71 research outputs found

    Efficient Model Checking: The Power of Randomness

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    Exploring annotations for deductive verification

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    Maximizing Reachability Probabilities in Rectangular Automata with Random Clocks

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    This paper proposes an algorithm to maximize reachability probabilities for rectangular automata with random clocks via a history-dependent prophetic scheduler. This model class incorporates time-induced nondeterminism on discrete behavior and nondeterminism in the dynamic behavior. After computing reachable state sets via a forward flowpipe construction, we use backward refinement to compute maximum reachability probabilities. The feasibility of the presented approach is illustrated on a scalable model

    Computer Aided Verification

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    This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book

    Tools and Algorithms for the Construction and Analysis of Systems

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    This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

    Behavioral validation in Cyber-physical systems: Safety violations and beyond

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    The advances in software and hardware technologies in the last two decades have paved the way for the development of complex systems we observe around us. Avionics, automotive, power grid, medical devices, and robotics are a few examples of such systems which are usually termed as Cyber-physical systems (CPS) as they often involve both physical and software components. Deployment of a CPS in a safety critical application mandates that the system operates reliably even in adverse scenarios. While effective in improving confidence in system functionality, testing can not ascertain the absence of failures; whereas, formal verification can be exhaustive but it may not scale well as the system complexity grows. Simulation driven analysis tends to bridge this gap by tapping key system properties from the simulations. Despite their differences, all these analyses can be pivotal in providing system behaviors as the evidence to the satisfaction or violation of a given performance specification. However, less attention has been paid to algorithmically validating and characterizing different behaviors of a CPS. The focus of this thesis is on behavioral validation of Cyber-physical systems, which can supplement an existing CPS analysis framework. This thesis develops algorithmic tools for validating verification artifacts by generating a variety of counterexamples for a safety violation in a linear hybrid system. These counterexamples can serve as performance metrics to evaluate different controllers during design and testing phases. This thesis introduces the notion of complete characterization of a safety violation in a linear system with bounded inputs, and it proposes a sound technique to compute and efficiently represent these characterizations. This thesis further presents neural network based frameworks to perform systematic state space exploration guided by sensitivity or its gradient approximation in learning-enabled control (LEC) systems. The presented technique is accompanied with convergence guarantees and yields considerable performance gain over a widely used falsification platform for a class of signal temporal logic (STL) specifications.Doctor of Philosoph

    Proceedings of the 22nd Conference on Formal Methods in Computer-Aided Design – FMCAD 2022

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    The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

    Tools and Algorithms for the Construction and Analysis of Systems

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    This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

    Certificates and Witnesses for Probabilistic Model Checking

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    The ability to provide succinct information about why a property does, or does not, hold in a given system is a key feature in the context of formal verification and model checking. It can be used both to explain the behavior of the system to a user of verification software, and as a tool to aid automated abstraction and synthesis procedures. Counterexample traces, which are executions of the system that do not satisfy the desired specification, are a classical example. Specifications of systems with probabilistic behavior usually require that an event happens with sufficiently high (or low) probability. In general, single executions of the system are not enough to demonstrate that such a specification holds. Rather, standard witnesses in this setting are sets of executions which in sum exceed the required probability bound. In this thesis we consider methods to certify and witness that probabilistic reachability constraints hold in Markov decision processes (MDPs) and probabilistic timed automata (PTA). Probabilistic reachability constraints are threshold conditions on the maximal or minimal probability of reaching a set of target-states in the system. The threshold condition may represent an upper or lower bound and be strict or non-strict. We show that the model-checking problem for each type of constraint can be formulated as a satisfiability problem of a system of linear inequalities. These inequalities correspond closely to the probabilistic transition matrix of the MDP. Solutions of the inequalities are called Farkas certificates for the corresponding property, as they can indeed be used to easily validate that the property holds. By themselves, Farkas certificates do not explain why the corresponding probabilistic reachability constraint holds in the considered MDP. To demonstrate that the maximal reachability probability in an MDP is above a certain threshold, a commonly used notion are witnessing subsystems. A subsystem is a witness if the MDP satisfies the lower bound on the optimal reachability probability even if all states not included in the subsystem are made rejecting trap states. Hence, a subsystem is a part of the MDP which by itself satisfies the lower-bounded threshold constraint on the optimal probability of reaching the target-states. We consider witnessing subsystems for lower bounds on both the maximal and minimal reachability probabilities, and show that Farkas certificates and witnessing subsystems are related. More precisely, the support (i.e., the indices with a non-zero entry) of a Farkas certificate induces the state-space of a witnessing subsystem for the corresponding property. Vice versa, given a witnessing subsystem one can compute a Farkas certificate whose support corresponds to the state-space of the witness. This insight yields novel algorithms and heuristics to compute small and minimal witnessing subsystems. To compute minimal witnesses, we propose mixed-integer linear programming formulations whose solutions are Farkas certificates with minimal support. We show that the corresponding decision problem is NP-complete even for acyclic Markov chains, which supports the use of integer programs to solve it. As this approach does not scale well to large instances, we introduce the quotient-sum heuristic, which is based on iteratively solving a sequence of linear programs. The solutions of these linear programs are also Farkas certificates. In an experimental evaluation we show that the quotient-sum heuristic is competitive with state-of-the-art methods. A large part of the algorithms proposed in this thesis are implemented in the tool SWITSS. We study the complexity of computing minimal witnessing subsystems for probabilistic systems that are similar to trees or paths. Formally, this is captured by the notions of tree width and path width. Our main result here is that the problem of computing minimal witnessing subsystems remains NP-complete even for Markov chains with bounded path width. The hardness proof identifies a new source of combinatorial hardness in the corresponding decision problem. Probabilistic timed automata generalize MDPs by including a set of clocks whose values determine which transitions are enabled. They are widely used to model and verify real-time systems. Due to the continuously-valued clocks, their underlying state-space is inherently uncountable. Hence, the methods that we describe for finite-state MDPs do not carry over directly to PTA. Furthermore, a good notion of witness for PTA should also take into account timing aspects. We define two kinds of subsystems for PTA, one for maximal and one for minimal reachability probabilities, respectively. As for MDPs, a subsystem of a PTA is called a witness for a lower-bounded constraint on the (maximal or minimal) reachability probability, if it itself satisfies this constraint. Then, we show that witnessing subsystems of PTA induce Farkas certificates in certain finite-state quotients of the PTA. Vice versa, Farkas certificates of such a quotient induce witnesses of the PTA. Again, the support of the Farkas certificates corresponds to the states included in the subsystem. These insights are used to describe algorithms for the computation of minimal witnessing subsystems for PTA, with respect to three different notions of size. One of them counts the number of locations in the subsystem, while the other two take into account the possible clock valuations in the subsystem.:1 Introduction 2 Preliminaries 3 Farkas certificates 4 New techniques for witnessing subsystems 5 Probabilistic systems with low tree width 6 Explications for probabilistic timed automata 7 Conclusio

    Computer Aided Verification

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    This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book
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