The Synthesis Problem of ConcurrentSystems Speci ed by Dynamic

We discuss the synthesis problem of concurrent systems from observations or speciication encoded in data table (information system) Pawlak,1991]. In the paper we rst introduce a new notion of a so-called dynamic information system, and then we apply this notion as a tool for speciication of concurrent systems behaviour Pawlak,1992], Pawlak,1997]. Finally, we present two methods of construction from any dynamic information system DS with its underlying system S, and transition system TS describing the behaviour of DS, a concurrent model in the form of an elementary net system N Thiagarajan,1987] with the following property: a given transition system TS is isomorphic to the transition system associated with the constructed net system N. In the rst method we assume that the data table representing a given dynamic information system DS contains the whole knowledge about the observed or speciied behaviour of the system. For this setting, we adopt a method of construction a solution of the synthesis problem of concurrent system models suggested by Desel and Reisig,1996]. A solution of the synthesis problem is any net which is constructed using the concept of regions of transition systems, introduced in Ehrenfeucht and Rozenberg,1990]. The second method presented in the paper is based on approach that a given data table consists of only partial knowledge about the system behaviour. Thus, we at rst compute an extension DS 0 of the dynamic information system DS, i.e. the system in which the set of all global states of DS 0 is consistent with all rules true in the underlying information system S of DS, and the set of all global states of DS 0 represents the largest extension of S consistent with the knowledge represented by S. Next, for nding a solution of the synthesis problem considered here we use the rst method. This approach is based on rough set theory Pawlak,1991] and Boolean reasoning Brown,1990]. We have implemented program on IBM PC generating a net model from a dynamic information system. In our approach we also use a modiication of the process independence definition presented in Pawlak,1992]. This paper is an attempt to present a new approach to concurrency based on the rough set philosophy. We illustrate our ideas by an intuitive example of traac signal control Paw-lak,1997]. We assume that the reader is familiar with the basic ideas of concurrent Our results seem to have some signiicance for methods of explanation of …