Every polynomial-time 1-degree collapses if and only if P = pspace

Journal of Symbolic Logic 69 (3):713-741 (2004)
A set A is m-reducible (or Karp-reducible) to B if and only if there is a polynomial-time computable function f such that, for all x, x ∊ A if and only if f(x) ∊ B. Two sets are: • 1-equivalent if and only if each is m-reducible to the other by one-one reductions; • p-invertible equivalent if and only if each is m-reducible to the other by one-one, polynomial-time invertible reductions; and • p-isomorphic if and only if there is an m-reduction from one set to the other that is one-one, onto, and polynomial-time invertible. In this paper we show the following characterization. THEOREM. The following are equivalent: (a) P = PSPACE. (b) Every two 1-equivalent sets are p-isomorphic. (c) Every two p-invertible equivalent sets are p-isomorphic
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1096901763
 Save to my reading list
Follow the author(s)
Edit this record
My bibliography
Export citation
Find it on Scholar
Mark as duplicate
Request removal from index
Revision history
Download options
Our Archive

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 31,838
Through your library
References found in this work BETA
Creative Sets.John Myhill - 1955 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 1 (2):97-108.
Creative Sets.John Myhill - 1955 - Mathematical Logic Quarterly 1 (2):97-108.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles
Added to PP index

Total downloads
16 ( #340,678 of 2,231,715 )

Recent downloads (6 months)
1 ( #446,071 of 2,231,715 )

How can I increase my downloads?

Monthly downloads
My notes
Sign in to use this feature