Logics and Automata for Verification: Expressiveness and Decidability Issues

This dissertation investigates and extends the mathematical foundations of logics and automata for the interleaving and synchronous noninterleaving view of system computations with an emphasis on decision procedures and relative expressive powers, and introduces extensions of these foundations to the emerging domain of noninterleaving asynchronous computations. System computations are described as occurrences of system actions, and tractable collections of such computations can be naturally represented by finite automata upon which one can do formal analysis. Specifications of system properties are usually described in formal logics, and the question whether the system at hand satisfies its specification is then solved by means of automata-theoretic constructions

An Expressive Extension of TLC

A temporal logic of causality (TLC) was introduced by Alur, Penczek, and Peled in [1]. It is basically a linear time temporal logic interpreted over Mazurkiewicz traces which allows quantification over causal chains. Through this device one can directly formulate causality properties of distributed systems. In this paper we consider an extension of TLC by strengthening the chain quantification operators. We show that our logic TLC # adds to the expressive power of TLC. We do so by defining an Ehrenfeucht-Fraïsse game to capture the expressive power of TLC. We then exhibit a property and by means of this game prove that the chosen property is not definable in TLC. We then show that the same property is definable in TLC # . We prove in fact the stronger result that TLC # is expressively stronger than TLC exactly when the dependency relation associated with the underlying trace alphabet is not transitive. We then show that TLC # defines only regular trace languages by embedding it into the..

This document in subdirectoryRS/99/26/ An Expressive Extension of TLC

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Dynamic Linear Time Temporal Logic

A simple extension of the propositional temporal logic of linear time is proposed. The extension consists of strengthening the until operator by indexing it with the regular programs of propositional dynamic logic (PDL). It is shown that DLTL, the resulting logic, is expressively equivalent to S1S, the monadic second-order theory of !-sequences. In fact a sublogic of DLTL which corresponds to propositional dynamic logic with a linear time semantics is already as expressive as S1S. We pin down in an obvious manner the sublogic of DLTL which correponds to the first order fragment of S1S. We show that DLTL has an exponential time decision procedure. We also obtain an axiomatization of DLTL. Finally, we point to some natural extensions of the approach presented here for bringing together propositional dynamic and temporal logics in a linear time setting

Dynamic Linear Time Temporal Logic

Reproduction of all or part of this work is permitted for educational or research use on condition that this copyright notice is included in any copy. See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRIC