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 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.

We consider Hintikka et al.'s `independence-friendly first-order logic'. We apply it to a modal logic setting, defining a notion of `independent' modal logic, and we examine the associated fixpoint logics.

Model checking of asynchronous systems is traditionally based on the interleaving model, where an execution is modeled by a total order between atomic events. Recently, the use of partial order semantics, representing the causal order between events, is becoming popular. This paper considers the model checking problem for partial-order temporal logics. Solutions to this problem exist for partial order logics over local states. For the more general global logics that are interpreted over global states, only undecidability results have been proved. In this paper, we present a decision procedure for a partial order temporal logic over global states. We also sharpen the undecidability results by showing that a single until operator is sufficient for undecidability.

We propose trace event structures as a starting point for constructing effective branching time temporal logics in a non-interleaved setting.

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Abstract. Local First Search (LFS) is a partial order technique for reducing the number of states to be explored when trying to decide reachability of a local (component) property in a parallel system; it is based on an analysis of the structure of the partial orders of executions in such systems. Intuitively, LFS is based on a criterion that allows to guide the search for such local properties by limiting the “concurrent progress ” of components. In this paper, we elaborate the analysis of the partial orders in question and obtain related but significantly stronger criteria for reductions, show their relation to the previously established criterion, and discuss the algorithmics of the proposed improvement. Our contribution is both fundamental in providing better insights into LFS and practical in providing an improvement of high potential.

Abstract. We present the implementation of the trace theory in a new model checking tool framework, POEM, that has a strong emphasis on Partial Order Methods. A tree structure is used to store trace systems, which allows sharing common prefixes among traces and therefore, reduces memory cost. This structure is easy to extend to incorporate additional features. Two applications are shown in the paper: An extended structure to support an adequate order for Local First Search, and an acceleration of event zone based state space search for timed automata. 1