Abstract state machines

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In computer science, an abstract state machine (ASM) is a state machine operating on states that are arbitrary data structures (structure in the sense of mathematical logic, that is a nonempty set together with a number of functions (operations) and relations over the set).

The ASM Method is a practical and scientifically well-founded systems engineering method that bridges the gap between the two ends of system development:

  • the human understanding and formulation of real-world problems (requirements capture by accurate high-level modeling at the level of abstraction determined by the given application domain)
  • the deployment of their algorithmic solutions by code-executing machines on changing platforms (definition of design decisions, system and implementation details).

The method builds upon three basic concepts:

  • ASM: a precise form of pseudo-code, generalizing Finite State Machines to operate over arbitrary data structures
  • ground model: a rigorous form of blueprints, serving as authoritative reference model for the design
  • refinement: a most general scheme for stepwise instantiations of model abstractions to concrete system elements, providing controllable links between the more and more detailed descriptions at the successive stages of system development.

In the original conception of ASMs, a single agent executes a program in a sequence of steps, possibly interacting with its environment. This notion was extended to capture distributed computations, in which multiple agents execute their programs concurrently.

Since ASMs model algorithms at arbitrary levels of abstraction, they can provide high-level, low-level and mid-level views of a hardware or software design. ASM specifications often consist of a series of ASM models, starting with an abstract ground model and proceeding to greater levels of detail in successive refinements or coarsenings.

Due to the algorithmic and mathematical nature of these three concepts, ASM models and their properties of interest can be analyzed using any rigorous form of verification (by reasoning) or validation (by experimentation, testing model executions).


The concept of ASMs is due to Yuri Gurevich, who first proposed it in the mid-1980s as a way of improving on Turing's thesis that every algorithm is simulated by an appropriate Turing machine. He formulated the ASM Thesis: every algorithm, no matter how abstract, is step-for-step emulated by an appropriate ASM. In 2000, Gurevich axiomatized the notion of sequential algorithms, and proved the ASM thesis for them. Roughly stated, the axioms are as follows: states are structures, the state transition involves only a bounded part of the state, and everything is invariant under isomorphisms of structures. (Structures can be viewed as algebras, which explains the original name evolving algebras for ASMs.) The axiomatization and characterization of sequential algorithms have been extended to parallel and interactive algorithms.

In the 1990s, by a community effort, the ASM method was developed, using ASMs for the formal specification and analysis (verification and validation) of computer hardware and software. Comprehensive ASM specifications of programming languages (including Prolog, C, and Java) and design languages (UML and SDL) have been developed. A detailed historical account can be found in the AsmBook (Chapter 9) or in this article.

A number of software tools for ASM execution and analysis are available.



Behavioral models for industrial standards[edit]


(in historical order since 2000)


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