize insights into the property of implementability. We use these conditions to show that MST implementability is PSPACE-complete. This improves upon a previous decision procedure that is in EXPSPACE and applies to a smaller class of MSTs. We demonstrate the effectiveness of our approach using a prototype implementation, which handles global types not supported by previous work without sacrificing performance.

Abstract is a new tool for checking linearizability proofs of highly complex concurrent search structures. The tool’s unique features are its parametric heap abstraction based on separation logic and the flow framework, and its support for hindsight arguments about future-dependent linearization points. We describe the tool, present a case study, and discuss implementation details.

There has been intense interest over the last decade in implementations of probabilistic proofs (IPs, SNARKs, PCPs, and so on): protocols in which an untrusted party proves to a verifier that a given computation was executed properly, possibly in zero knowledge. Nevertheless, implementations still do not scale beyond small computations. A central source of overhead is the front-end: translating from the abstract computation to a set of equivalent arithmetic constraints. This paper introduces a general-purpose framework, called Distiller, in which a user translates to constraints not the original computation but an abstracted specification of it. Distiller is the first in this area to perform such transformations in a way that is provably safe. Furthermore, by taking the idea of "encode a check in the constraints" to its literal logical extreme, Distiller exposes many new opportunities for constraint reduction, resulting in cost reductions for benchmark computations of 1.3–50×, and in some cases, better asymptotics.

Abstract We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows, rules out vanishing flows, and has an easy to understand notion of footprint as needed for soundness of the frame rule. In addition, we present algorithms for automating the frame rule, which we evaluate on graph updates extracted from linearizability proofs for concurrent data structures. The evaluation demonstrates that our algorithms help to automate key aspects of these proofs that have previously relied on user guidance or heuristics.

Automatically proving linearizability of concurrent data structures remains a key challenge for verification. We present temporal interpolation as a new proof principle to guide automated proof search using hindsight arguments within concurrent separation logic. Temporal interpolation offers an easy-to-automate alternative to prophecy variables and has the advantage of structuring proofs into easy-to-discharge hypotheses. Additionally, we advance hindsight theory by integrating it into a program logic, bringing formal rigor and complementary proof machinery. We substantiate the usefulness of temporal interpolation by implementing it in a tool and using it to automatically verify the Logical Ordering tree. The proof is challenging due to future-dependent linearization points and complex structure overlays. It is the first formal proof of this data structure. Interestingly, our formalization revealed an unknown bug and an existing informal proof as erroneous.

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.

Abstract We present algorithms and techniques for the repair of timed system models, given as networks of timed automata (NTA). The repair is based on an analysis of timed diagnostic traces (TDTs) that are computed by real-time model checking tools, such as UPPAAL, when they detect the violation of a timed safety property. We present an encoding of TDTs in linear real arithmetic and use the MaxSMT capabilities of the SMT solver Z3 to suggest a minimal number of possible syntactic repairs of the analyzed model. The suggested repairs include modified values for clock bounds in location invariants and transition guards, adding or removing clock resets, etc. We then present an admissibility criterion, called functional equivalence, which ensures that the proposed repair preserves the functional behavior of the considered NTA. We discuss a proof-of-concept tool called TarTar that we have developed, implementing the repair and admissibility analysis, and give insights into its design and architecture. We evaluate the proposed repair technique on faulty mutations generated from a diverse suite of case studies taken from the literature. We show that TarTar can admissibly repair for 69– $$88\%$$ 88 % of the seeded errors in the considered system models.

Multicopy search structures such as log-structured merge (LSM) trees are optimized for high insert/update/delete (collectively known as upsert) performance. In such data structures, an upsert on key k , which adds ( k , v ) where v can be a value or a tombstone, is added to the root node even if k is already present in other nodes. Thus there may be multiple copies of k in the search structure. A search on k aims to return the value associated with the most recent upsert. We present a general framework for verifying linearizability of concurrent multicopy search structures that abstracts from the underlying representation of the data structure in memory, enabling proof-reuse across diverse implementations. Based on our framework, we propose template algorithms for (a) LSM structures forming arbitrary directed acyclic graphs and (b) differential file structures, and formally verify these templates in the concurrent separation logic Iris. We also instantiate the LSM template to obtain the first verified concurrent in-memory LSM tree implementation.

