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Time and Petri Nets (Paperback, Softcover reprint of the original 1st ed. 2013)
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Time and Petri Nets (Paperback, Softcover reprint of the original 1st ed. 2013)
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At first glance the concepts of time and of Petri nets are quite
contrary: while time determines the occurrences of events in a
system, classic Petri nets consider their causal relationships and
they represent events as concurrent systems. But if we take a
closer look at how time and causality are intertwined we realize
that there are many possible ways in which time and Petri nets
interact. This book takes a closer look at three time-dependent
Petri nets: Time Petri nets, Timed Petri nets, and Petri nets with
time windows. The author first explains classic Petri nets and
their fundamental properties. Then the pivotal contribution of the
book is the introduction of different algorithms that allow us to
analyze time-dependent Petri nets. For Time Petri nets, the author
presents an algorithm that proves the behavioral equivalence of a
net where time is designed once with real and once with natural
numbers, so we can reduce the state space and consider the integer
states exclusively. For Timed Petri nets, the author introduces two
time-dependent state equations, providing a sufficient condition
for the non-reachability of states, and she also defines a local
transformation for converting these nets into Time Petri nets.
Finally, she shows that Petri nets with time-windows have the
ability to realize every transition sequence fired in the net
omitting time restrictions. These classes of time-dependent Petri
nets show that time alone does not change the power of a Petri net,
in fact time may or may not be used to force firing. For Time Petri
nets and Timed Petri nets we can say that they are Turing-powerful,
and thus more powerful than classic Petri nets, because there is a
compulsion to fire at some point in time. By contrast, Petri nets
with time-windows have no compulsion to fire, their expressiveness
power is less than that of Turing-machines. This book derives from
advanced lectures, and the text is supported throughout with
examples and exercises. It is suitable for graduate courses in
computer science, mathematics, engineering, and related
disciplines, and as a reference for researchers.
General
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