Three paths to effectiveness

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Abstract

Over the past two decades, Gurevich and his colleagues have developed axiomatic foundations for the notion of algorithm, be it classical, interactive, or parallel, and formalized them in a new framework of abstract state machines. Recently, this approach was extended to suggest axiomatic foundations for the notion of effective computation over arbitrary countable domains. This was accomplished in three different ways, leading to three, seemingly disparate, notions of effectiveness. We show that, though having taken different routes, they all actually lead to precisely the same concept. With this concept of effectiveness, we establish that there is - up to isomorphism - exactly one maximal effective model across all countable domains.

Original languageEnglish
Title of host publicationFields of Logic and Computation - Essays Dedicated to Yuri Gurevich on the Occasion of His 70th Birthday
Pages135-146
Number of pages12
DOIs
StatePublished - 2010
Event35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010, and 19th EACSL Annual Conference on Computer Science Logic, CSL 2010 - Brno, Czech Republic
Duration: 22 Aug 201022 Aug 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6300 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference35th International Symposium on Mathematical Foundations of Computer Science, MFCS 2010, and 19th EACSL Annual Conference on Computer Science Logic, CSL 2010
Country/TerritoryCzech Republic
CityBrno
Period22/08/1022/08/10

Keywords

  • ASM
  • Turing machines
  • computability
  • constructiveness
  • effectiveness
  • recursive functions

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