Tham khảo tài liệu 'petri net part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Timed Hierarchical Object-Oriented Petri Net 261 temporal interval tightly. In order to analyze the dynamics of TOPN the definition of schedule and path is given in the following. Definition 8 In Petri net N if the state Mn is reachable from the initial state M0 then there exists a sequence of fired transitions from M0 to Mn. This sequence is called a path or a schedule w from M0 to Mn. It can be represented as Path Mo t1 M1 . tn Mn or w Mo t1 M1 . . t Mn 1 i n And the schedule set of Petri net N with initial marking M0 is represented as L N M0 . Just like those in TPN Merlin Farber 1976 Harel Gery 1996 if the number of solid tokens residing in the input place equals or exceeds the weight of the input arc the forward transition is enabled. However when one TABP is marked by enough hollow tokens compared with the weight of internal arcs in its refined TOPN it is also enabled at this time. After its internal behaviors have completed the color of tokens residing in it become from hollow to solid which are similar to those in common places. So TABPs also manifest actions in TOPN. An extended definition of path in TOPN is given in the following in which TABP is extended into the schedule. Definition 9 If the state Mn is reachable from the initial state M0 then there exists a sequence of marked abstract places and fired transitions from M0 to Mn. This sequence is called a path or a schedule w from M0 to Mn. It can be represented as Path PA1 PA2 . PAn or w PA1 PA2 . PAn where PAieTuTABP and 1 i n. Definition 10 Let t be a TOPN transition and let PA1 PA2 . PAn be a path add ti into the path is expressed as PA1 PA2 . PAn t PA1 PA2 . PAn t . Let p be an abstract place and let PA1 PA 2 . PAn be a path add p into the path is expressed as PA1 PA2 . PAn p PA1 PA2 . PAn p where PAieTuTABP and 1 i n . Definition 11 For a TOPN N with schedule w we denote the state reached by starting in N s initial state and firing each transition in w at its associated time ọ N w . The time
