Necessary and Sufficient Condition of Structural Liveness for General Petri Nets with Globally Structural Live Minimal Deadlocks

スポンサーリンク

概要

• 論文の詳細を見る

• If a general Petri net N=(S, T, F, M_o) is transition-live under M_o, it is evident that each maximal structural deadlock SDL (N_D) in N as well as each minimal structural deadlock MSDL (N_D) in each N_D is also transition-live under M_o. However, since the converse of the latter of the above is not always true, it is important to obtain the conditions for this converse to be true if we want to have a useful necessary and sufficient "initial-marking-based" or "structural" liveness condition for N. Up to now, usefull and well-known structural or initial-marking-based necessary and sufficient liveness conditions of Petri nets have only been those of an asymmetric choice (AC) net and its subclasses such as an EFC net, an FC net, an FCF net, MG, and SM. However, all the above subclasses are activated only by real or virtual deadlock-trap properties which are local liveness for each minimal deadlocks ; in other words, the above topics of this paper are unconditionally satisfied in those subclasses because of their special structure of nets. In this paper, a necessary and sufficient structural liveness condition for a general Petri net N with globally structural live minimal structural deadlocks is presented as follows : The next (I) or (II) is satisfied. (I) N has no SDL N_D. (II) If N has at least one SDL N_D, (i) or (ii) is satisfied under the condition that each MSDL N_D in N is transition-live under M_o. (i) N has no singular MSDL (α) (i.e., (α-I) and (α-II)). (ii) If N has at least one singular MSDL (α-I) ((α-II), resp.), every semi-MSDL (I) ((II), resp. )N_<DS> = (S_<DS>, T_<DS>, F_<DS>, M_<oDS>) with respect to each singular MSDL (α-I) ((α-II), resp.), is transition-live under the M_<oDS> under the condition of "the condition (**)", where the locally structural liveness for this N_<DS> means (1) or (2) ((3), resp.) of Lemma 4-4 and "the condition (**)" is defined in Lemma 4-7 of this paper. The relationship between the above results and the liveness problem for N is also shown.

• 社団法人電子情報通信学会の論文
• 1995-12-25

著者

• Matsumoto Tadashi

  The Faculty Of Engineering Fukui University

• Yamazaki Shinichi

  The Faculty of Engineering, Fukui University

• Yamazaki Shinichi

  The Faculty Of Engineering Fukui University

関連論文

• Minimum Number of Live Minimal Structural Traps to Make a Minimal Deadlock Locally Live in General Petri Nets
• Necessary and Sufficient Condition of Structural Liveness for General Petri Nets with Globally Structural Live Minimal Deadlocks
• New Time-Domain Stability Criterion for Fuzzy Control Systems (Special Section on Nonlinear Theory and its Applications)

スポンサーリンク