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1
Content available remote Towards a solution to a plan-formation problem
EN
The paper deals with the problem of achieving a goal in a system in which certain actions can be executed. The initial state and the states that may be reached from this state by executing actions are represented by sets of sente nces, each sentence saying that some objects are or are not in a relation. Available actions are represented as instances of rewriting rules. The problem consists in finding a sequence of actions that leads from the initia l state to a state in which the goal is achieved. The presented solution to this problem for a class of systems is based on reducing it to the problem of reachability in contextual Petri nets.
PL
Praca dotyczy problemu osiągania celu w systemie, w którym można wykonywać pewne akcje. Stan początkowy i stany, które moga być z tego stanu osiągnięte przez wykohnywanire akcji, są reprezentowane przez zbiory zadań, z których każde orzeka, że pewne obiekty są lub nie są w pewnych relacjach. Możliwe akcje sa reprezentowane jako instancje pewnych reguł przekształcania. Problem polega na znalezieniu ciągu akcji prowadzącego ze stanu początkowego do stanu, w którym cel jest osiągnięty. Proponowane rozwiązanie tego problemu dla pewnej klasy systemów polega na jego redukowaniu do problemu osiągalności w kontekstowych sieciach Petriego.
2
Content available remote Reachability in Contextual Nets
EN
Contextual nets, or Petri nets with read arcs, are models of concurrent systems with context dependent actions. The problem of reachability in such nets consists in finding a sequence of transitions that leads from the initial marking of a given contextual net to a given goal marking. The solution to this problem that is presented in this paper consists in constructing a finite complete prefix of the unfolding of the given contextual net, that is a finite prefix in which all the markings that are reachable from the initial marking are present, and in searching in each branch of this prefix for the goal marking by solving an appropriate linear programming problem.
3
Content available remote Reachability in contextual nets
PL
Sieci kontekstowe, albo inaczej sieci Petriego z krawędziami odczytu, są modelami systemów współbieżnych z akcjami zależnymi od kontekstu. Problem osiągalności w takich sieciach polega na znalezieniu ciągu akcji prowadzącego od oznakowania początkowego danej sieci kontekstowej do zadanego oznakowania docelowego. Zaprezentowane w pracy rozwiązanie tego problemu polega na konstruowaniu skończonego zupełnego prefiksu rozwinięcia danej sieci kontekstowej, tzn. skończonego prefiksu, w którym są obecne wszystkie oznakowania osiągalne z oznakowania początkowego, oraz na poszukiwaniu w każdej gałęzi tego prefiksu oznakowania docelowego przez rozwiązywanie odpowiedniego problemu programowania liniowego.
EN
Contextual nets, or Petri nets with read arcs, are models of concurrent systems with context dependent actions. The problem of reachability in such nets consist in finding a sequence of transitions that leads from the initial marking of a given contextual net to a given goal marking. The solution to this problem that is presented in this paper consists in constructing a finite complete prefix of the unfolding of the given contextual net, that is a finite prefix in which all the markings that are reachable from the initial marking are present, and in searching in each branch of this prefix for the goal marking by solving an appropriate linear programming problem.
EN
The paper is centered around the study and comparison of truly concurrent semantics for P/T nets with inhibitor and read arcs (called henceforth contextual P/T nets). We start proposing a causal semantics for P/T nets, that we prove to be equivalent to history preserving bisimulation defined on nonsequential processes. Then we develop a conservative extension of the causal semantics to contextual P/T nets and we prove this one to be finer than step semantics. Finally, a comparison of causal semantics with the process based semantics for contextual P/T systems proposed in [7] is carried out.
5
Content available remote Process semantics for Place/Transition nets with inhibitor and read arcs
EN
In this paper we introduce a truly concurrent semantics for P/T nets with inhibitor and read arcs, called henceforth Contextual P/T nets. The semantics is based on a proper extension of the notion of process to cope with read and inhibitor arcs: we show that most of the properties enjoined by the classical process semantics for P/T nets continue to hold and we substantiate the adequateness of our notion by comparing it with the step semantics.
6
Content available remote Process of contextual nets and their characteristics
PL
Rozważane są uogólnione sieci Petriego zwane sieciami kontekstowymi i procesy takich sieci. Procesy sieci kontekstowych są definiowane jako porządki częściowe z pewna dodatkową strukturą. Definiuje się operacje składania procesów tak, że każdy proces sieci kontekstowej można otrzymać składając procesy odpowiadające miejscom i tranzycjom tej sieci. Definiuje się podobne do macierzy i zwane tablicami charakterystyki procesów i operacje składania tych charakterystyk tak, że odpowiedniość między procesami i charakterystykami jest homomorfizmem.
EN
Generalized Place/Transition Petri nets, called contextual nets, and processes of such nets are considered. Processes of contextual nets are represented as partial orders with some extra structure. Operations of composing processes are defined such that each process of a contextual net can be obtained by combining processes corresponding to places and transitions of this net. Matrix-like characteristics of processes, called tables, and natural operations on such characteristics are defined such that the correspondence between processes and their characteristics is a homomorphism.
7
Content available remote Processes of contextual nets and their characteristics
EN
Generalized Place/Transition Petri nets, called contextual nets, and processes of such nets are considered. Processes of contextual nets are represented as partial orders with some extra structure. Operations of composing processes are defined such that each process of a contextual net can be obtained by combining processes corresponding to places and transitions of this net. Matrix-like characteristics of processes, called tables, and natural operations on such characteristics are defined such that the correspondence between processes and their characteristics is a homomorphism.
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