Abstract
The principal result of this paper is a “positive relativization” of the open question “ P = ? NP ⌢ co-NP.” That is, the nondeterministic polynomial time-bounded oracle Turing machine endowed with designated accepting states and with designated rejecting states is considered, and suitable restrictions R of this device are developed such that P = NP ⌢ co-NP if and only if for every oracle D, P( D) = NP R ( D), where NP R ( D) is the class of languages LϵNP( D) that are accepted by oracle machines operating with restrictions R. Positive relativizations are obtained for the P = ? U ⌢ co - U and U = ? NP questions also, where U is the class of languages L in NP accepted by nondeterministic machines that operate in polynomial time and that have for each input at most one accepting computation. The restrictions developed here are “qualitative” in the sense that they restrict the form and pattern of access to the oracle. In contrast, a previous paper [3] developed quantitative relativizations-the number of distinct queries to the oracle is restricted-but no quantitative positive relativization of P = ? NP ⌢ co-NP is known.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
