Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Hilbert's tenth problem
P ≠ NP over the nonstandard reals implies P ≠ NP over R
Selected papers of the workshop on Continuous algorithms and complexity
Accessible telephone directories
Journal of Symbolic Logic
Complexity and real computation
Complexity and real computation
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
The P-DNP problem for infinite Abelian groups
Journal of Complexity
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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The paper presents two situations where unit-cost complexity results are closely related with results from the classical computability. * In Section 2 we study an important theorem by Koiran and Fournier from an axiomatic point of view. It is proved that the algebraic Knapsack problem belongs to P over some ordered abelian semi-group iff P=NP classically. In this case there would exist a unit-cost machine solving the algebraic Knapsack problem over all ordered abelian semi-groups in some uniform polynomial time. * In Section 3 we apply the theorem of Matiyasevich in order to construct a ring with PNBPNP and such that its polynomial hierarchy does not collapse at any level.