This paper explores the application of rewriting logic to the executable formal modeling of real-time and hybrid systems. We give general techniques by which such systems can be specified as ordinary rewrite theories, and show that a wide range of real-time and hybrid system models, including object-oriented systems, timed automata [4], hybrid automata [2], timed and phase transition systems [28], and timed extensions of Petri nets [1,37], can indeed be expressed in rewriting logic quite naturally and directly. Since rewriting logic is executable and is supported by several language implementations, our approach complements property-oriented methods and tools less well suited for execution purposes. The relationships with the timed rewriting logic approach of Kosiuczenko and Wirsing [24,25] are also studied. 1 Introduction This paper explores the application of rewriting logic to the executable formal modeling of real-time and hybrid systems. The general conceptual advantage of using...

We propose rewriting logic as a unifying framework for a wide range of Petri nets models. We treat in detail place/transition nets and important extensions of the basic model by individual tokens, test arcs, and time. Based on the idea that "Petri nets are monoids" suggested by Meseguer and Montanari we define a rewriting semantics that maps place/transition nets into rewriting logic specifications. We furthermore generalize this result to a general form of algebraic net specifications subsuming also colored Petri nets as a special case. The soundness and completeness results we state relate the commutative process semantics of Petri nets proposed by Best and Devillers to the model-theoretic semantics of rewriting logic in the sense of natural isomorphisms between suitable functors. In addition we show how place/transition nets with test arcs and timed Petri nets can be equipped with a rewriting semantics and discuss how other extensions can be treated along similar lines.

2 Dedicated with affection to my beloved parents Cecilia and Miklós 3 4

This work investigates the suitability of rewriting logic as a semantic framework for modeling real-time and hybrid systems. We present a general method to specify and symbolically simulate such systems in rewriting logic and illustrate it with a well-known benchmark. We also show how a wide range of real-time and hybrid system models can be naturally expressed and are unified within our approach. The relationships with timed rewriting logic [9,10] are also investigated. 1 Introduction Rewriting logic is a flexible and expressive framework in which many different models of concurrent computation and many different types of systems can be naturally specified [13,16,12,14]. It seems therefore natural to investigate the question of how rewriting logic can be applied to the specification of realtime and hybrid systems. From the semantic point of view this offers the possibility of integrating real-time aspects with other features and models already supported by rewriting logic. The first ...

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