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The Abstract State Machines Method for High-Level System Design and Analysis

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Formal Methods: State of the Art and New Directions

Abstract

We explain the main ingredients of the Abstract State Machines (ASM) method for high-level system design and analysis and survey some of its application highlights in industrial software-based system engineering. We illustrate the method by defining models for three simple control systems (sluice gate, traffic light, package router) and by characterising Event-B machines as a specific class of ASMs.We point to directions for future research and applications of the method in other areas than software engineering.

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Notes

  1. 1.

    However, this paper is neither an introduction to the ASM method nor a survey of its achievements. For the former see [29], for the latter [27], or Chaps. 2 and 9 of the AsmBook [46].

  2. 2.

    For example in Cremers’ and Hibbard’s data spaces [53], the operational transformations of abstract states are described by means of static functions, which form what is called there an information structure.

  3. 3.

    The definition of the ground model may change during the design phase, namely if it is recognised during the implementation process that some important feature is missing in the ground model or has to be changed there. The process of building a ground model is iterative; it ends only with the completion of the design and may be re-opened during maintenance for change management. But at each moment of the development process, there is one ground model, documenting the current understanding of the problem the system has to solve.

  4. 4.

    Note that the evaluation of the design against the ground model also provides an objective, rational ground for settling disputes on the code after its completion.

  5. 5.

    Thus the ASM method satisfies Parnas’ request [95] to base the foundation for a reliable software engineering discipline on standard mathematics, avoiding the introduction of complicated specification languages and theories of language semantics.

  6. 6.

    In general, in an ASM all updates are executed in parallel, though in this example also a sequential reading will do.

  7. 7.

    The definition of the seq constructor in the context of the parallel ASM execution model is defined in [45].

  8. 8.

    For reasons of space we leave out the operator commands to stop or start the conveyor. Adding them would involve adding an operator machine.

  9. 9.

    This is well-defined since by assumption, switch can be flipped only when there is no package in it, i.e., succ(switch) and thereby the exit point of switch can change only when queue(switch) is empty.

  10. 10.

    The original definition of ASMs in [79] was motivated by a different goal: an epistemological desire to generalise Turing’s thesis.

  11. 11.

    We consider here deterministic FSMs, since non-deterministic FSMs can be modelled using the ASM choose construct described below. For the sake of simplicity of exposition, we suppose each input to be consumed by executing a transition, technically speaking in to be a monitored function as explained below.

  12. 12.

    This view of Tarski structures supports a generalisation of Parnas’ table technique [96, 95] as a convenient notation for ASMs, as detailed in [22, 23].

  13. 13.

    More precisely: to execute one step of an ASM in a given state S determine all the fireable rules in S (s.t. Condition is true in S), compute all expressions t i , t in S occuring in the updates f(t 1, …, t n ) : = t of those rules and then perform simultaneously all these location updates. This yields the successor state S′ of S.

  14. 14.

    See the use of modes in [95] as a means to structure the set of states.

  15. 15.

    This avoids the alleged, though unjustified and in fact destructive, dichotomy between declarative and operational design elements, which unfortunately has been strongly advocated in the literature over the last 30 years. See the discussion at the end of Sect. 3.6.2.

  16. 16.

    The naming is influenced by its pendant in Parnas’ Four-Variable-Model [95].

  17. 17.

    The minimality avoids to define ground models that restrict the problem solution unnecessarily. Thus, it helps to leave the design space open as much as possible.

  18. 18.

    Experience in the following domains has confirmed that the ASM language is understandable for domain experts without computer science education: railway, control and telephony systems [32, 42, 50], business and aviation security processes [35, 7, 13, 77, 78], linguistics [85, 92, 93, 55], biology [89], social sciences [48, 47].

  19. 19.

    As already observed in Sect. 3.1 for ground models, this distinction does not pertain to the process of model building. The classification of what belongs to the “essence” of the system and what only to its implementation may change during the design process, typically when “implementation decisions are made before specification is complete and the decisions can have a major effect on the further specification of the system” [108, p. 440]. The final definition, yielding a document with the hierarchy of stepwise refined models, can be given only at the end of the design process. This document too is typically re-opened during maintenance for change management, where it has to be synchronised with the decisions taken for the system change.

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  1. Dipartimento di Informatica, Universita di Pisa, Pisa, Italy

    Egon Börger

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    Paul Boca

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    Jonathan P. Bowen

  3. Informatics Research Group, Sheffield Hallam University, City Campus, Sheffield, S1 1WB, United Kingdom

    Jawed Siddiqi

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Börger, E. (2010). The Abstract State Machines Method for High-Level System Design and Analysis. In: Boca, P., Bowen, J., Siddiqi, J. (eds) Formal Methods: State of the Art and New Directions. Springer, London. https://doi.org/10.1007/978-1-84882-736-3_3

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