Refinement types enable lightweight verification of functional programs. Algorithms for statically inferring refinement types typically work by reduction to solving systems of constrained Horn clauses extracted from typing derivations. An example is Liquid type inference, which solves the extracted constraints using predicate abstraction. However, the reduction to constraint solving in itself already signifies an abstraction of the program semantics that affects the precision of the overall static analysis. To better understand this issue, we study the type inference problem in its entirety through the lens of abstract interpretation. We propose a new refinement type system that is parametric with the choice of the abstract domain of type refinements as well as the degree to which it tracks context-sensitive control flow information. We then derive an accompanying parametric inference algorithm as an abstract interpretation of a novel data flow semantics of functional programs. We further show that the type system is sound and complete with respect to the constructed abstract semantics. Our theoretical development reveals the key abstraction steps inherent in refinement type inference algorithms. The trade-off between precision and efficiency of these abstraction steps is controlled by the parameters of the type system. Existing refinement type systems and their respective inference algorithms, such as Liquid types, are captured by concrete parameter instantiations. We have implemented our framework in a prototype tool and evaluated it for a range of new parameter instantiations (e.g., using octagons and polyhedra for expressing type refinements). The tool compares favorably against other existing tools. Our evaluation indicates that our approach can be used to systematically construct new refinement type inference algorithms that are both robust and precise.

We present TarTar , an automatic repair analysis tool that, given a timed diagnostic trace (TDT) obtained during the model checking of a timed automaton model, suggests possible syntactic repairs of the analyzed model. The suggested repairs include modified values for clock bounds in location invariants and transition guards, adding or removing clock resets, etc. The proposed repairs guarantee that the given TDT is no longer feasible in the repaired model, while preserving the overall functional behavior of the system. We give insights into the design and architecture of TarTar , and show that it can successfully repair 69% of the seeded errors in system models taken from a diverse suite of case studies.

Abstract Separation logics are widely used for verifying programs that manipulate complex heap-based data structures. These logics build on so-called separation algebras, which allow expressing properties of heap regions such that modifications to a region do not invalidate properties stated about the remainder of the heap. This concept is key to enabling modular reasoning and also extends to concurrency. While heaps are naturally related to mathematical graphs, many ubiquitous graph properties are non-local in character, such as reachability between nodes, path lengths, acyclicity and other structural invariants, as well as data invariants which combine with these notions. Reasoning modularly about such graph properties remains notoriously difficult, since a local modification can have side-effects on a global property that cannot be easily confined to a small region. In this paper, we address the question: What separation algebra can be used to avoid proof arguments reverting back to tedious global reasoning in such cases? To this end, we consider a general class of global graph properties expressed as fixpoints of algebraic equations over graphs. We present mathematical foundations for reasoning about this class of properties, imposing minimal requirements on the underlying theory that allow us to define a suitable separation algebra. Building on this theory, we develop a general proof technique for modular reasoning about global graph properties expressed over program heaps, in a way which can be directly integrated with existing separation logics. To demonstrate our approach, we present local proofs for two challenging examples: a priority inheritance protocol and the non-blocking concurrent Harris list.

Concurrent separation logics have had great success reasoning about concurrent data structures. This success stems from their application of modularity on multiple levels, leading to proofs that are decomposed according to program structure, program state, and individual threads. Despite these advances, it remains difficult to achieve proof reuse across different data structure implementations. For the large class of search structures, we demonstrate how one can achieve further proof modularity by decoupling the proof of thread safety from the proof of structural integrity. We base our work on the template algorithms of Shasha and Goodman that dictate how threads interact but abstract from the concrete layout of nodes in memory. Building on the recently proposed flow framework of compositional abstractions and the separation logic Iris, we show how to prove correctness of template algorithms, and how to instantiate them to obtain multiple verified implementations.

We present algorithms and techniques for the repair of timed system models, given as networks of timed automata (NTA). The repair is based on an analysis of timed diagnostic traces (TDTs) that are computed by real-time model checking tools, such as UPPAAL, when they detect the violation of a timed safety property. We present an encoding of TDTs in linear real arithmetic and use the MaxSMT capabilities of the SMT solver Z3 to compute possible repairs to clock bound values that minimize the necessary changes to the automaton. We then present an admissibility criterion, called functional equivalence, that assesses whether a proposed repair is admissible in the overall context of the NTA. We have implemented a proof-of-concept tool called TarTar for the repair and admissibility analysis. To illustrate the method, we have considered a number of case studies taken from the literature and automatically injected changes to clock bounds to generate faulty mutations. Our technique is able to compute a feasible repair for $$91\%$$ of the faults detected by UPPAAL in the generated mutants.

