| Summary: | 碩士 === 國立海洋大學 === 電機工程學系 === 85 === This thesis is divided into three parts: an augmented
reachability tree (ART), a new algorithm for finding minimal
siphons and traps, and a class of nets, called process nets with
resources (PNRs). An augmented reachability tree (ART)
extends the ability of the classical reachability tree for
solving the liveness problem of a class of Petri nets where
there exists at most one unbounded place. The idea is based on
the computation of the minimal token number of the unbounded
place. An algorithm for obtaining the minimal token number is
shown. The proposed method can also be used to solve the
shortest path problem in graphs with negative costs.
Classical theorems that adopt siphons and traps to verify
reachability and liveness of Petri nets are shown to be only
tied to minimal siphons and traps. A new algorithm for finding
minimal siphons and traps has been presented using two proposed
theorems that enhances the efficiency of the algorithm. A
class of nets, called process nets with resources (PNRs), models
shared-resource automated manufacturing systems based on the
concept of separately specifying operation and resource
requirements. A PNR is built from a live net that is an acyclic
net after removing so called process idle places, and a set of
places called resource idle places modeling the availability of
system resources. It is shown that the liveness, reversibility
and reachability of a PNR only depends on whether all minimal
siphons are marked. An algorithms is presented to show how the
state equation is used to examine the reachability with a
restriction. Liveness of PNRs can be obtained by checking the
reachability of PNRs.
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