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On the Structure of Highlevel Nets
 Helsinki University of Technology
, 1995
"... : The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is ..."
Abstract

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: The structure of Highlevel nets is studied from an algebraic and a logical point of view using Algebraic nets as an example. First the category of Algebraic nets is defined and the semantics given through an unfolding construction. Other kinds of Highlevel net formalisms are then presented. It is shown that nets given in these formalisms can be transformed into equivalent Algebraic nets. Then the semantics of nets in terms of universal constructions is discussed. A definition of Algebraic nets in terms of structured transition systems is proposed. The semantics of the Algebraic net is then given as a free completion of this structured transition system to a category. As an alternative also a sheaf semantics of nets is examined. Here the semantics of the net arises as a limit of a diagram of sheaves. Next Algebraic nets are characterized as encodings of special morphisms called foldings. Each algebraic net gives rise to a surjective morphism between Petri nets and conversely each sur...
An Application of a Temporal Linear Logic to Timed Petri Nets
 Proc. Petri Nets'99 Workshop on Applications of Petri
, 1999
"... It is well known that the Petri net reachability is equivalent to the provability for the corresponding sequent of linear logic. It is a system which has expressive powers of resources, but does not provide a concept of time to encode timed Petri nets naturally. So we introduce a resourceconscious ..."
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Cited by 5 (3 self)
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It is well known that the Petri net reachability is equivalent to the provability for the corresponding sequent of linear logic. It is a system which has expressive powers of resources, but does not provide a concept of time to encode timed Petri nets naturally. So we introduce a resourceconscious and timedependent system, that is, temporal linear logic. The aim of the paper is to show the (discrete) timed Petri net reachability is equivalent to the provability in the subsystem of temporal linear logic for the corresponding sequent. Our final target is to analyze the dynamic behavior of timed Petri nets by means of the logic. 1