On the Structure of High-level Nets

Reference:

Johan Lilius. On the structure of high-level nets. Research Report A33, Helsinki University of Technology, Department of Computer Science and Engineering, Digital Systems Laboratory, Espoo, Finland, March 1995. Doctoral dissertation.

Abstract:

The structure of High-level 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 High-level 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 surjective morphism between Petri nets gives rise to an algebraic net. Finally it is shown how Algebraic nets can be described as sets of formulae in a typed version of intuitionistic predicate linear logic.

Keywords:

net theory, category theory, algebraic specification, linear logic, petri nets, high-level nets

Suggested BibTeX entry:

@techreport{HUT-TCS-A33,
    address = {Espoo, Finland},
    author = {Johan Lilius},
    institution = {Helsinki University of Technology, Department of Computer Science and Engineering, Digital Systems Laboratory},
    month = {March},
    note = {Doctoral dissertation},
    number = {A33},
    pages = {136},
    title = {On the Structure of High-level Nets},
    type = {Research Report},
    year = {1995},
}