Abstract We present Taco , a toolsuite for the development and automatic verification of fault-tolerant and threshold-based distributed algorithms. Our toolsuite implements three approaches for model checking threshold automata in different decidable fragments known from the literature and two semi-decision procedures going beyond these decidable fragments. Moreover, Taco is a modular, extensible, and well-documented framework for developing algorithms and tools for threshold automata. We present important features, give an overview of the implemented algorithms, and evaluate their performance experimentally.

We consider parameterized verification problems for networks of timed automata (TAs) based on different communication primitives. To this end, we first consider disjunctive timed networks (DTNs), i.e., networks of TAs that communicate via location guards that enable a transition only if there is another process in a certain location. We solve for the first time the case with unrestricted clock invariants, and establish that the parameterized model checking problem (PMCP) over finite local traces can be reduced to the corresponding model checking problem on a single TA. Moreover, we prove that the PMCP for networks that communicate via lossy broadcast can be reduced to the PMCP for DTNs. Finally, we show that for networks with k-wise synchronization, and therefore also for timed Petri nets, location reachability can be reduced to location reachability in DTNs. As a consequence we can answer positively the open problem from Abdulla et al. (2018) whether the universal safety problem for timed Petri nets with multiple clocks is decidable.

Abstract We present an algorithm for the repair of parameterized systems that can be represented as well-structured transition systems. The repair problem is, for a given process implementation, to find a refinement such that a given safety property is satisfied by the resulting parameterized system, and deadlocks are avoided. Our algorithm uses a parameterized model checker to determine the correctness of candidate solutions and employs a constraint system to rule out candidates. Parameterized systems that fall into our class include disjunctive systems, pairwise rendezvous systems, broadcast protocols, and certain global synchronization protocols. Moreover, we show that parameterized deadlock detection and similar global properties can be decided in EXPTIME for disjunctive systems, and that deadlock detection is in general undecidable for broadcast protocols.

The problem of learning a computational model from examples has been receiving growing attention. For the particularly challenging problem of learning models of distributed systems, existing results are restricted to models with a fixed number of interacting processes. In this work we look for the first time (to the best of our knowledge) at the problem of learning a distributed system with an arbitrary number of processes, assuming only that there exists a cutoff, i.e., a number of processes that is sufficient to produce all observable behaviors. Specifically, we consider fine broadcast protocols, these are broadcast protocols (BPs) with a finite cutoff and no hidden states. We provide a learning algorithm that can infer a correct BP from a sample that is consistent with a fine BP, and a minimal equivalent BP if the sample is sufficiently complete. On the negative side we show that (a) characteristic sets of exponential size are unavoidable, (b) the consistency problem for fine BPs is NP hard, and (c) that fine BPs are not polynomially predictable.

Abstract Threshold automata are a computational model that has proven to be versatile in modeling threshold-based distributed algorithms and enabling their completely automatic parameterized verification. We present novel techniques for the verification of threshold automata, based on well-structured transition systems, that allow us to extend the expressiveness of both the computational model and the specifications that can be verified. In particular, we extend the model to allow decrements and resets of shared variables, possibly on cycles, and the specifications to general coverability. While these extensions of the model in general lead to undecidability, our algorithms provide a semi-decision procedure. We demonstrate the benefit of our extensions by showing that we can model complex round-based algorithms such as the phase king consensus algorithm and the Red Belly Blockchain protocol (published in 2019), and verify them fully automatically for the first time.

Abstract Distributed agreement-based (DAB) systems use common distributed agreement protocols such as leader election and consensus as building blocks for their target functionality. While automated verification for DAB systems is undecidable in general, recent work identifies a large class of DAB systems for which verification is efficiently-decidable. Unfortunately, the conditions characterizing such a class can be opaque and non-intuitive, and can pose a significant challenge to system designers trying to model their systems in this class. In this paper, we present a synthesis-driven tool, Cinnabar, to help system designers building DAB systems ensure that their intended designs belong to an efficiently-decidable class. In particular, starting from an initial sketch provided by the designer, Cinnabar generates sketch completions using a counterexample-guided procedure. The core technique relies on compactly encoding root-causes of counterexamples to varied properties such as efficient-decidability and safety. We demonstrate Cinnabar ’s effectiveness by successfully and efficiently synthesizing completions for a variety of interesting DAB systems including a distributed key-value store and a distributed consortium system.

