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Petri nets applications Part 5

Tham khảo tài liệu 'petri nets applications part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Using Petri nets for modeling and verification of Hybrid Systems 151 There are other Petri net extensions that have been developed such as hybrid and continuous Petri nets as well as fuzzy Petri nets. Continuous Petri nets are a model where the mark number in the places is a decimal point number instead of an integer. On another hand hybrid Petri nets are characterized by having a discrete part and a continuous part. 5.4 Enhanced Petri net model Traditional Petri nets have inherent disadvantages. Some of these disadvantages are deficiency of flexible descriptions for negative relations and necessity to formalize the original KB before beginning the verification process such is the case of the example of a logical system or production systems due to the difficulty of expressing logical disjunctions He et al. 2003 Nazareth 1993 Wu Lee 1997 Tsai et al. 1999 Yang et al. 1998 . In order to overcome these problems an enhanced Petri net model is proposed by us. Definition An enhanced Petri net is a sextuple. N P T F C I_ I F Fb Fr 1 Where 1 P is a set of places T is a set of transitions and F contains the set of inhibitor or activator relations between CC and CA. Therefore F Fb F . 2 C means that for any p e P C p is a collection of possible colors in P . For any t eT C t is the collection of possible colors in the transition T . 3 I_ and I are negative and positive functions of PxT respectively. For any p t e PxT . I_ and I are the previous and later transition matrices respectively. The elements P T Fb Fr are named predicate symbols places implications transitions activator arcs and inhibitor arcs respectively. For a transition t e T a positive place pb e P of t is a place that connects to t with an activator arc and presents a positive relation between pb and t. A negative place pr e P of t is a place that connects to t with an inhibitor arc and presents a negative relation between p r and t. The elements of the EPN modeling are shown in the figure 9. Elements of a .