Our growing dependence on increasingly complex computer and software systems necessitates the development of formalisms, techniques, and tools for assessing functional properties of these systems. One such technique that has emerged in the last twenty years is model checking, which systematically (and automatically) checks whether a model of a given system satisfies a desired property such as deadlock freedom, invariants, and request-response properties. This automated technique for verification and debugging has developed into a mature and widely used approach with many applications. Principles of Model Checking offers a comprehensive introduction to model checking that is not only a text suitable for classroom use but also a valuable reference for researchers and practitioners in the field. The book begins with the basic principles for modeling concurrent and communicating systems, introduces different classes of properties (including safety and liveness), presents the notion of fairness, and provides automata-based algorithms for these properties. It introduces the temporal logics LTL and CTL, compares them, and covers algorithms for verifying these logics, discussing real-time systems as well as systems subject to random phenomena. Separate chapters treat such efficiency-improving techniques as abstraction and symbolic manipulation. The book includes an extensive set of examples (most of which run through several chapters) and a complete set of basic results accompanied by detailed proofs. Each chapter concludes with a summary, bibliographic notes, and an extensive list of exercises of both practical and theoretical nature.

/pdf/principles-of-model-checking-249iimickz.pdf

Principles of Model Checking

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

This paper describes a major new release of the PRISMprobabilistic model checker, adding, in particular, quantitative verification of (priced) probabilistic timed automata. These model systems exhibiting probabilistic, nondeterministic and real-time characteristics. In many application domains, all three aspects are essential; this includes, for example, embedded controllers in automotive or avionic systems, wireless communication protocols such as Bluetooth or Zigbee, and randomised security protocols. PRISM, which is open-source, also contains several new components that are of independent use. These include: an extensible toolkit for building, verifying and refining abstractions of probabilistic models; an explicit-state probabilistic model checking library; a discrete-event simulation engine for statistical model checking; support for generation of optimal adversaries/strategies; and a benchmark suite.

http://www.prismmodelchecker.org/papers/cav11.pdf

PRISM 4.0: verification of probabilistic real-time systems

This paper presents the overal structure, the design criteria, and the main features of the tool box Uppaal. It gives a detailed user guide which describes how to use the various tools of Uppaal version 2.02 to construct abstract models of a real-time system, to simulate its dynamical behavior, to specify and verify its safety and bounded liveness properties in terms of its model. In addition, the paper also provides a short review on case-studies where Uppaal is applied, as well as references to its theoretical foundation.

UPPAAL in a Nutshell

Real and Complex Analysis

This book constitutes the refereed proceedings of the 22nd International Conference on Concurrency Theory, CONCUR 2011, held in Aachen, Germany, September 5-10, 2011. The 32 revised full papers were carefully reviewed and selected from 94 submissions. The papers are organized in topics such as real-time systems, probabilistic systems, automata, separation logic, pi-calculus, Petri nets, process algebra and modeling, verification, games, and bisimulation.

CONCUR 2011 - concurrency theory : 22st International Conference, CONCUR 2011, Aachen, Germany, September 6-9, 2011, proceedings

We study the verification of a finite continuous-time Markov chain (CTMC) C against a linear real-time specification given as a deterministic timed automaton (DTA) A with finite or Muller acceptance conditions. The central question that we address is: what is the probability of the set of paths of C that are accepted by A, i.e., the likelihood that C satisfies A? It is shown that under finite acceptance criteria this equals the reachability probability in a finite piecewise deterministic Markov process (PDP), whereas for Muller acceptance criteria it coincides with the reachability probability of terminal strongly connected components in such a PDP. Qualitative verification is shown to amount to a graph analysis of the PDP. Reachability probabilities in our PDPs are then characterized as the least solution of a system of Volterra integral equations of the second type and are shown to be approximated by the solution of a system of partial differential equations. For single-clock DTA, this integral equation system can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations. As the coefficients are in fact transient probabilities in CTMCs, this result implies that standard algorithms for CTMC analysis suffice to verify single-clock DTA specifications.

Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications

Many systems that are subject to verification give rise to probabilities; examples include randomized distributed algorithms, security, systems biology, or embedded systems. State-of-the-art probabilistic model checkers like PRISM [7] mostly work under the assumption that all model probabilities are a priori known. However, at early development stages, certain system quantities require parametric probabilistic models to be specified, where transition probabilities are given by real-valued parameters. Here, we focus on so-called parametric Markov chains (pMC), see Figure 1(a). The model checking goal is to compute rational functions, i. e., a fraction of polynomials

Parameter synthesis for probabilistic systems

Model checking is an automated verification method guaranteeing that a mathematical model of a system satisfies a formally described property. It can be used to assess both qualitative and quantitative properties of complex software and hardware systems. Model checking suffers from the well-known state space explosion problem where the number of states grows exponentially in the number of program variables, channels and parallel components. Reduction techniques can be used to shrink the state space of system models by hiding redundant information and removing irrelevant details. The reduced state space can then be used for analysis provided it preserves a rich class of properties of interest. This thesis presents reduction techniques for a wide range of nondeterministic and probabilistic models. Our reduction techniques are based on the notions of equivalence relations and layering. Equivalence relations reduce the state space of system models, by aggregating equivalent states into a single state. The reduced state space obtained under an equivalence relation, is called a quotient system. An example equivalence relation that is widely used to reduce the state space of nondeterministic and probabilistic models is bisimulation. On the other hand, layering involves carrying out structural transformations for the systems that are modeled as a network of system models, e.g., distributed systems. As a result of these structural transformations, the new state space obtained is smaller than the original non-layered one. The first part of this thesis focuses on developing new equivalence relations for nondeterministic and Markovian models. For each of these relations, we define a quotient system, investigate its relationship with bisimulation and prove that it preserves interesting linear-time properties. In the second part of this thesis we focus on layering based state space reduction for more expressive specification formalisms that support a stepwise refinement methodology. We develop a framework of layering for modal transition systems and probabilistic versions thereof. This involves a layered composition

Reduction Techniques for Nondeterministic and Probabilistic Systems

We present a new game-based abstraction technique for probabilistic automata (PA). The key idea is to use distribution-based abstraction – preserving novel distribution-based (alternating) simulation relations – rather than classical state-based abstraction. These abstractions yield (simple) probabilistic game automata (PGA), turn-based 2 player stochastic games in which moves of both players – as opposed to classical stochastic games – yield distributions over states. As distribution-based (alternating) simulation relations are pre-congruences for composite PGA, abstraction can be done compositionally. Our abstraction yields tighter upper and lower bounds on (extremal) reachability probabilities than state-based abstraction. This shows the potential superiority over state-based abstraction of PA and Markov decision processes.

Joost-Pieter Katoen

Papers

CONCUR 2011 - concurrency theory : 22st International Conference, CONCUR 2011, Aachen, Germany, September 6-9, 2011, proceedings

Model Checking of Continuous-Time Markov Chains Against Timed Automata Specifications

Parameter synthesis for probabilistic systems

Reduction Techniques for Nondeterministic and Probabilistic Systems

Tight Game Abstractions of Probabilistic Automata