On the power of single-valued nondeterministic polynomial time computations
The aim of this paper is to characterize the power of single-valued nondeterministic polynomial-time computations. As it is shown, the sets P, NP and NP∩co-NP are the domains or ranges respectively of certain types of functions computable in this way. With the help of polynomial time-bounded oracle Turing machines different computability concepts are introduced which turn out to be stronger and/or weaker than deterministic and single-valued nondeterministic polynomial-time computability. Whether they are properly stronger or weaker depends on the solution of NP=?co-NP, P=?NP∩co-NP and P=?NP, respectively.
KeywordsPolynomial Time Partial Function Converse Implication Computation Path State Query
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