Edward Ochmanski

Mathematical Foundations of Computer Science 2008

This book constitutes the refereed proceedings of the 33rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2008, held in Torun, Poland, in August 2008. The 45 revised full papers presented together with 5 invited lectures were carefully reviewed and selected from 119 submissions. All current aspects in theoretical computer science and its mathematical foundations are addressed, ranging from algorithmic game theory, algorithms and data structures, artificial intelligence, automata and formal languages, bioinformatics, complexity, concurrency and petrinets, cryptography and security, logic and formal specifications, models of computations, parallel and distributed computing, semantics and verification.

Decidability of the Star Problem in A * × b *

We adress in this paper the decidability of the Star Problem in trace manoids: Let L be a recognizable trace language, is L∗ recognizable? We prove that this problem is decidable when the trace monoid is a direct product of free monoids A∗ × {b}∗. This result shows, for the first time and contrary to a possible intuition, that the Star Problem is of distinct nature than the Recognizability Problem: Let L be a rational trace language, is L recognizable?

On Morphisms of Trace Monoids

Morphisms of trace monoids are studied in the paper. Their relations to morphisms of free monoids are described. Injective trace morphisms are investigated and decidability of injectivity is proved for morphisms of abelian trace monoids. An effective general characterization of trace morphisms preserving regularity (recognizability) is given.

On lexicographic semi-commutations

Abstract We give a characterization of the commutation graphs for which there exists a complete semi-commutation system. From which, we deduce a characterization of semi-commutation systems for which the set of minimal words and the set of irreducible words are equal.

On confluent semi-commutations: decidability and complexity results

Abstract The subject of this paper is the confluence of finite semi-commutation systems. Confluence of such systems is proved to be decidable property. Existence of a finite complete presentation of a trace monoid using rules only from another given trace monoid is proved to be reducible to the existence of a confluent semi-commutation system. Complexity results related to the preceding problems are proved: deciding the existence of finite complete presentations is Σ P 2 -complete, whereas deciding confluence of semi-commutation systems is Co-NP-complete. Additionally, an open problem about trace synchronizations is solved: The local checking property is Co-NP-complete.

Semi-Commutation and Deterministic Petri Nets

Semi-commutation rewriting systems have been introduced and investigated by Clerbout/Latteux [1]. Starting from those, the notions of semitraces, semi-commutative monoids and an order on those monoids are defined. Behaviours of Petri nets are represented by sets of semitraces. Using that tool, properties of Petri nets, mainly concerning determinism, are discussed. Deterministic Petri nets are characterized in terms of their configurations. The present approach is a generalization of the well-known Mazurkiewiczs [7] trace model.

Inevitability in concurrent systems

Abstract This paper deals with the concurrent systems viewed as partially ordered sets. A set of system states is called inevitable if each exucution of the system sooner or later meets this set. A formal definition of inevitability in arbitrary concurrent systems is proposed. Some properties of inevitable sets are proved.

A star operation for star-free trace languages

The paper deals with star-free languages in trace monoids. We define a constrained star operation, named star-free star, and show a new characterisation of star-free trace languages, using this operation instead of complement. We obtain this characterisation combining a star-free star characterisation for word languages and logical characterisation of trace languages (Ebinger/Muscholl). Moreover, some new, simple proofs of known results are presented in the paper.

Modelling Concurrency with Semi-Commutations

The aim of this paper is to propose a mathematical tool, as well general as precise, for reasoning about concurrent systems. Ordered semi-commutative monoids are chosen for this purpose; their directed subsets represent processes of concurrent systems. Properties of such processes are proved; the main one is the diamond property. Infinite semitraces and their graphs are defined. Special sequences of actions, called linearizations and fair linearizations, are distinguished in order to represent finite and infinite processes. Finally, the approach is applied for modelling behaviours of general Petri-nets. Some kind of fairness, oriented on tokens, is introduced. It is shown that complete processes of general petri-nets, contrary to those of elementary nets, are not always fair.

Covering Fairness against Conspiracies

The paper takes advantage and develops the fundamental Best’s ideas about fairness hierarchy and conspiracies in concurrent systems. Near to the start we characterize liveness with the notion of ∞-fairness. Next we show that the conspiracy-freeness problem is decidable for elementary nets and undecidable for place/transition nets. The main aim of the paper was to put places into work against conspiracies. We show, how marking fairness effectively fights with conspiracies in elementary nets. Next, we introduce the notion of covering fairness, as a tool against conspiracies in place/transition systems. Results of the paper say that one can ensure global fairness on a local level of executions of the systems.