Partially ordered sets are a natural framework in which the semantics of concurrent processes can be defined and studied. From a partial order, two interesting binary relations can be immediately defined: one can be interpreted as a causal dependence, the other as causal independence. Both are symmetric, but in general non transitive. By applying standard techniques in lattice theory, one can then derive from each of them a closure operator on the underlying set of the partial order, and a corresponding complete lattice, whose elements are the closed subsets of the partially ordered set. In a recent paper, we applied this idea to the independence (or concurrency) relation; in this paper we deal with the dependence relation; some structural properties of the corresponding closed sets are given, and a subclass of closed sets, called spatially closed sets, is identified. The main result states that this subclass forms an algebraic lattice.

Bernardinello, L., Ferigato, C., POMELLO CHINAGLIA POMELLO, L., Rombola', S. (2009). Closure operators associated to partially ordered sets. In Workshop on Non-Classical Models for Automata and Applications (pp.47-60). Wien : Austrian Computer Society.

### Closure operators associated to partially ordered sets

#### Abstract

Partially ordered sets are a natural framework in which the semantics of concurrent processes can be defined and studied. From a partial order, two interesting binary relations can be immediately defined: one can be interpreted as a causal dependence, the other as causal independence. Both are symmetric, but in general non transitive. By applying standard techniques in lattice theory, one can then derive from each of them a closure operator on the underlying set of the partial order, and a corresponding complete lattice, whose elements are the closed subsets of the partially ordered set. In a recent paper, we applied this idea to the independence (or concurrency) relation; in this paper we deal with the dependence relation; some structural properties of the corresponding closed sets are given, and a subclass of closed sets, called spatially closed sets, is identified. The main result states that this subclass forms an algebraic lattice.
##### Scheda breve Scheda completa Scheda completa (DC)
paper
closure operators; partially ordered sets; dependence relation
English
Workshop on Non-Classical Models for Automata and Applications
2009
Bordihn, H; Freund, R; Holzer, M; Kutrib, M; Otto, F
Workshop on Non-Classical Models for Automata and Applications
978-3-85403-256-4
2009
47
60
none
Bernardinello, L., Ferigato, C., POMELLO CHINAGLIA POMELLO, L., Rombola', S. (2009). Closure operators associated to partially ordered sets. In Workshop on Non-Classical Models for Automata and Applications (pp.47-60). Wien : Austrian Computer Society.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/22760`
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