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Abstract machine

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An abstract machine, also called an abstract computer, is a theoretical model of a computer hardware or software system used in automata theory. Abstraction of computing processes is used in both the computer science and computer engineering disciplines and usually assumes discrete time paradigm.

In the theory of computation, abstract machines are often used in thought experiments regarding computability or to analyze the complexity of algorithms (see computational complexity theory). A typical abstract machine consists of a definition in terms of input, output, and the set of allowable operations used to turn the former into the latter. The best-known example is the Turing machine.

More complex definitions create abstract machines with full instruction sets, registers and models of memory. One popular model more similar to real modern machines is the RAM model, which allows random access to indexed memory locations. As the performance difference between different levels of cache memory grows, cache-sensitive models such as the external-memory model and cache-oblivious model are growing in importance.

An abstract machine can also refer to a microprocessor design which has yet to be (or is not intended to be) implemented as hardware. An abstract machine implemented as a software simulation, or for which an interpreter exists, is called a virtual machine.

Through the use of abstract machines it is possible to compute the amount of resources (time, memory, etc.) necessary to perform a particular operation without having to construct an actual system to do it.

Articles concerning Turing-equivalent sequential abstract machine models

An approach is to take a somewhat formal taxonomic approach to classify the Turing equivalent abstract machines. This taxonomy does not include finite automata:

Family: Turing-equivalent (TE) abstract machine:

Subfamilies:

Subfamily (1) Sequential TE abstract machine
Subfamily (2) Parallel TE abstract machine

Subfamily (1)-- Sequential TE abstract machine model: There are two classes (genera) of Sequential TE abstract machine models currently in use (cf van Emde Boas, for example):

Genus (1.1) Tape-based Turing machine model
Genus (1.2) Register-based register machine

Genus (1.1) -- Tape-based Turing machine model: This includes the following "species":

{ single tape, Multi-tape Turing machine, deterministic Turing machine, Non-deterministic Turing machine, Wang B-machine, Post-Turing machine, Oracle machine, Universal Turing machine }

Genus (1.2)-- The register machine model: This includes (at least) the following four "species" (others are mentioned by van Emde Boas):

{ (1.2.1) Counter machine, (1.2.2) Random access machine RAM, (1.2.3) Random access stored program machine RASP, (1.2.4) Pointer machine }
Species (1.2.1) -- Counter machine model:
{ abacus machine, Lambek machine, Melzak model, Minsky machine, Shepherdson-Sturgis machine, program machine, etc. }
Species (1.2.2) -- Random access machine (RAM) model:
{ any counter-machine model with additional indirect addressing, but with instructions in the state machine in the Harvard architecture; any model with an "accumulator" with additional indirect addressing but instructions in the state machine in the Harvard architecture }
Species (1.2.3) -- Random access stored program machine (RASP) model includes
{ any RAM with program stored in the registers similar to the Universal Turing machine i.e. in the von Neumann architecture }
Species (1.2.4)-- Pointer machine model includes the following:
= { Schönhage Storage Modification Machine SMM, Kolmogorov-Uspensky KU-machine, Knuth linking automaton }


Other abstract machines

See also

References

  • Macura, Wiktor K. "Abstract Machine". MathWorld.
  • Peter van Emde Boas, Machine Models and Simulations pp. 3–66, appearing in:
Jan van Leeuwen, ed. "Handbook of Theoretical Computer Science. Volume A: Algorithms and Complexity, The MIT PRESS/Elsevier, 1990. ISBN 0-444-88071-2 (volume A). QA 76.H279 1990.
  • Stephan Diehl, Pieter Hartel and Peter Sestoft, Abstract Machines for Programming Language Implementation, Future Generation Computer Systems, Vol. 16(7), Elsevier, 2000.

This article is based on material taken from the Free On-line Dictionary of Computing prior to 1 November 2008 and incorporated under the "relicensing" terms of the GFDL, version 1.3 or later.

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