Abstract not found

The main results of the present paper are the equivalence of definability by monadic second-order logic and recognizability for real trace languages, and that first-order definable, star-free, and aperiodic real trace languages form the same class of languages. This generalizes results on infinite words and on finite traces to infinite traces. It closes an important gap in the different characterizations of recognizable languages of infinite traces. 1 Introduction In the late 70's, A. Mazurkiewicz introduced the notion of trace as a suitable mathematical model for concurrent systems [16] (for surveys on this topic see also [1, 6, 10, 17]). In this framework, a concurrent system is seen as a set \Sigma of atomic actions together with a fixed irreflexive and symmetric independence relation I ` \Sigma \Theta \Sigma. The relation I specifies pairs of actions which can be carried out in parallel. It generates an equivalence relation on the set of sequential observations of the system. As ...

This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by some I-diamond deterministic Muller automaton. 1 Introduction A. Mazurkiewicz introduced the concept of traces as a suitable semantics for concurrent systems [Maz77]. A concurrent system is given by a set of atomic actions \Sigma = fa; b; c; : : :g together with an independence relation I ` \Sigma \Theta \Sigma, which specifies pairs of actions which can be performed concurrently. This leads to an equivalence relation on \Sigma generated by the independence relation I. More precisely, if a and b denote independent...

. We consider the basic problem of finding irreducible forms w.r.t. a finite noetherian rewriting system over a free partially commutative monoid where the underlying dependence alphabet is a cograph. A linear time algorithm is developed which determines irreducible normal forms w.r.t. finite, length-reducing trace rewriting systems over cograph monoids. This generalizes well-known results for free monoids and commutative monoids and is a significant improvement to the previously known square time algorithm. 1 Introduction Free partially commutative monoids were introduced in combinatorics by Cartier and Foata [4]. In computer science these monoids are known as trace monoids, cf. Mazurkiewicz [7]. For background material we refer to [1, 8] or [5]. The theory of rewriting over trace monoids combines combinatorial aspects from string rewriting (modulo some commutations) and graph rewriting. The restriction to traces leads to feasible algorithms, but some interesting complexity questions...

for graph groups

We present direct subset automata constructions for asynchronous (asynchronous cellular, resp.) automata. This provides a solution to the problem of direct determinization for automata with distributed control for languages of finite traces. We use the subset automaton construction and apply Klarlund's progress measure technique in order to complement non-deterministic asynchronous cellular Buchi automata for infinite traces.

this paper, we show that this result holds for every trace monoid, which is neither free nor free commutative. Furthermore we show that conuence for special trace rewriting systems over a xed trace monoid is decidable in polynomial time

This paper generalizes the concept of Mazurkiewicz traces to a fuzzy description of a concurrent process, where a known prefix is given in a first component and a second alphabetic component yields necessary information about future actions. This allows to define a good semantic domain where the concatenation is continuous with respect to the Scott- and to the Lawson topology. For this we define the notion of ff\Gamma and of ffi -trace. We show various mathematical results proving thereby the soundness of our approach. Our theory is a proper generalization of the theory of finite and infinite words (with explicit termination) and of the theory of finite and infinite (real and complex) traces. We make use of trace theory, domain theory, and topology. 1 Introduction The theory of Mazurkiewicz traces has been recognized as an important tool for investigating concurrent systems, overviews are in [Maz87, AR88, Per89, Die90, DR95]. The underlying idea is that for a given alphabet...

Trace rewriting systems, i.e., rewriting systems over trace monoids, generalize both semi-Thue systems and vector replacement systems. In [NO88], a particular trace monoid M is constructed such that confluence is undecidable for the class of length-reducing trace rewriting systems over M. In this paper, we show that this result holds for every trace monoid, which is neither free nor free commutative. Confluence for length-reducing semi-Thue systems is shown to be P-complete. Furthermore we introduce a restricted notion of confluence, called (; )-confluence, where ; 1. We prove that (; )-confluence is decidable for trace rewriting sytems and use this result in order to obtain new classes of trace rewriting systems with a decidable confluence problem.

. We consider some basic problems on the decidability and complexity of trace rewriting systems. The new contribution of this paper is an O(n log(n)) algorithm for some computing irreducible normal forms in the case of certain one-rule systems. 1 Introduction The notes of this paper are based on the Font Romeu Lecture and on an invited lecture at FCT-93 conference [11] of the second author. In the first part of the paper we give some basic background about trace rewriting systems. There is some overlap with the published notes from FCT-93. However, the second part is original and constitutes a new contribution to the theory of trace rewriting systems. The theory of rewriting over free partially commutative monoids (trace rewriting) combines combinatorial aspects from string rewriting (modulo a congruence) and graph rewriting. This restriction of graph rewriting leads to feasible algorithms, but some interesting complexity questions are still open. For example, a challenging open probl...