A note on a P ≠ NP result for a restricted class of real machines
Journal of Complexity
Separation of complexity classes in Koiran's weak model
Selected papers of the workshop on Continuous algorithms and complexity
Relativizations of the P=?NP question over the reals (and other ordered rings)
Selected papers of the workshop on Continuous algorithms and complexity
Computing over the reals with addition and order
Selected papers of the workshop on Continuous algorithms and complexity
On NP-completeness for linear machines
Journal of Complexity
Complexity and real computation
Complexity and real computation
Computable functions and semicomputable sets on many-sorted algebras
Handbook of logic in computer science
The P-DNP problem for infinite Abelian groups
Journal of Complexity
P = NP for some structures over the binary words
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
Implicit complexity over an arbitrary structure: quantifier alternations
Information and Computation
An explicit solution to post's problem over the reals
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We consider the uniform model of computation over arbitrary structures with two constants. For several structures, including structures over the reals, we construct oracles which imply that the relativized versions of P and NP are equal or are not equal. Moreover we discuss some special features of these oracles resulting from the undecidability of halting problems in order to explain the difficulties to define structures of finite signature which satisfy P = NP. We show that there are oracles which lose their non-deterministic self-reducibility which is sufficient for a recursive definition if their elements are compressed to tuples of fixed length.