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The complexity of problems involving structurally bounded and conservative Petri nets
We examine the reachability, containment, and equivalence problems for structurally bounded and conservative Petri nets. Using techniques from the theory of linear optimization, we derive an upper bound on the size of any reachable marking for a structurally bounded Petri net. By employing Savitch's Theorem, we use this bound to show all three problems for both structurally bounded and conservative Petri nets to be in PSPACE. These three problems are already known to be PSPACE-complete for 1-conservative Petri nets; therefore, since 1-conservative Petri nets are both conservative and structurally bounded, it follows that all three problems for consecutive and structurally bounded Petri nets are PSPACE-complete
Rede de planos: uma proposta para a solução de problemas de planejamento em inteligência artificial usando redes de Petri
This thesis dissertation reports on the investigation of the relationships between the problems of planning, in the sense of Artificial Intelligence, and that of reachability, in the sense of Petri nets. The research approaches different ways to represent a planning problem as a Petri net, as well as the comparison of the given net with the plan graph. The main advantages and disadvantages in applying Petri nets compared to the plan graph method. We claim that, the use of Petri nets allows more precise and compact representation of action relationships than those obtained with the counter part method. One of the main research aims is to eliminate representational redundancies of the plan graph by projecting them against the dynamic aspects of the net. Examples of the comparative improvements are shown in the text, particularly for the relationships of inconsistency and the mutual exclusion of actions.Este documento apresenta uma investigação sobre os relacionamentos entre os problemas de planejamento em inteligência artificial e de alcançabilidade em redes de Petri. O trabalho trata da análise de algumas maneiras de se representar um problema de planejamento como uma rede de Petri e da comparação da rede obtida com o grafo de planos. São destacadas as principais vantagens e desvantagens do uso das redes de Petri em comparação com o grafo de planos. Procura-se argumentar em favor da primeira, pois ela permite representar de maneira ao mesmo tempo precisa e econômica os mesmos relacionamentos contidos na segunda estrutura. Um dos focos da pesquisa é encontrar a melhor maneira de substituir as redundâncias presentes no grafo de planos pela dinâmica da rede de Petri. Em particular, na rede, consegue-se uma melhor representação para as relações de inconsistência e de exclusão mútua entre ações