Limit, logic, and computation

Michael H. Freedman

Research output: Contribution to journalArticlepeer-review


We introduce 'ultrafilter limits' into the classical Turing model of computation and develop a paradigm for interpreting the problem of distinguishing the class P from NP as a logical problem of decidability. We use P(NP) to denote decision problems which can be solved on a (non- deterministic) Turing machine in polynomial time. The concept is that in an appropriate limit it may be possible to prove that problems in P are still decidable, so a problem whose limit is undecidable would be established as lying outside of P.

Original languageEnglish
Pages (from-to)95-97
Number of pages3
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number1
StatePublished - 6 Jan 1998
Externally publishedYes

ASJC Scopus subject areas

  • General


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