TAILIEUCHUNG - Báo cáo " Some methods for transforming sequential processes into concurrent ones "

In this paper we investigate and build up three methods for transforming sequential processes of a net system into concurrent ones. These methods are based on: trace languages, shiftleft and case graphs. They are also presented by detail algorithms and can be applied to other models of concurrent systems. Keywords: net system, reliance alphabet, trace language, maximal concurrent steps, case graph. 1. Introduction The behaviour of a system often is represented by the set of the system’s processes. . | VNU Journal of Science Mathematics - Physics 23 2007 113-121 Some methods for transforming sequential processes into concurrent ones Hoang Chi Thanh Department of Mathematic Mechanics Informatics College of Science VNU 334 Nguyen Trai Thanh Xuan Hanoi Vietnam Received 31 October 2006 received in revised form 2 August 2007 Abstract In this paper we investigate and build up three methods for transforming sequential processes of a net system into concurrent ones. These methods are based on trace languages shiftleft and case graphs. They are also presented by detail algorithms and can be applied to other models of concurrent systems. Keywords net system reliance alphabet trace language maximal concurrent steps case graph. 1. Introduction The behaviour of a system often is represented by the set of the system s processes. The behaviour shows what the system can do in the way of performing processes. It is easy to formalize sequential behaviour of a given system. The behaviour usually is presented by the language generated by the system. Concurrent process with maximal concurrent steps points out an optimal way to perform the corresponding sequential process. Therefore constructing methods to transform sequential processes of a system into concurrent processes is still a meaningful problem in system controls. This paper concentrates in building up three methods for transforming sequential processes into concurrent ones. The first method is based on trace languages and the normal form of traces 1-3 . The trace language generated by a system can be determined by the language generated by a system and the detached relation over events of the system. The algorithm finding the normal form of a trace shows us how to find maximal concurrent steps on each trace. After normalizing the trace language generated by a system gives us the whole concurrent behaviour of the system. The second method is based on the following observation 4 an event in a sequence of events can be .

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