A common problem for developers is applications exhibiting new bugs after deployment. Many of these bugs can be traced to unexpected network, operating system, and file system differences that cause program executions that were successful in a development environment to fail once deployed. Preventing these bugs is difficult because it is impractical to test an application in every environment. Enter Simulating Environmental Anomalies (SEA), a technique that utilizes evidence of one application's failure in a given environment to generate tests that can be applied to other applications, to see whether they suffer from analogous faults. In SEA, models of unusual properties extracted from interactions between an application, A, and its environment guide simulations of another application, B, running in the anomalous environment. This reveals faults B may experience in this environment without the expense of deployment. By accumulating these anomalies, applications can be tested against an increasing set of problematic conditions. We implemented a tool called CrashSimulator, which uses SEA, and evaluated it against Linux applications selected from coreutils and the Debian popularity contest. Our tests found a total of 63 bugs in 31 applications with effects including hangs, crashes, data loss, and remote denial of service conditions.

Modern enterprises rely on Data Leakage Prevention (DLP) systems to enforce privacy policies that prevent unintentional flow of sensitive information to unauthorized entities. However, these systems operate based on rule sets that are limited to syntactic analysis and therefore completely ignore the semantic relationships between participants involved in the information exchanges. For similar reasons, these systems cannot enforce complex privacy policies that require temporal reasoning about events that have previously occurred.

Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting are much harder to reason about in a concurrent setting due to complex sharing and overlays. To solve this problem, we propose a novel approach to abstracting regions in the heap by encoding the data structure invariant into a local condition on each individual node. This condition may depend on a quantity associated with the node that is computed as a fixpoint over the entire heap graph. We refer to this quantity as a flow . Flows can encode both structural properties of the heap (e.g. the reachable nodes from the root form a tree) as well as data invariants (e.g. sortedness). We then introduce the notion of a flow interface , which expresses the relies and guarantees that a heap region imposes on its context to maintain the local flow invariant with respect to the global heap. Our main technical result is that this notion leads to a new semantic model of separation logic. In this model, flow interfaces provide a general abstraction mechanism for describing complex data structures. This abstraction mechanism admits proof rules that generalize over a wide variety of data structures. To demonstrate the versatility of our approach, we show how to extend the logic RGSep with flow interfaces. We have used this new logic to prove linearizability and memory safety of nontrivial concurrent data structures. In particular, we obtain parametric linearizability proofs for concurrent dictionary algorithms that abstract from the details of the underlying data structure representation. These proofs cannot be easily expressed using the abstraction mechanisms provided by existing separation logics.

Systems for verifiable outsourcing incur costs for a prover, a verifier, and precomputation; outsourcing makes sense when the combination of these costs is cheaper than not outsourcing. Yet, when prior works impose quantitative thresholds to analyze whether outsourcing is justified, they generally ignore prover costs. Verifiable ASICs (VA)---in which the prover is a custom chip---is the other way around: its cost calculations ignore precomputation.

Designing programmable privacy logic frameworks that correspond to social, ethical, and legal norms has been a fundamentally hard problem. Contextual integrity (CI) (Nissenbaum, 2010) offers a model for conceptualizing privacy that is able to bridge technical design with ethical, legal, and policy approaches. While CI is capable of capturing the various components of contextual privacy in theory, it is challenging to discover and formally express these norms in operational terms. In the following, we propose a crowdsourcing method for the automated discovery of contextual norms. To evaluate the effectiveness and scalability of our approach, we conducted an extensive survey on Amazon's Mechanical Turk (AMT) with more than 450 participants and 1400 questions. The paper has three main takeaways: First, we demonstrate the ability to generate survey questions corresponding to privacy norms within any context. Second, we show that crowdsourcing enables the discovery of norms from these questions with strong majoritarian consensus among users. Finally, we demonstrate how the norms thus discovered can be encoded into a formal logic to automatically verify their consistency.

