The Synthesis Problem of Concurrent Systems Specified by Dynamic Information Systems

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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].Key wordsInformation systemsrough setsconcurrent systemsPetri nets.