Products Of Transition Systems Research Articles

Articulations and Products of Transition Systems and their Applications to Petri Net Synthesis

In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.

On Products of Transition Systems

For an arbitrary set endofunctor F we give a sufficient and necessary criterium for the existence of products of F-coalgebras. In the case of transition systems, where F=P is the covariant powerset functor, we introduce impeding paths whose existence impedes the existence of the product. Moreover we show, that the product A⊗A of a finite transition system A exists if and only if the product A⊗B for each finite transition system B exists.