THE EXPRESSIVE POWER OF ABSTRACT-STATE MACHINES
Abstract:
Abstract. Conventional computation models assume symbolic representations of states and actions. Gurevich's "Abstract-State Machine " model takes a more liberal position: Any mathematical structure may serve as a state. This results in "a computational model that is more powerful and more universal than standard computation models " [5]. We characterize the Abstract-State Machine model as a special class of transition systems that widely extends the class of "computable " transition systems. This characterization is based on a fundamental Theorem of Y. Gurevich. 1 DETERMINISTIC TRANSITION SYSTEMS In the rst volume of his seminal opus [8], Don Knuth introduces the notation of algorithms. As a framework for the semantics of algorithms, Knuth suggests computational methods: A computational method is what nowadays would be called an initialized, deterministic transition system, i.e. a triple C = (Q; I; F) where Q is a set (its elements are denoted as states), I Q (the initial states), and F: Q! Q (the next-state function). Furthermore, Knuth assumes a set of
Citations
| 343 | Evolving algebras 1993: Lipari guide – Gurevich - 1995 |
| 167 | The Art of Computer Programming, Vol. 1: Fundamental Algorithms – KNUTH - 1968 |
| 11 | Sequential Abstract-State Machines Capture Sequential Algorithms – Gurevich - 2000 |
| 9 | A new Thesis – Gurevich - 1985 |
| 5 | On Gurevich’s Theorem on Sequential Algorithms – Reisig - 2003 |
| 1 | E.: The Origin of the ASM method for High Level System Design and Analysis – orger - 2002 |
| 1 | St ark, R.: Abstract State Machines { A Method for High-Level System Design and Analysis – orger, E - 2003 |
