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2 Fundamenta Informaticae

2 2008

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Synthesis of Elementary Net Systems with Context Arcs and Localities

Koutny M., Pietkiewicz-Koutny M.

Fundamenta Informaticae

2008

Vol. 88, nr 3

307-328

We investigate the synthesis problem for ENCL-systems, defined as Elementary Net Systems extended with context (inhibitor and activator) arcs and explicit event localities. Since colocated events are meant to be executed synchronously, the behaviour of such systems is captured by step transition systems, where arcs are labelled by sets of events rather than by single events. We completely characterise transition systems generated by ENCL-systems after extending the standard notion of a region - defined as a certain set of states - with explicit information about events which, in particular, are responsible for crossing its border. As a result, we are able to construct, for each such transition system, a suitable ENCL-system generating it.

Causal Semantics of Algebraic Petri Nets distinguishing Concurrency and Synchronicity

Juhás G., Lorenz R., Mauser S.

Fundamenta Informaticae

2008

Vol. 86, nr 3

255-298

In this paper, we show how to obtain causal semantics distinguishing "earlier than" and "not later than" causality between events from algebraic semantics of Petri nets. Janicki and Koutny introduced so called stratified order structures (so-structures) to describe such causal semantics. To obtain algebraic semantics, we redefine our own algebraic approach generating rewrite terms via partial operations of synchronous composition, concurrent composition and sequential composition. These terms are used to produce so-structures which define causal behavior consistent with the (operational) step semantics. For concrete Petri net classes with causal semantics derived from processes minimal so-structures obtained from rewrite terms coincide with minimal so-structures given by processes. This is demonstrated for elementary nets with inhibitor arcs.