Translating linear temporal logic formulas to automata has proven to be an effective approach for implementing linear-time model-checking, and for obtaining many extensions and improvements to this verification method. On the other hand, for branching temporal logic, automata-theoretic techniques have long been thought to introduce an exponential penalty, making them essentially useless for model-checking. Recently, Bernholtz and Grumberg have shown that this exponential penalty can be avoided, though they did not match the linear complexity of non-automata-theoretic algorithms. In this paper we show that alternating tree automata are the key to a comprehensive automata-theoretic framework for branching temporal logics. Not only, as was shown by Muller et al., can they be used to obtain optimal decision procedures, but, as we show here, they also make it possible to derive optimal model-checking algorithms. Moreover, the simple combinatorial structure that emerges from the a...

Games given by transition graphs of pushdown processes are considered. It is shown that

The µ-calculus can be viewed as essentially the "ultimate" program logic, as it expressively subsumes all propositional program logics, including dynamic logics, process logics, and temporal logics. It is known that the satisfiability problem for the µ-calculus is EXPTIME-complete. This upper bound, however, is known for a version of the logic that has only forward modalities, which express weakest preconditions, but not backward modalities, which express strongest postconditions. Our main result in this paper is an exponential time upper bound for the satisfiability problem of the µ-calculus with both forward and backward modalities. To get this result we develop a theory of two-way alternating automata on infinite trees.

We present a theory of timed interfaces, which is capable of specifying both the timing of the inputs a component expects from the environment, and the timing of the outputs it can produce. Two timed interfaces are compatible if there is a way to use them together such that their timing expectations are met. Our theory provides algorithms for checking the compatibility between two interfaces and for deriving the composite interface; the theory can thus be viewed as a type system for real-time interaction. Technically, a timed interface is encoded as a timed game between two players, representing the inputs and outputs of the component. The algorithms for compatibility checking and interface composition are thus derived from algorithms for solving timed games.

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this paper have been presented at the 4th European Summer School in Logic, Language and Information, University of Essex, 1992; at the Tempus Summer School for Algebraic and Categorical Methods in Computer Science, Masaryk University, Brno, 1993; and the Summer School in Logic Methods in Concurrency, Aarhus University, 1993. I would like to thank the organisers and the participants of these summer schools, and of the Banff higher order workshop. I would also like to thank Julian Bradfield for use of his Tex tree constructor for building derivation trees and Carron Kirkwood, Faron Moller, Perdita Stevens and David Walker for comments on earlier drafts.

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. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional -calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the -calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the -calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...

We study the decidability of the model checking problem for linear and branching time logics, and two models of concurrent computation, namely Petri nets and Basic Parallel Processes. 1 Introduction Most techniques for the verification of concurrent systems proceed by an exhaustive traversal of the state space. Therefore, they are inherently incapable of considering systems with infinitely many states. Recently, some new methods have been developed in order to at least palliate this problem. Using them, several verification problems for some restricted infinite-state models have been shown to be decidable. These results can be classified into those showing the decidability of equivalence relations [8, 9, 24, 26], and those showing the decidability of model checking for different modal and temporal logics. In this paper, we contribute to this second group. The model checking problem has been studied so far for three infinite-state models: context-free processes, pushdown processes, and...

Guarded fixed point logics are obtained by adding least and greatest fixed points to the guarded fragments of firstorder logic that were recently introduced by Andr eka, van Benthem and N emeti. Guarded fixed point logics can also be viewed as the natural common extensions of the modal µ-calculus and the guarded fragments. We prove that the satisfiability problems for guarded fixed point logics are decidable and complete for deterministic double exponential time. For guarded fixed point sentences of bounded width, the most important case for applications, the satisfiability problem is EXPTIME-complete.