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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 ..."
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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...
How to Transform Canonical Decreasing CTRSs into Equivalent Canonical TRSs
 In Proceedings of the 4th International Workshop on Conditional Term Rewriting Systems
, 1994
"... We prove constructively that the class of groundconfluent and decreasing conditional term rewriting systems (CTRSs) (without extra variables) coincides with the class of orthogonal and terminating, unconditional term rewriting systems (TRSs). TRSs being included in CTRSs, this result follows from a ..."
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We prove constructively that the class of groundconfluent and decreasing conditional term rewriting systems (CTRSs) (without extra variables) coincides with the class of orthogonal and terminating, unconditional term rewriting systems (TRSs). TRSs being included in CTRSs, this result follows from a transformation from any groundconfluent and decreasing CTRS specifying a computable function f into a TRS with the mentioned properties for f . The generated TRS is ordersorted, but we outline a similar transformation yielding an unsorted TRS.
On the folding of Algebraic Nets
, 1994
"... A folding in General Net theory is morphism that is surjective on places and transitions. Foldings can be used to relate CEsystems to "highlevel system". In this paper we study the problem of relating Petri Nets to nonstrict Highlevel Nets. We give a construction that given a morphism ..."
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A folding in General Net theory is morphism that is surjective on places and transitions. Foldings can be used to relate CEsystems to "highlevel system". In this paper we study the problem of relating Petri Nets to nonstrict Highlevel Nets. We give a construction that given a morphism of Petri Nets produces an Algebraic Net that characterises the folding in a canonical way. We also prove that the construction is functorial. Then we show how the construction can be made to work on Algebraic Nets directly. Finally we discuss an application of the construction.