Choiceless polynomial time

Andreas Blass*, Yuri Gurevich, Saharon Shelah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

79 Scopus citations

Abstract

Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured a negative answer. The problem motivated a quest for stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic expresses all properties expressible in any other PTime logic in the literature. A more difficult theorem shows that the logic does not capture all of PTime.

Original languageEnglish
Pages (from-to)141-187
Number of pages47
JournalAnnals of Pure and Applied Logic
Volume100
Issue number1-3
DOIs
StatePublished - 15 Oct 1999

Keywords

  • Abstract state machine
  • Choice
  • Parallelism
  • Polynomial time
  • Unordered structures

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