Results 1  10
of
14
Logical Definability on Infinite Traces
 Theoretical Computer Science
, 1993
"... The main results of the present paper are the equivalence of definability by monadic secondorder logic and recognizability for real trace languages, and that firstorder definable, starfree, and aperiodic real trace languages form the same class of languages. This generalizes results on infinite w ..."
Abstract

Cited by 31 (4 self)
 Add to MetaCart
The main results of the present paper are the equivalence of definability by monadic secondorder logic and recognizability for real trace languages, and that firstorder definable, starfree, 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 ...
Deterministic Asynchronous Automata for Infinite Traces
 Acta Informatica
, 1993
"... 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 tra ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
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 Idiamond 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...
Efficient Rewriting in Cograph Trace Monoids
 Proc. of the 10th FCT '95, Dresden (Germany) 1995, number 965 in LNCS
, 1995
"... . 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, lengt ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
. 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, lengthreducing trace rewriting systems over cograph monoids. This generalizes wellknown 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...
Partially commutative inverse monoids
 PROCEEDINGS OF THE 31TH INTERNATIONAL SYMPOSIUM ON MATHEMATICAL FOUNDATIONS OF COMPUTER SCIENCE (MFCS 2006), BRATISLAVE (SLOVAKIA), NUMBER 4162 IN LECTURE NOTES IN COMPUTER SCIENCE
, 2006
"... Free partially commutative inverse monoids are investigated. Analogously to free partially commutative monoids (trace monoids), free partially commutative inverse monoid are the quotients of free inverse monoids modulo a partially defined commutation relation on the generators. An O(n log(n)) algo ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
Free partially commutative inverse monoids are investigated. Analogously to free partially commutative monoids (trace monoids), free partially commutative inverse monoid are the quotients of free inverse monoids modulo a partially defined commutation relation on the generators. An O(n log(n)) algorithm on a RAM for the word problem is presented, and NPcompleteness of the generalized word problem and the membership problem for rational sets is shown. Moreover, free partially commutative inverse monoids modulo a finite idempotent presentation are studied. For these monoids, the word problem is decidable if and only if the complement of the commutation relation is transitive.
On the complementation of asynchronous cellular Büchi automata
 Theoretical Computer Science
, 1996
"... 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 Kla ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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 nondeterministic asynchronous cellular Buchi automata for infinite traces.
Confluence Problems for Trace Rewriting Systems
, 2001
"... 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 ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
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