Abstract
Networks for information flow were invented in the dissertation of C.A. Petri (1961) xc21 at the University of Bonn. A. W. Holt and F. Commoner (1970, (xc9) extended them and called them Petri nets. Peterson (1981, xc20) and Reisig (1985, (xc23) provide treatises and the theory of Petri nets, that are used nowadays to model flows such as parts and materials in manufacturing processes (Zhou and Leu, 1991 (xc32), and logical truths in machine reasoning systems (Looney, 1988, xc15, and Murata et al, 1991 xc19).
For our purposes, a logic Petri net P consists of i) a net architecture; and ii) an operational procedure. Architecturally, it is directed graph that consists of two kinds of nodes: a) conditions, designated by circles; and b) vents, denoted by bars. The conditions and events are connected by arrows according to two rules: 1) an arrow may connect from a condition to an event, or from an event to a condition; and 2) an arrow may never connect two nodes of the same kind. Figure 1 is an example of such a scheme.
Procedurally, the net uses tokens, representes graphically by dots inside condition nodes, to activate the conditions where they appear. A token denotes a Boolean truth value of 1 for the condition, while the absence of a token indicates a value of 0. An event is enabled when every arrow entering it comes from a condition that contains a token. An enables event fires to activate (i.e., make true) all conditions to which its departing arrows directly connect, by sending them tokens. In Figure 1, Condotion C2 is activated, i.e., made tru, with a token. A clock is implicit in the net in that it connects to each event so that upon being enabled, an event fires on the next clock pulse. A clock is necessary to maintain sequential order.
A logi Petri net that interacts with the external world has boundary nodes that connect to the external environment. In figure 1, Condition C1, and Events E5, and E6, are boundary nodes. Arrows enter boundary conditions from the environment, and arrows depart boundary events to the environment. External events that activate boundary conditions are called sources, while external conditions that are activated by boundary events are calledsinks. The operation of a logoc Petri net is initiated when certain source events fire to activate boundary conditions. These enable events that fire to activate other conditions, which may in turn enable other events to fire to activate other conditions, etc.
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Looney, C.G. (1994). Fuzzy Petri Nets and Applications. In: Fuzzy Reasoning in Information, Decision and Control Systems. International Series on Microprocessor-Based and Intelligent Systems Engineering, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-0-585-34652-6_19
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DOI: https://doi.org/10.1007/978-0-585-34652-6_19
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