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1

Synthesis of Transition Systems from Quantum Logics

Bernardinello L., Ferigato C., Pomello L., Puerto Aubel A.

Fundamenta Informaticae

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2017

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Vol. 154, nr 1/4

25--36

EN

The set of elementary regions of a transition system, ordered by set inclusion, forms an orthomodular poset, also referred to as quantum logic, which is regular and rich. Starting from an abstract regular and rich quantum logic, one can construct an elementary transition system such that the orginal logic embeds into its set of regions, and which is saturated of transitions. We study the problem of selecting subsets of transitions on the same set of states, which generate the same set of regions.

2

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.

3

Closure Operators and Lattices Derived from Concurrency in Posets and Occurrence Nets

Bernardinello L., Pomello L., Rombola S.

Fundamenta Informaticae

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2011

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Vol. 105, nr 3

211-235

EN

Partially ordered sets (posets), and among them occurrence nets, are a natural formal tool for studying concurrent processes. In a poset, the concurrency relation between elements is explicit. Starting from this relation, and applying standard techniques of lattice theory, one can build a complete lattice whose elements are subsets of the given poset. We study structural properties of such closed subsets, and of the lattice they form. In particular, we show that, if a poset is Ndense, then the lattice of closed subsets is orthomodular. A characterization of K-density, valid for posets, is given on the basis of a relation between lines, or chains, and closed sets. In the case of occurrence nets, we give a characterization of the closed subsets, and define the related notion of "causally closed subset"; a constructive characterization of such subsets is given, which justifies their interpretation as causally closed subprocesses of the occurrence net. We show that, for K-dense occurrence nets, closed subsets and causally closed subsets coincide. By using causally closed subsets, we give another characterization of K-density, related to the algebraicity of the lattice of closed sets.

4

A Multi-facet Approach to Dynamic Agent Systems

Bednarczyk M.A., Pawłowski A., Bernardinello L., Pomello L., Borzyszkowski T.

Fundamenta Informaticae

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2008

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Vol. 85, nr 1-4

19-33

EN

We are concerned with the problem of defining a complex, hybrid, agent based discrete system in a modular way. The modularity results from looking at the system from a number of different perspectives, each dealing with a specific aspect of the system. As a solution a synchronization operator is proposed which glues agent aware systems on shared agents and transitions. The construction turns out to be a categorical product. We also show that a logic to talk about the temporal and the structural properties of the product can be obtained by gluing suitable logical frameworks from the components.

5

A multi-facet approach to dynamic agent systems

Bednarczyk M., Bernardinello L., Borzyszkowski T., Pawłowski W., Pomello L.

Prace Instytutu Podstaw Informatyki Polskiej Akademii Nauk

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2007

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Nr 1001

1-22

EN

We are concerned with the problem of defining a complex, hybrid, agent based discrete system in a modular way. The modularity results from looking at the system from a numbci of different perspectives, each dealing with a specific aspect of the system. As a solution a synchronisation operator is proposed which glues agent aware systems on shared agents and transitions. The construction turns out to be a categorical product. We also show that a logic to talk about the temporal and the structural properties of the product can be obtained by gluing suitable logical frameworks from the components.

PL

W pracy rozważa się problem modularnego definiowania złożonych, hybrydowych, dyskretnych systemów agentowych. Modularność wynika z patrzenia na system z różnych perspektyw, z których każda opisuje pewne specyficzne jego aspekty. Zdefiniowano operator, który synchronizuje systemy agentoiuo zorientowane w oparciu o wspólnych agentów oraz tranzycje. Konstrukcja operatora synchonizującego okazuje się być produktem w odpowiedniej kategorii. Pokazano także, że logikę opisu temporalnych i strukturalnych własności systemu agentowego, będącego produktem perspektyw, można otrzymać przez odpowiednie złożenie systemów logicznych dla perspektyw.

6

On Preserving Structural and Behavioural Properties by Composing Net Systems on Interfaces

Bernardinello L., Monticelli E., Pomello L.

Fundamenta Informaticae

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2007

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Vol. 80, nr 1-3

31-47

EN

We study several properties of an operation which combines two net systems by identifying local states and synchronizing events according to morphisms towards an interface. We propose this operation as a tool for modular system design, where different components are required to comply with a shared interface, or protocol of communication. We prove results on the preservation of structural properties, expressed as invariants, and of behavioural properties, in particular of deadlock-freeness.