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Verification Techniques for a Network Algebra

Brodo Linda, Olarte Carlos

Fundamenta Informaticae

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2020

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Vol. 172, nr 1

1--38

EN

The Core Network Algebra (CNA) is a model for concurrency that extends the point-to-point communication discipline of Milner’s CCS with multiparty interactions. Links are used to build chains describing how information flows among the different agents participating in a multiparty interaction. The inherent non-determinism in deciding both the number of participants in an interaction, and how they synchronize, makes it difficult to devise verification techniques for this language. We propose a symbolic semantics and a symbolic bisimulation for CNA which are more amenable for automating reasoning. Unlike the operational semantics of CNA, the symbolic semantics is finitely branching and it represents, compactly, a possibly infinite number of transitions. We give necessary and sufficient conditions to efficiently check the validity of symbolic configurations. We also propose the Symbolic Link Modal Logic, a seamless extension of the Hennessy-Milner logic which is able to characterize the (symbolic) transitions of CNA processes. Finally, we specify both the symbolic semantics and the modal logic as an executable rewriting theory. We thus obtain several verification procedures to analyze CNA processes.

2

Regular Orthomodular Posets

Borzyszkowski Andrzej M.

Fundamenta Informaticae

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2019

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Vol. 166, nr 1

15--28

EN

Rozenberg and Ehrenfeucht has shown a duality between 2-structures (a.k.a. transition systems) and (elementary) Petri nets. The tool has been the notion of a region of a 2-structure, the regions then define a Petri net. Bernardinello et al. has observed that the regions of a 2-structure form an orthomodular poset and there is a similar relation between 2-structures and orthomodular posets. While in the theory of 2-structures we may ask if a 2-structure is full and forward closed, the analogous notion for orthomodular posets is their regularity. In the present paper we study the problem of closing a given orthomodular poset to a regular one. This is a dual problem to closing a 2-structure, which has been studied by the author earlier. Also, as in a seminal work of Rozenberg and Ehrenfeucht, one can be interested in a concrete representation, i.e. as a family of sets. We show here an appropriate construction for orthomodular posets too.

3

Closed Sets in Occurrence Nets with Conflicts

Bernardinello L., Ferigato C., Haar S., Pomello L.

Fundamenta Informaticae

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2014

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Vol. 133, nr 4

323--344

EN

The semantics of concurrent processes can be defined in terms of partially ordered sets. Occurrence nets, which belong to the family of Petri nets, model concurrent processes as partially ordered sets of occurrences of local states and local events. On the basis of the associated concurrency relation, a closure operator can be defined, giving rise to a lattice of closed sets. Extending previous results along this line, the present paper studies occurrence nets with forward conflicts, modelling families of processes. It is shown that the lattice of closed sets is orthomodular, and the relations between closed sets and some particular substructures of an occurrence net are studied. In particular, the paper deals with runs, modelling concurrent histories, and trails, corresponding to possible histories of sequential components. A second closure operator is then defined by means of an iterative procedure. The corresponding closed sets, here called ‘dynamically closed’, are shown to form a complete lattice, which in general is not orthocomplemented. Finally, it is shown that, if an occurrence net satisfies a property called B-density, which essentially says that any antichain meets any trail, then the two notions of closed set coincide, and they form a complete, algebraic orthomodular lattice.

4

Analysis of timed concurrent models based on testing equivalence

Andreeva M.V., Bozhenkova E.N., Virbitskaite I.B.

Fundamenta Informaticae

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2000

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Vol. 43, Nr 1-4

1-20

EN

The intention of the paper is to extend the testing methodology to a model of event structures with a dense time domain. Alternative characterizations of timed testing re-lations are provided. We also present algorithms for deciding timed testing for a sub-class of the model under consideration. The key to our decision algorithms is that timed testing equivalences can be reduced to appropriate symbolic bisimulations.