Model Checking Synchronized Products of Infinite Transition Systems

Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of reachability properties. The present paper is a study on what can be achieved for infinite transition systems under these premises. As models we consider products of infinite transition systems with different synchronization constraints. We introduce finitely synchronized transition systems, i.e. product systems which contain only finitely many (parameterized) synchronized transitions, and show that the decidability of FO(R), first-order logic extended by reachability predicates, of the product system can be reduced to the decidability of FO(R) of the components. This result is optimal in the following sense: (1) If we allow semifinite synchronization, i.e. just in one component infinitely many transitions are synchronized, the FO(R)-theory of the product system is in general undecidable. (2) We cannot extend the expressive power of the logic under consideration. Already a weak extension of first-order logic with transitive closure, where we restrict the transitive closure operators to arity one and nesting depth two, is undecidable for an asynchronous (and hence finitely synchronized) product, namely for the infinite grid.Comment: 18 page

A technique for detecting wait-notify deadlocks in Java

Deadlock analysis of object-oriented programs that dynamically create threads and objects is complex, because these programs may have an infinite number of states. In this thesis, I analyze the correctness of wait - notify patterns (e.g. deadlock freedom) by using a newly introduced technique that consists in an analysis model that is a basic concurrent language with a formal semantic. I detect deadlocks by associating a Petri Net graph to each process of the input program. This model allows to check if a deadlock occur by analysing the reachability tree. The technique presented is a basic step of a more complex and complete project, since in my work I only consider programs with one object

TRACTABLE DATA-FLOW ANALYSIS FOR DISTRIBUTED SYSTEMS

Automated behavior analysis is a valuable technique in the development and maintainence of distributed systems. In this paper, we present a tractable dataflow analysis technique for the detection of unreachable states and actions in distributed systems. The technique follows an approximate approach described by Reif and Smolka, but delivers a more accurate result in assessing unreachable states and actions. The higher accuracy is achieved by the use of two concepts: action dependency and history sets. Although the technique, does not exhaustively detect all possible errors, it detects nontrivial errors with a worst-case complexity quadratic to the system size. It can be automated and applied to systems with arbitrary loops and nondeterministic structures. The technique thus provides practical and tractable behavior analysis for preliminary designs of distributed systems. This makes it an ideal candidate for an interactive checker in software development tools. The technique is illustrated with case studies of a pump control system and an erroneous distributed program. Results from a prototype implementation are presented

Model checking synchronized products of infinite transition systems

Abstract. Formal verification using the model checking paradigm has to deal with two aspects: The system models are structured, often as products of components, and the specification logic has to be expressive enough to allow the formalization of reachability properties. The present paper is a study on what can be achieved for infinite transition systems under these premises. As models we consider products of infinite transition systems with different synchronization constraints. We introduce finitely synchronized transition systems, i.e. product systems which contain only finitely many (parameterized) synchronized transitions, and show that the decidability of FO(R), first-order logic extended by reachability predicates, of the product system can be reduced to the decidability of FO(R) of the components. This result is optimal in the following sense: (1) If we allow semifinite synchronization, i.e. just in one component infinitely many transitions are synchronized, the FO(R)-theory of the product system is in general undecidable. (2) We cannot extend the expressive power of the logic under consideration. Already a weak extension of firstorder logic with transitive closure, where we restrict the transitive closure operators to arity one and nesting depth two, is undecidable for an asynchronous (and hence finitely synchronized) product, namely for the infinite grid. 1

A parametric analysis of the state-explosion problem in model checking

AbstractIn model checking, the state-explosion problem occurs when one checks a nonflat system, i.e., a system implicitly described as a synchronized product of elementary subsystems. In this paper, we investigate the complexity of a wide variety of model-checking problems for nonflat systems under the light of parameterized complexity, taking the number of synchronized components as a parameter. We provide precise complexity measures (in the parameterized sense) for most of the problems we investigate, and evidence that the results are robust

Visibly Pushdown Modular Games

Games on recursive game graphs can be used to reason about the control flow of sequential programs with recursion. In games over recursive game graphs, the most natural notion of strategy is the modular strategy, i.e., a strategy that is local to a module and is oblivious to previous module invocations, and thus does not depend on the context of invocation. In this work, we study for the first time modular strategies with respect to winning conditions that can be expressed by a pushdown automaton. We show that such games are undecidable in general, and become decidable for visibly pushdown automata specifications. Our solution relies on a reduction to modular games with finite-state automata winning conditions, which are known in the literature. We carefully characterize the computational complexity of the considered decision problem. In particular, we show that modular games with a universal Buchi or co Buchi visibly pushdown winning condition are EXPTIME-complete, and when the winning condition is given by a CARET or NWTL temporal logic formula the problem is 2EXPTIME-complete, and it remains 2EXPTIME-hard even for simple fragments of these logics. As a further contribution, we present a different solution for modular games with finite-state automata winning condition that runs faster than known solutions for large specifications and many exits.Comment: In Proceedings GandALF 2014, arXiv:1408.556