Model Checking Markov Chains Against Unambiguous Buchi Automata

We give a polynomial-time algorithm for model checking finite Markov chains against omega-regular specifications given as unambiguous Buchi automata

Verification of linear-time properties for finite probabilistic systems

With computers becoming ubiquitous there is an ever growing necessity to ensure that they are programmed to behave correctly. Formal verification is a discipline within computer science that tackles issues related to design and analysis of programs with the aim of producing well behaved systems. One of the core problems in this domain is what is called the model checking problem: given a mathematical model of a computer and a correctness specification, does the model satisfy the specification? In this thesis we explore this question for Markov Decision Processes (MDPs), which are finite state models involving stochastic and non-deterministic behaviour over discrete time steps. The kind of specifications we focus on are those that describe the correctness of individual executions of the model, called linear time properties. We delve into two different semantics for assigning meaning to the model checking problem: execution based semantics and distribution based semantics. In the execution based semantics we look at specifications described using Linear Temporal Logic (LTL). The model checking problem under this semantics are of two kinds: qualitative and quantitative. In the qualitative version we are interested in finding out if the specification is satisfied with non-zero probability, and in the more general quantitative version we want to know whether the probability of satisfaction is greater than a given quantity. The standard way to do model checking for both cases involves translating the LTL formula into an automaton which is then used to analyze the given MDP. One of the contributions of this thesis is a new translation of LTL to automata that are provably smaller than previously known ones. This translation helps us in reducing the asymptotic complexity of qualitative model checking of MDPs against certain fragments of LTL. We implement this translation in a tool called Büchifier to show its benefits on real examples. Our second main contribution involves a new automata-based algorithm for quantitative model checking that along with known translations of LTL to automata, which gives us new complexity results for the problem for different fragments of LTL. In the distribution based semantics we view MDPs as producing a sequence of probability distributions over its state space. At each point of time we are interested in the truth of atomic propositions, each of which tells us whether the probability of being in a certain states is above or below a given threshold. Linear time properties over these propositions are then used to describe correctness criteria. The model checking problem here happens to be undecidable in general, and therefore we consider restrictions on the problem. First we consider propositions which are robust: a proposition is said to be robust when the probability of being in its associated set of states is always well separated from its given threshold. For properties described over such propositions we observe that the model checking problem becomes decidable. But checking for robustness itself is an undecidable problem for MDPs. So we focus our attention on a subclass of MDPs called Markov Chains which exhibit stochastic behaviour without non-determinism. For Markov Chains we show that checking for robustness and model checking under robustness become tractable and we provide an analysis of the computational complexity of these problems

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Tools and Algorithms for the Construction and Analysis of Systems

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

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 25th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2022, which was held during April 4-6, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 23 regular papers presented in this volume were carefully reviewed and selected from 77 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems

Computer Aided Verification

This open access two-volume set LNCS 10980 and 10981 constitutes the refereed proceedings of the 30th International Conference on Computer Aided Verification, CAV 2018, held in Oxford, UK, in July 2018. The 52 full and 13 tool papers presented together with 3 invited papers and 2 tutorials were carefully reviewed and selected from 215 submissions. The papers cover a wide range of topics and techniques, from algorithmic and logical foundations of verification to practical applications in distributed, networked, cyber-physical, and autonomous systems. They are organized in topical sections on model checking, program analysis using polyhedra, synthesis, learning, runtime verification, hybrid and timed systems, tools, probabilistic systems, static analysis, theory and security, SAT, SMT and decisions procedures, concurrency, and CPS, hardware, industrial applications

Tools and Algorithms for the Construction and Analysis of Systems

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