A parallel algorithm for computing all
                    homomorphisms of deterministic finite
                    automata

Mikolajczak, Bolesław

doi:10.1090/dimacs/022/10

Cited by 1 publication

(2 citation statements)

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“…An algorithm that computes the set of all net morphisms between two Petri nets is unknown as of today. Its computational complexity would be excessive taking into account complexity of computing morphisms between two deterministic automata [8].…”

Section: Discussionmentioning

confidence: 99%

“…Moreover, the concept of morphisms originated from the category theory and algebras in mathematics, it can be applied to state machines [8] as well as Petri nets [9]. There exist several different concepts of Petri net morphisms which have already been introduced in literature, such as vicinity respecting morphisms [2], Winskel s morphisms [16], Lakos net morphisms and system morphisms [7], and general morphisms [1].…”

Section: Motivation and Introductionmentioning

confidence: 99%

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Conceptual Modeling of Concurrent Systems through Stepwise Abstraction and Refinement Using Petri Net Morphisms

Mikolajczak

Wang

2003

Conceptual Modeling - ER 2003

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Abstract. Development of complex concurrent systems is very often performed in a top-down or bottom-up approach depending on design circumstances. Such design reflects vertical conceptual modeling of concurrent systems with certain number of abstraction/ refinement layers. Petri net morphisms have been proven to be useful in this process as long as certain desired structural and behavioral properties of such systems are preserved. We use example of a renting agency to illustrate applicability of morphisms in systematic development of distributed systems. Preservation of structural and behavioral properties of Petri net morphisms is also discussed. Motivation and IntroductionPetri nets are formal, graphical, and executable mathematical models that are appropriate for the development of concurrent, discrete-event dynamic systems. It has been under development since the beginning of the 1960's. After forty years of research and development, Petri nets have been proven to be applicable to a variety of areas. It can be used in design and analysis of concurrent and distributed systems, workflow management systems, requirement specifications in software engineering, specifications of communication protocols, and so on.Usually there are two different approaches in Petri net system modeling. One is the top-down approach and the other is the bottom-up approach. In top-down approach, one can start modeling a system from the highest conceptual level of abstraction, then refine the system using techniques such as rule-based refinement [11], general refinement [4], and hierarchical modeling [5] until reaching a satisfying level of detail of the system. In bottom-up approach, one starts the modeling of a system at the lowest level of abstraction, then abstracts the system model step by step until reaching the highest level of abstraction.In practice, the top-down approach is relatively easy to achieve. Yet modeling a system using the bottom-up approach is very difficult, because there are very few techniques about 'how to shrink' a system model to a higher level of abstraction without losing the structural and behavioral properties of the system. However, this approach is practically very important in system modeling.

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Section: Discussionmentioning

confidence: 99%