Compilers for statically typed functional programming languages are notorious for generating confusing type error messages. When the compiler detects a type error, it typically reports the program location where the type checking failed as the source of the error. Since other error sources are not even considered, the actual root cause is often missed. A more adequate approach is to consider all possible error sources and report the most useful one subject to some usefulness criterion. In our previous work, we showed that this approach can be formulated as an optimization problem related to satisfiability modulo theories (SMT). This formulation cleanly separates the heuristic nature of usefulness criteria from the underlying search problem. Unfortunately, algorithms that search for an optimal error source cannot directly use principal types which are crucial for dealing with the exponential-time complexity of the decision problem of polymorphic type checking. In this paper, we present a new algorithm that efficiently finds an optimal error source in a given ill-typed program. Our algorithm uses an improved SMT encoding to cope with the high complexity of polymorphic typing by iteratively expanding the typing constraints from which principal types are derived. The algorithm preserves the clean separation between the heuristics and the actual search. We have implemented our algorithm for OCaml. In our experimental evaluation, we found that the algorithm reduces the running times for optimal type error localization from minutes to seconds and scales better than previous localization algorithms.

We present VERMEER, a new automated debugging tool for C. VERMEER combines two functionalities: (1) a dynamic tracer that produces a linearized trace from a faulty C program and a given test input; and (2) a static analyzer that explains why the trace fails. The tool works in phases that simplify the input program to a linear trace, which is then analyzed using an automated theorem prover to produce the explanation. The output of each phase is a valid C program. VERMEER is able to produce useful explanations of non trivial traces for real C programs within a few seconds. The tool demo can be found at http://youtu.be/E5lKHNJVerU.

Automatic type inference is a popular feature of functional programming languages. If a program cannot be typed, the compiler typically reports a single program location in its error message. This location is the point where the type inference failed, but not necessarily the actual source of the error. Other potential error sources are not even considered. Hence, the compiler often misses the true error source, which increases debugging time for the programmer. In this paper, we present a general framework for automatic localization of type errors. Our algorithm finds all minimum error sources, where the exact definition of minimum is given in terms of a compiler-specific ranking criterion. Compilers can use minimum error sources to produce more meaningful error reports, and for automatic error correction. Our approach works by reducing the search for minimum error sources to an optimization problem that we formulate in terms of weighted maximum satisfiability modulo theories (MaxSMT). The reduction to weighted MaxSMT allows us to build on SMT solvers to support rich type systems and at the same time abstract from the concrete criterion that is used for ranking the error sources. We have implemented an instance of our framework targeted at Hindley-Milner type systems and evaluated it on existing OCaml benchmarks for type error localization. Our evaluation shows that our approach has the potential to significantly improve the quality of type error reports produced by state of the art compilers.

An integral part of all debugging activities is the task of diagnosing the cause of an error. Most existing fault diagnosis techniques rely on the availability of high quality test suites because they work by comparing failing and passing runs to identify the error cause. This limits their applicability. One alternative are techniques that statically analyze an error trace of the program without relying on additional passing runs to compare against. Particularly promising are novel proof-based approaches that leverage the advances in automated theorem proving to obtain an abstraction of the program that aids fault diagnostics. However, existing proof-based approaches still have practical limitations such as reduced scalability and dependence on complex mathematical models of programs. Such models are notoriously difficult to develop for real-world programs. Inspired by concolic testing, we propose a novel algorithm that integrates concrete execution and symbolic reasoning about the error trace to address these challenges. Specifically, we execute the error trace to obtain intermediate program states that allow us to split the trace into smaller fragments, each of which can be analyzed in isolation using an automated theorem prover. Moreover, we show how this approach can avoid complex logical encodings when reasoning about traces in low-level C programs. We have conducted an experiment where we applied our new algorithm to error traces generated from faulty versions of UNIX utils such as gzip and sed. Our experiment indicates that our concolic fault abstraction scales to real-world error traces and generates useful error diagnoses.

