Comparison of Different Algorithms to Synthesize a Petri Net from a Partial Language

Synthesis of Petri nets from infinite partial languages

“…The definition of regions considered in this paper is similar to the one developed in [4]. But the idea of considering token flows is replaced by using so called transition regions (compare [3]). Since in general there are infinitely many regions, in [4] a finite set of so called basis regions representing all feasible places is computed.…”

“…The basic idea is to append events to LPOs given by the language of the term such that the resulting behaviour, called a wrong continuation of the term, is not specified by the term. Then for each wrong continuation a region is computed such that the corresponding feasible place separates the wrong continuation (compare [3]), if such a place exists. In the positive case the place is added to the net and the next wrong continuation is considered, in the negative case it is directly proceeded with the next wrong continuation.…”

“…It was shown in [3] that such basis representation is often inappropriate for practical applications, because the set of places corresponding to basis regions is usually very large causing unreadable nets. Therefore, in this paper we change the synthesis algorithm from [4] by computing so called separating regions, which proved to yield good synthesis results [3].…”

“…Therefore, in this paper we change the synthesis algorithm from [4] by computing so called separating regions, which proved to yield good synthesis results [3]. Moreover we use the region type called transition regions instead of the token flow regions considered in [4].…”

“…Moreover we use the region type called transition regions instead of the token flow regions considered in [4]. But this is only a design decision, because we showed in [3] that both region types have advantages in different settings. While exchanging the region type of token flow regions by transition regions only requires minor changes of the synthesis algorithm, it is difficult to use the principle of computing a separating representation of all regions instead of a basis representation.…”