Abstract AIGEN is an open source tool for the generation of transition systems in a symbolic representation. To ensure diversity, it employs a uniform random sampling over the space of all Boolean functions with a given number of variables. AIGEN relies on reduced ordered binary decision diagrams (ROBDDs) and canonical disjunctive normal form (CDNF) as canonical representations that allow us to enumerate Boolean functions, in the former case with an encoding that is inspired by data structures used to implement ROBDDs. Several parameters allow the user to restrict generation to Boolean functions or transition systems with certain properties, which are then output in AIGER format. We report on the use of AIGEN to generate random benchmark problems for the reactive synthesis competition SYNTCOMP 2019, and present a comparison of the two encodings with respect to time and memory efficiency in practice.

The last decade has sparked several valiant efforts in deductive verification of distributed agreement protocols such as consensus and leader election. Oddly, there have been far fewer verification efforts that go beyond the core protocols and target applications that are built on top of agreement protocols. This is unfortunate, as agreement-based distributed services such as data stores, locks, and ledgers are ubiquitous and potentially permit modular, scalable verification approaches that mimic their modular design. We address this need for verification of distributed agreement-based systems through our novel modeling and verification framework, QuickSilver, that is not only modular, but also fully automated. The key enabling feature of QuickSilver is our encoding of abstractions of verified agreement protocols that facilitates modular, decidable, and scalable automated verification. We demonstrate the potential of QuickSilver by modeling and efficiently verifying a series of tricky case studies, adapted from real-world applications, such as a data store, a lock service, a surveillance system, a pathfinding algorithm for mobile robots, and more.

Inspired by distributed applications that use consensus or other agreement protocols for global coordination, we define a new computational model for parameterized systems that is based on a general global synchronization primitive and allows for global transition guards. Our model generalizes many existing models in the literature, including broadcast protocols and guarded protocols. We show that reachability properties are decidable for systems without guards, and give sufficient conditions under which they remain decidable in the presence of guards. Furthermore, we investigate cutoffs for reachability properties and provide sufficient conditions for small cutoffs in a number of cases that are inspired by our target applications.

Observational models make tractable the analysis of information flow properties by providing an abstraction of side channels. We introduce a methodology and a tool, Scam-V, to validate observational models for modern computer architectures. We combine symbolic execution, relational analysis, and different program generation techniques to generate experiments and validate the models. An experiment consists of a randomly generated program together with two inputs that are observationally equivalent according to the model under the test. Validation is done by checking indistinguishability of the two inputs on real hardware by executing the program and analyzing the side channel. We have evaluated our framework by validating models that abstract the data-cache side channel of a Raspberry Pi 3 board with a processor implementing the ARMv8-A architecture. Our results show that Scam-V can identify bugs in the implementation of the models and generate test programs which invalidate the models due to hidden microarchitectural behavior.

Self-stabilization in distributed systems is a technique to guarantee convergence to a set of legitimate states without external intervention when a transient fault or bad initialization occurs. Recently, there has been a surge of efforts in designing techniques for automated synthesis of self-stabilizing algorithms that are correct by construction. Most of these techniques, however, are not parameterized, meaning that they can only synthesize a solution for a fixed and predetermined number of processes. In this paper, we report a breakthrough in parameterized synthesis of self-stabilizing algorithms in symmetric rings. First, we develop tight cutoffs that guarantee (1) closure in legitimate states, and (2) deadlock-freedom outside the legitimates states. We also develop a sufficient condition for convergence in silent self-stabilizing systems. Since some of our cutoffs grow with the size of local state space of processes, we also present an automated technique that significantly increases the scalability of synthesis in symmetric networks. Our technique is based on SMT-solving and incorporates a loop of synthesis and verification guided by counterexamples. We have fully implemented our technique and successfully synthesized solutions to maximal matching, three coloring, and maximal independent set problems.

We present an outline of the field of Design Understanding and summarize state-of-the-art research in deriving human-understandable knowledge in form of logic properties from an unknown design.