The Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems
Zbigniew Suraj · Studies in fuzziness and soft computing · 1998
We discuss the synthesis problem of concurrent systems from observations or specification encoded in data table (information system) [Pawlak,1991]. In the paper we first introduce a new notion of a so-called dynamic information system, and then we apply this notion as a tool for specification 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 first method we assume that the data table representing a given dynamic information system DS contains the whole knowledge about the observed or specified 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 first compute an extension DS ′ of the dynamic information system DS , i.e. the system in which the set of all global states of DS ′ is consistent with all rules true in the underlying information system S of DS , and the set of all global states of DS ′ represents the largest extension of S consistent with the knowledge represented by S . Next, for finding a solution of the synthesis problem considered here we use the first 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 modification 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 traffic signal control [Pawlak, 1997]. We assume that the reader is familiar with the basic ideas of concurrent systems [Milner, 1989], Petri nets [Murata, 1989], [Reisig, 1985] and information systems [Pawlak, 1991]. Our results seem to have some significance for methods of explanation of the system behavior. Besides, the proposed approach can be seen as basis for a certain class of control system design [Pawlak, 1997], and it could be also used for software specification [Hurley, 1983].