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URN: urn:nbn:de:0030-drops-24737
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Evolving Multialgebras Unify All Usual Sequential Computation Models

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Abstract

It is well-known that Abstract State Machines (ASMs) can simulate ``step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some type do not constitute a natural class among all ASMs. We modify Gurevich's notion of ASM to that of EMA (``Evolving MultiAlgebra") by replacing the program (which is a syntactic object) by a semantic object: a functional which has to be very simply definable over the static part of the ASM. We prove that very natural classes of EMAs correspond via ``literal identifications'' to slight extensions of the usual machine models and also to grammar models. Though we modify these models,we keep their computation approach: only some contingencies are modified. Thus, EMAs appear as the mathematical model unifying all kinds of sequential computation paradigms.

BibTeX - Entry

@InProceedings{grigorieff_et_al:LIPIcs:2010:2473,
  author =	{Serge Grigorieff and Pierre Valarcher},
  title =	{{Evolving Multialgebras Unify All Usual Sequential Computation Models}},
  booktitle =	{27th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{417--428},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-16-3},
  ISSN =	{1868-8969},
  year =	{2010},
  volume =	{5},
  editor =	{Jean-Yves Marion and Thomas Schwentick},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2010/2473},
  URN =		{urn:nbn:de:0030-drops-24737},
  doi =		{http://dx.doi.org/10.4230/LIPIcs.STACS.2010.2473},
  annote =	{Keywords: Abstract state machines, Models of machines, Computability, Universality, Logic in computer science, Theory of algorithms}
}

Keywords: Abstract state machines, Models of machines, Computability, Universality, Logic in computer science, Theory of algorithms
Seminar: 27th International Symposium on Theoretical Aspects of Computer Science
Issue date: 2010
Date of publication: 2010


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