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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 ..."
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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...
Twophase distributed observation problems
 in 5th Intl. Conf. on Application of Concurrency to System Design (ACSD’05). IEEE
, 2005
"... We introduce and study problems of distributed observation with bounded or unbounded memory. We are given a system modeled as a finiteword language L over some finite alphabet Σ and subalphabets Σ1,..., Σn of Σ modeling n distinct observation points. We want to build (when there exist) n observers ..."
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Cited by 4 (0 self)
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We introduce and study problems of distributed observation with bounded or unbounded memory. We are given a system modeled as a finiteword language L over some finite alphabet Σ and subalphabets Σ1,..., Σn of Σ modeling n distinct observation points. We want to build (when there exist) n observers which collect projections of a behavior in L onto Σ1,..., Σn, then send them to a central decision point. The latter must determine whether the original behavior was in a given K ⊆ L. In the unboundedmemory case, observers record the entire sequence they observe. In the boundedmemory case, they are required to be finitestate automata. We show that, when L is traceclosed with respect to the usual dependence relation induced by Σ1,..., Σn, unboundedmemory observability is equivalent to K being centrally observable and traceclosed, thus decidable. When L is not traceclosed, the problem is undecidable, even if K and L are regular. We also show that boundedmemory observability is equivalent to unboundedmemory observability (thus decidable) when L is traceclosed and Σi are pairwise disjoint. Otherwise, the problem remains open. In the decidable cases, observers and decision function can be automatically synthesized. 1
Code Problems on Traces
 Szalas (Eds.), Proc. 21st Internat. Sympos. on Mathematical Foundations of Computer Science (MFCS'96), Lecture Notes in Comput. Sci
, 1996
"... . The topic of codes in the framework of trace monoids leads to interesting and challenging decision problems of combinatorial flavour. We give an overview of the current state of some basic questions in this field. Among these, we consider the existence problem for strong codings, cliquepreserving ..."
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Cited by 2 (0 self)
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. The topic of codes in the framework of trace monoids leads to interesting and challenging decision problems of combinatorial flavour. We give an overview of the current state of some basic questions in this field. Among these, we consider the existence problem for strong codings, cliquepreserving morphisms and the unique decipherability problem (code problem). 1 Introduction Free partially commutative monoids [7] offer a mathematically sound framework for modelling and analyzing concurrent systems. This was made popular by the work of Mazurkiewicz. He investigated originally the behaviour of safe 1labelled Petri nets [17] and the computer science community quickly recognized the importance of this work. The basic concept is to consider a system as a finite set of actions \Sigma , together with a fixed symmetric independence relation I ` \Sigma \Theta \Sigma , denoting pairs of actions which can be scheduled in parallel. In the setting defined by a pair (\Sigma ; I) we identify seq...
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 ..."
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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
On the confluence of trace rewriting systems
 PROCEEDINGS OF THE 18TH CONFERENCE ON FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE, (FSTTCS'98), CHENNAI (INDIA), NUMBER 1530 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... Trace rewriting systems, i.e., rewriting systems over trace monoids, generalize both semiThue systems and vector replacement systems. In [NO88], a particular trace monoid M is constructed such that confluence is undecidable for the class of lengthreducing trace rewriting systems over M. In this pa ..."
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Trace rewriting systems, i.e., rewriting systems over trace monoids, generalize both semiThue systems and vector replacement systems. In [NO88], a particular trace monoid M is constructed such that confluence is undecidable for the class of lengthreducing 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 lengthreducing semiThue systems is shown to be Pcomplete. 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.
On Efficient ReductionAlgorithms for Some Trace Rewriting Systems
, 1993
"... . 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 onerule systems. 1 Introduction The notes of this paper are based on th ..."
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. 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 onerule systems. 1 Introduction The notes of this paper are based on the Font Romeu Lecture and on an invited lecture at FCT93 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 FCT93. 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...