ABSTRACT The capability of representing in an highly communicable way the concurrency among auton... more ABSTRACT The capability of representing in an highly communicable way the concurrency among autonomous subsystems is frequently crucial in real systems modelling, whichever the nature of the system can be.
The paper presents a notion of preorder with related equivalence between concurrent systems which... more The paper presents a notion of preorder with related equivalence between concurrent systems which supports functional abstraction and refinement. Such abstraction and refinement disregard action names (the action alphabet can be changed) while they require to preserve local state transformations. Since Petri Nets explicitly model both states and state transformations, concurrent systems are considered as modelled by Petri nets, precisely
... Science, Florence, 1995. [Fer96] C. Ferigato, Note su a]ctme Propriet£ Algebriche, Logiche, T... more ... Science, Florence, 1995. [Fer96] C. Ferigato, Note su a]ctme Propriet£ Algebriche, Logiche, Topologiche della Concorrenza, Tesi di Dottorato di Ricerca in Informatica, Universit~ degli Stud] eli Milano, 1996. [ER90] A. Ehrenfeueht ...
ABSTRACT This paper surveys various notions of equivalence for concurrent systems in the framewor... more ABSTRACT This paper surveys various notions of equivalence for concurrent systems in the framework of Elementary Net Systems, a fundamental class in the family of Petri Net models. Two types of equivalences are considered: equivalences based on observations of ...
Electronic Proceedings in Theoretical Computer Science, 2014
ABSTRACT We start from two closure operators defined on the elements of a special kind of partial... more ABSTRACT We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events. If every maximal chain (line) of such a partially ordered set meets every maximal antichain (cut), then the two closure operators coincide, and generate a complete orthomodular lattice. In this paper we recall that, for any closed set in this lattice, every line meets either it or its orthocomplement in the lattice, and show that to any line, a two-valued state on the lattice can be associated. Starting from this result, we delineate a logical language whose formulas are interpreted over closed sets of a causal net, where every line induces an assignment of truth values to formulas. The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence "classical") substructures of the overall quantum logic.
In this paper, we study partially ordered structures associated to occurrence nets. An occurrence... more In this paper, we study partially ordered structures associated to occurrence nets. An occurrence net is endowed with a symmetric, but in general non transitive, concurrency relation. By applying known techniques in lattice theory, from any such relation one can derive a closure operator, and then an orthocomplemented lattice. We prove that, for a general class of occurrence nets, those
ABSTRACT The capability of representing in an highly communicable way the concurrency among auton... more ABSTRACT The capability of representing in an highly communicable way the concurrency among autonomous subsystems is frequently crucial in real systems modelling, whichever the nature of the system can be.
The paper presents a notion of preorder with related equivalence between concurrent systems which... more The paper presents a notion of preorder with related equivalence between concurrent systems which supports functional abstraction and refinement. Such abstraction and refinement disregard action names (the action alphabet can be changed) while they require to preserve local state transformations. Since Petri Nets explicitly model both states and state transformations, concurrent systems are considered as modelled by Petri nets, precisely
... Science, Florence, 1995. [Fer96] C. Ferigato, Note su a]ctme Propriet£ Algebriche, Logiche, T... more ... Science, Florence, 1995. [Fer96] C. Ferigato, Note su a]ctme Propriet£ Algebriche, Logiche, Topologiche della Concorrenza, Tesi di Dottorato di Ricerca in Informatica, Universit~ degli Stud] eli Milano, 1996. [ER90] A. Ehrenfeueht ...
ABSTRACT This paper surveys various notions of equivalence for concurrent systems in the framewor... more ABSTRACT This paper surveys various notions of equivalence for concurrent systems in the framework of Elementary Net Systems, a fundamental class in the family of Petri Net models. Two types of equivalences are considered: equivalences based on observations of ...
Electronic Proceedings in Theoretical Computer Science, 2014
ABSTRACT We start from two closure operators defined on the elements of a special kind of partial... more ABSTRACT We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of events. If every maximal chain (line) of such a partially ordered set meets every maximal antichain (cut), then the two closure operators coincide, and generate a complete orthomodular lattice. In this paper we recall that, for any closed set in this lattice, every line meets either it or its orthocomplement in the lattice, and show that to any line, a two-valued state on the lattice can be associated. Starting from this result, we delineate a logical language whose formulas are interpreted over closed sets of a causal net, where every line induces an assignment of truth values to formulas. The resulting logic is non-classical; we show that maximal antichains in a causal net are associated to Boolean (hence "classical") substructures of the overall quantum logic.
In this paper, we study partially ordered structures associated to occurrence nets. An occurrence... more In this paper, we study partially ordered structures associated to occurrence nets. An occurrence net is endowed with a symmetric, but in general non transitive, concurrency relation. By applying known techniques in lattice theory, from any such relation one can derive a closure operator, and then an orthocomplemented lattice. We prove that, for a general class of occurrence nets, those
Uploads