eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2010-03-09
417
428
10.4230/LIPIcs.STACS.2010.2473
article
Evolving Multialgebras Unify All Usual Sequential Computation Models
Grigorieff, Serge
Valarcher, Pierre
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol005-stacs2010/LIPIcs.STACS.2010.2473/LIPIcs.STACS.2010.2473.pdf
Abstract state machines
Models of machines
Computability
Universality
Logic in computer science
Theory of algorithms