We describe a method for reducing the complexity of temporal logic model checking in systems composed of many parallel processes. The goal is to check properties of the components of a system and then deduce global properties from these local properties. The main difficulty with this type of approach is that local properties are often not preserved at the global level. We present a general framework for using additional interface processes to model the environment for a component. These interface processes are typically much simpler than the full environment of the component. By composing a component with its interface processes and then checking properties of this composition, we can guarantee that these properties will be preserved at the global level. We give two example compositional systems based on the logic CTL*.

this paper we consider the problem of modelchecking for different fragments of propositional ¯-calculus. This logic was studied by many authors [6, 9] for specifying the properties of concurrent programs. It has been shown to be as expressive of automata on infinite trees. Most of the known temporal and dynamic logics can be translated into this logic. The modelchecking problem for this logic was first considered in [7]. In this paper, the authors presented an algorithm that is O((mn)

In this paper we study induction in the context of the first-order µ-calculus with explicit approximations. We present and compare two Gentzen-style proof systems each using a different type of induction. The first is

We show strict lower bounds for the complexity of several model checking problems for BPA (Basic Process Algebra). Model checking BPA with Hennessy-Milner Logic is PSPACE-hard, while model checking BPA with the (alternation-free) modal ¯- calculus is EXPTIME-hard. Model checking BPA with LTL is also EXPTIME- hard. By combining these results with already established upper bounds, it follows that the model checking problems are PSPACE-complete and EXPTIME-complete, respectively. 1 Introduction Basic Process Algebra (BPA) processes were defined by Bergstra and Klop in [1]. They are transition systems associated with Greibach normal form (GNF) context-free grammars in which only left-most derivations are permitted. BPA-processes are also called context-free processes. They are a subclass of pushdown processes, where the finite control of the pushdown automaton has only one state. It has been known for some time that model checking pushdown processes with the modal ¯-calculus is EXPTIME...

We investigate a Gentzen-style proof system for the first-order µ-calculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge condition which ensures the well-foundedness of inductive reasoning. As the main result of this paper we propose a new syntactic discharge condition based on traces and establish its equivalence with the semantical condition. We give an automata-theoretic reformulation of this condition which is more suitable for practical proofs. For a detailed

Abstract. We extend the automata-theoretic framework for reasoning about infinitestate sequential systems to handle also the global model-checking problem. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisfies a temporal property can then be done by a two-way automaton that navigates through the tree. The framework is known for local model checking. For branching time properties, the framework uses two-way alternating automata. For linear time properties, the framework uses two-way path automata. In order to solve the global model-checking problem we show that for both types of automata, given a regular tree, we can construct a nondeterministic word automaton that accepts all the nodes in the tree from which an accepting run of the automaton can start. 1

This paper presents a symbolic model checking algorithm for Fixpoint Logic with Chop, an extension of the modal -calculus capable of defining non-regular properties. Some empirical data about running times of a naive implementation of this algorithm are given as well.

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