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Synthesis of Petri Nets from Term Based Representations of Infinite Partial Languages

Bergenthum R., Desel J., Mauser S., Lorenz R.

Fundamenta Informaticae

2009

Vol. 95, nr 1

187-217

In this paper we present an algorithm to synthesize a finite unlabelled place/transition Petri net (p/t-net) from a possibly infinite partial language, which is given by a term over a finite set of labelled partial orders using operators for union, iteration, parallel composition and sequential composition. The synthesis algorithm is based on the theory of regions for partial languages presented in [17] and produces a p/t-net having minimal net behaviour including the given partial language. The algorithm uses linear programming techniques that were already successfully applied in [22] for the synthesis of p/t-nets from finite partial languages. Also, an equality test algorithm to check whether the behaviour of the synthesized p/t-net equals the given partial language is shown. Moreover, we present an implementation of the developed synthesis algorithm together with an example case study. Finally, a possible generalization of the presented term based representation of infinite partial languages is discussed.

Synthesis of Petri Nets from Finite Partial Languages

Bergenthum R., Desel J., Lorenz R., Mauser S.

Fundamenta Informaticae

2008

Vol. 88, nr 4

437-468

In this paper we present two algorithms that effectively synthesize a finite place/transition Petri net (p/t-net) froma finite set of labeled partial orders (a finite partial language). The synthesized p/t-net either has exactly the non-sequential behavior specified by the partial language, or there is no such p/t-net. The first algorithm is based on the theory of token flow regions for partial languages developed by Lorenz and Juh´as. Thus, this paper shows the applicability of this concept. The second algorithm uses the classical theory of regions applied to the set of step sequences generated by the given partial language. We finally develop an algorithm to test whether the net synthesized by either of the two algorithms has exactly the non-sequential behavior specified by the partial language. We implemented all algorithms in our framework VipTool. In this paper, the implementations of the first two algorithms are used to compare the algorithms by means of experimental results.

The synthesis problem for Elementary Net Systems with Inhibitor Arcs

Pietkiewicz-Koutny M.

Fundamenta Informaticae

1999

Vol. 40, Nr 2,3

251-283

We investigate the synthesis problem for the Elementary Net Systems with Inhibitor Arcs (ENI-systems) executed according to the a-priori semantics. We characterise transition systems generated by ENI-systems, called TSENI transition systems, by adapting the notion of a step transition system whose arcs are labelled by sets of concurrently executed events. The relationship between the ENI-systems and TSENI transition systems is established via the notion of a region. We define, and show consistency of, two behaviour preserving translations between nets and transition systems. We also discuss how to optimise the synthesis procedure by using only minimal regions and selected inhibitor arcs.