Tham khảo tài liệu 'petri nets applications part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Towards Rewriting Semantics of Software Architecture Specification 111 In the following we define the relation between an occurrence for a transition t e T of a PrT net and a rewriting step A. Definition 6 An occurrence for a transition t e T a guard g e G of a PrT net N is a rewriting step At p q if Ai Ci with the following conditions a transition t is initial if g t e Term X and At is initial. a transition t is enabled if t is initial and At is enabled. a transition t is fired once under marking M1 and reach marking M2 if At is one step. This characterization is needed to prove the correspondence between PrT nets and rewriting theory RPrT given a PrT net N there is a one-to-one correspondence between the computation sequence of PrT net N and the rewriting theory RPrT . Proposition 1 One-step Correspondence Let t e T be a transition in PrT net N Ml and M2 be two markings before and after t is fired then a one step computation sequence for PrT net N is M1tM2. If RPrT entails an initial one-step rewriting step A pre t q p a post t p a then there is a computation sequence M1tM2 with pre t q p a e Ml and post t q p a e M2 defined for PrT nets. Proof. The proof has two steps on the definition of rewriting step. For any transition t e T from Subsection with a one step computation sequence for PrT net N M1tM2 3consuming-token-p L p t TermsS X such that consuming-token-p L p t TermsS X e Ml and 3producing-token-q L t q TermsS X such that producing-token-q L t q TermsS X e M2. Based on the definition 1 we can conclude the above proposition. endProof. We already observed in previous section that each place defines an --signature on the set of sorts and the fixed sort marking as the operation function with arguments. The markings are connected by transition firing defined by the Petri net semantics 19 . Thus we can conclude this section by the correspondence result between Petri net computational sequence semantics and the rewriting theory semantics. Corollary 1 Let Mi
