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On conflict-free executions of elementary nets

100%

Ochmański E.

tom nr 921

1-12

The paper deals with analysis of elementary Petri nets with respect to possibilities of avoiding conflicts during their executions. In concurrent systems, unlike to the sequential ones, avoiding of potential conflicts is not impossible. The basic notion of the paper is the notion of fairness, in sequential (fair run) and concurrent (fair process) versions. Main results: 1. The proof of decidability, for elementary nets, of problem of existence of a conflict-avoidable fair process (and an algorithm producing all fair runs) and 2. Construction, for arbitrary given elementary net, a conflict-avoidable net with the same behaviour.

Tematem pracy jest analiza elementarnych sieci Petriego pod katem mozliwości unikania sytuacji konfliktowych w trakcie ich działania. W systemach współbieżnych, w odróżnieniu od sekwencyjnych, unikanie potencjalnych konfliktów nie jest niemożliwe. Podstawowym pojęciem jest pojęcie uczciwości (fairness), zarówno w wersji sekwencyjnej (uczciwy przebieg liniowy), jak i współbieżnej (uczciwy proces). Najważniejsze wyniki pracy to: 1. Dowód rozstrzygalności problemu istnienia dla danej sieci elementarnej, bezkonfliktowego procesu uczciwego (wraz z algorytmem produkującym wszystkie uczciwe przebiegi) i 2. Konstrukcja dla dowolnej danej sieci elementarnej, sieci potencjalnie bezkonfliktowej o tym samym zachowaniu.

On Ethics of Mazurkiewicz Traces

63%

Ochmański E. , Pieckowska J.

2007

tom Vol. 80, nr 1-3

259-272

We extend the well-known hierarchy ∞-fair ⊆0-fair ⊆ just for sequences (sequential computations) to that of traces (concurrent processes). The fairness hierarchy for traces is similar, but more involved than for sequences. We study this hierarchy, first in general, abstracting from concrete concurrent system, then for basic classes of Petri nets - elementary and place/transition nets. Finally, we define the fairness notions in a non-interleaving way and compare them with the former ones.

On Trace-Expressible Behaviour of Petri Nets

63%

Jółkowska J. , Ochmański E.

2008

tom Vol. 85, nr 1-4

281-295

We propose a trace-based approach to description behaviours of concurrent systems. First, we define the independency relation induced by arbitrary transition system, forming this way an asynchronous transition system. Then we introduce the notion of traceability of transition systems and study some decision problems, related to computing independency and deciding traceability for basic classes of Petri nets. Main results: traceability is decidable for place/transition nets and undecidable in broader classes of nets - inhibitor, reset and transfer nets

On Star-Connected Flat Languages

51%

Klunder B. , Ochmański E. , Stawikowska K.

tom Vol. 67, nr 1-3

93--105

Up to now, star-connected rational expressions were considered only as expressions defining trace languages. In this paper we study the class of flat languages defined by this kind of rational expressions. We consider regular languages inducing recognizable trace languages and its subclasses: languages of finite ranks and star-connected languages. Main results are the following: rank of any star-connected language is finite; any star-connected language has an automaton with connected simple cycles; two pumping lemmas for star-connected languages. Moreover, we show that none of the investigated classes is closed under complement and that the class of languages of finite ranks is not closed under intersection. Finally, we briefly mention some decision problems and formulate several open questions.