Craig interpolation has been a valuable tool for formal methods with interesting applications in program analysis and verification. Modern SMT solvers implement interpolation procedures for the theories that are most commonly used in these applications. However, many application-specific theories remain unsupported, which limits the class of problems to which interpolation-based techniques apply. In this paper, we present a generic framework to build new interpolation procedures via reduction to existing interpolation procedures. We consider the case where an application-specific theory can be formalized as an extension of a base theory with additional symbols and axioms. Our technique uses finite instantiation of the extension axioms to reduce an interpolation problem in the theory extension to one in the base theory. We identify a model-theoretic criterion that allows us to detect the cases where our technique is complete. We discuss specific theories that are relevant in program verification and that satisfy this criterion. In particular, we obtain complete interpolation procedures for theories of arrays and linked lists. The latter is the first complete interpolation procedure for a theory that supports reasoning about complex shape properties of heap-allocated data structures. We have implemented this procedure in a prototype on top of existing SMT solvers and used it to automatically infer loop invariants of list-manipulating programs.

A code fragment is inconsistent if it is not part of any normally terminating execution. Examples of such inconsistencies include code that is unreachable, code that always fails due to a run-time error, and code that makes conflicting assumptions about the program state. In this paper, we consider the problem of automatically explaining inconsistent code. This problem is difficult because traditional fault localization techniques do not apply. Our solution relies on a novel algorithm that takes an infeasible code fragment as input and generates a so-called error invariant automaton. The error invariant automaton is an abstraction of the input code fragment that only mentions program statements and facts that are relevant for understanding the cause of the inconsistency. We conducted a preliminary usability study which demonstrated that error invariant automata can help programmers better understand inconsistencies in code taken from real-world programs. In particular, access to an error invariant automata tripled the speed at which programmers could diagnose the cause of a code inconsistency.

The static scheduling problem often arises as a fundamental problem in real-time systems and grid computing. We consider the problem of statically scheduling a large job expressed as a task graph on a large number of computing nodes, such as a data center.

Cloud computing aims to give users virtually unlimited pay-per-use computing resources without the burden of managing the underlying infrastructure. We claim that, in order to realize the full potential of cloud computing, the user must be presented with a pricing model that offers flexibility at the requirements level, such as a choice between different degrees of execution speed and the cloud provider must be presented with a programming model that offers flexibility at the execution level, such as a choice between different scheduling policies. In such a flexible framework, with each job, the user purchases a virtual computer with the desired speed and cost characteristics, and the cloud provider can optimize the utilization of resources across a stream of jobs from different users. We designed a flexible framework to test our hypothesis, which is called FlexPRICE (Flexible Provisioning of Resources in a Cloud Environment) and works as follows. A user presents a job to the cloud. The cloud finds different schedules to execute the job and presents a set of quotes to the user in terms of price and duration for the execution. The user then chooses a particular quote and the cloud is obliged to execute the job according to the chosen quote. FlexPRICE thus hides the complexity of the actual scheduling decisions from the user, but still provides enough flexibility to meet the users actual demands. We implemented FlexPRICE in a simulator called PRICES that allows us to experiment with our framework. We observe that FlexPRICE provides a wide range of execution options-from fast and expensive to slow and cheap-- for the whole spectrum of data-intensive and computation-intensive jobs. We also observe that the set of quotes computed by FlexPRICE do not vary as the number of simultaneous jobs increases.

Cloud computing is an emerging paradigm aimed to offer users pay-per-use computing resources, while leaving the burden of managing the computing infrastructure to the cloud provider. We present a new programming and pricing model that gives the cloud user the flexibility of trading execution speed and price on a per-job basis. We discuss the scheduling and resource management challenges for the cloud provider that arise in the implementation of this model. We argue that techniques from real-time and embedded software can be useful in this context. Categories and Subject Descriptors

The automated inference of quantified invariants is considered one of the next challenges in software verification. The question of the right precision-efficiency tradeoff for the corresponding program analyses here boils down to the question of the right treatment of disjunction below and above the universal quantifier. In the closely related setting of shape analysis one uses the focus operator in order to adapt the treatment of disjunction (and thus the efficiency-precision tradeoff) to the individual program statement. One promising research direction is to design parameterized versions of the focus operator which allow the user to fine-tune the focus operator not only to the individual program statements but also to the specific verification task. We carry this research direction one step further. We fine-tune the focus operator to each individual step of the analysis (for a specific verification task). This fine-tuning must be done automatically. Our idea is to use counterexamples for this purpose. We realize this idea in a tool that automatically infers quantified invariants for the verification of a variety of heap-manipulating programs.