Pure future local temporal logics are

A temporal logic for causality (Tlc) is introduced. The logic is interpreted over causal structures corresponding to partial order executions of programs. For causal structures describing the behavior of a finite fixed set of processes, a Tlc-formula can, equivalently, be interpreted over their linearizations. The main result of the paper is a tableau construction that gives a singly-exponential translation from a Tlc formula ' to a Streett automaton that accepts the set of linearizations satisfying '. This allows both checking the validity of Tlc formulas and model-checking of program properties. As the logic Tlc does not distinguish among different linearizations of the same partial order execution, partial order reduction techniques can be applied to alleviate the state-space explosion problem of model-checking. 1 Introduction One of the most successful techniques for automatic verification of finite-state systems has been model-checking . A model-checking algorithm decides wheth...

We investigate the model checking problem for branching time logics and Basic Parallel Processes. We show that the problem is undecidable for the logic 8L(O; F; U) (equivalent to CTL*) in the usual interleaving semantics, but decidable in a standard partial order interpretation.

A long standing open problem in the theory of (Mazurkiewicz) traces has been the question whether LTL (Linear Time Logic) is expressively complete with respect to the rst order theory. We solve this problem positively for nite and in nite traces and for the simplest temporal logic, which is based only on next and until modalities. Similar results were established previously, but they were all weaker, since they used additional past or future modalities. Another feature of our work is that our proof is direct and does not use any reduction to the word case.

. A finite representation of the prime event structure corresponding to the behaviour of a program is suggested. The algorithm of linear complexity using this representation for model checking of the formulas of Discrete Event Structure Logic without past modalities is given. A method of building finite representations of event structures in an efficient way by applying partial order reductions is provided. 1 Introduction Model checking is one of the most successful methods of automatic verification of program properties. A model-checking algorithm decides whether a finite-state concurrent system satisfies its specification, given as a formula of a temporal logic [3, 10]. Behaviour of a concurrent system can be modeled in two ways. In the interleaving semantics, the meaning of a program is an execution tree, temporal-logic assertions are interpreted over paths of this tree. In partial-order semantics (or event structure semantics), behaviour is an event structure, where the ordering r...

Mazurkiewicz traces ⋆

Mazurkiewicz traces are a widely accepted model of concurrent systems. We introduce a linear time temporal logic LTL f which has the same expressive power as the first order theory FO(<) of finite (infinite resp.) traces. The main contribution of the paper is that we only use future tense modalities in order to obtain expressive completeness. Our proof is direct using no reduction to words and Kamp's theorem for both finite and infinite words becomes a corollary. This direct approach became possible due to a proof technique of Wilke developed for the case of finite words.

Abstract. Recently, local logics for Mazurkiewicz traces are of increasing interest. This is mainly due to the fact that the satisfiability problem has the same complexity as in the word case. If we focus on a purely local interpretation of formulae at vertices (or events) of a trace, then the satisfiability problem of linear temporal logics over traces turns out to be PSPACE–complete. But now the difficult problem is to obtain expressive completeness results with respect to first order logic. The main result of the paper shows such an expressive completeness result, if the underlying dependence alphabet is a cograph, i.e., if all traces are series parallel posets. Moreover, we show that this is the best we can expect in our setting: If the dependence alphabet is not a cograph, then we cannot express all first order properties.

An Asynchronous Buchi Automaton is a collection of concurrently executing automata, able to perform operations that are shared between one or more of their concurrent components. These automata can be used to specify properties of distributed protocols. In this paper, an efficient method for verifying that a protocol satisfies its Asynchronous Buchi Automaton specification is presented. In order to alleviate a potential state space explosion while verifying a protocol, a state reduction technique is used. The construction results in a reduced state space that contains at least one representative sequence for each equivalence class of infinite sequences. This guarantees that the full state space contains an accepting execution if and only if the reduced state space contains one. This method can also be used to check for the emptyness of an Asynchronous Buchi Automaton. Thus, it can be used to check the validity of specification languages that can be translated into such automata, such a...

. Structures called concatenable weighted pomsets are introduced which can serve as models of processes of Petri nets, including nets with time features. Operations on such structures are defined which allow to combine them sequentially and in parallel. These operations correspond to natural operations on processes. They make the universe of concatenable weighted pomsets a partial algebra which appears to be a symmetric strict monoidal category. Sets of processes of timed and time Petri nets are characterized as subsets of this algebra. Keywords: concatenable weighted pomset, symmetry, table, sequential composition, parallel composition, interchange, algebra, timed Petri net, time Petri net, process, potential timed process, actual timed process. 1. Motivation The idea of representing behaviours of concurrent systems with the aid of partial orders has appeared to be fruitful. From one side, it has allowed to develop an adequate theory of Petri nets (cf. [P 77], [Maz 77], [Wi...