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Minimal Regions of ENL-Transition Systems

Koutny M., Pietkiewicz-Koutny M.

Fundamenta Informaticae

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2010

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Vol. 101, nr 1/2

45-58

EN

One of the possible ways of constructing concurrent systems is their automated synthesis from behavioural specifications. In this paper, we look at a particular instance of this approach which aims at constructing GALS (globally asynchronous locally synchronous) systems from specifications given in terms of transition systems with arcs labelled by steps of executed actions. GALS systems are represented by Elementary Net Systems with Localities (ENL-systems), each locality defining a set of co-located actions. The synthesis procedure is based on the regions of transition systems and we provide a number of criteria aimed at generating a minimal set of regions (conditions) of an ENL-system generating a given transition system.

2

Synthesis of Elementary Net Systems with Context Arcs and Localities

Koutny M., Pietkiewicz-Koutny M.

Fundamenta Informaticae

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2008

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Vol. 88, nr 3

307-328

EN

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.

3

Causal Semantics of Algebraic Petri Nets distinguishing Concurrency and Synchronicity

Juhás G., Lorenz R., Mauser S.

Fundamenta Informaticae

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2008

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Vol. 86, nr 3

255-298

EN

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.

4

Processes of Petri Nets with Range Testing

Kleijn J., Koutny M.

Fundamenta Informaticae

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2007

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Vol. 80, nr 1-3

199-219

EN

We are concerned with causality semantics in the executions of Petri nets with range arcs. Range arcs combine (and subsume) the distinctive features of inhibitor and activator arcs, and each such arc provides a means of specifying a range (a finite or infinite interval of non-negative integers) for the number of tokens in a place which makes enabling of a given transition possible. We demonstrate that the existing treatment of causality developed for Petri nets with inhibitor arcs based on structures generalising partial orders can also be applied to nets with range arcs.