5-Abstract State Machines for the Classroom

5-Abstract State Machines for the Classroom - Abstract...

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Abstract State Machines for the Classroom – The Basics – Wolfgang Reisig Institut f¨ur Informatik, Math.-Nat. Fakult¨at II, Humboldt-Universit¨at zu Berlin, Unter den Linden 6, DE 10099 Berlin, Germany, [email protected] . . . we should have achieved a mathematical model of computation, perhaps highly abstract in contrast with the concrete nature of paper and register machines, but such that programming languages are merely executable fragments of the theory . . . Robin Milner [16] Summary. Abstract State Machines (hencefort referred to as just ASM) were in- troduced as “a computation model that is more powerful and more universal than standard computation models” by Yuri Gurevich in 1985. Here we provide some intuitive and motivating arguments, and characteristic examples for (the elementary version of) ASM. The intuition of ASM as a formal framework for “pseudocode” algorithms is highlighted. Generalizing variants of the fundamental “sequential small-step” version of ASM are also considered. Introduction Many people Fnd ASM difficult to understand. Most of these people are con- ventionally educated computer scientists, and hence have ba set of implicit or explicit assumptions and expectations about “yet another” speciFcation language or computation model. ASM challenge some of those assumptions and expectations. It is this aspect that makes people struggle when trying to understand ASM. If computer science education start out with ASM (and there are many good reasons to do so), people would see the basic ideas of ASM as the most simple and natural approach to the notion of “algorithm”. This chapter addresses the conventionally educated computer scientist. To meet his or her implicit and explicit assumptions, Part I of this presentation addresses the intuition and foundations of ASM in great detail and various aspects. Part II then focuses technical details of the most elementary class of ASM. Part III considers various variants and extensions.
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16 Wolfgang Reisig I: Intuition and Foundations of ASM Section 1 addresses the fundamental aspects that make ASM a technique quite diFerent from other techniques, to describe algorithms or, more generally, discrete systems. Without going into detail, the central idea is highlighted, and the ASM approach is embedded into the context of ±rst-order logic and computable functions. Section 2 is devoted to some small examples. As the central idea of ASM is, to some extent, independent of concrete syntactical representations, we represent each example in a pseudocode notation, in a form that is particularly intuitive for the respective algorithm. The translation of pseudocode to a “syntactically correct” ASM is postponed to Sect. 5. This translation can itself be conceived as part of the ASM formalism, because ASM can be considered as a formal basis for pseudocode. As we restrict ourselves in this chapter to a version of ASM that can be described by transition systems , we start the section with this fundamental notion.
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5-Abstract State Machines for the Classroom - Abstract...

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