Complexity Classes as Mathematical Axioms II

Complexity Classes as Mathematical Axioms

Complexity theory, being the metrical version of decision theory, has long been suspected of harboring undecidable statements among its most prominent conjectures. Taking this possibility seriously, we add one such conjecture, P 6= NP , as a new “axiom” and find that it has an implication in 3-dimensional topology. This is reminiscent of Harvey Friedman’s work on finitistic interpretations of l...

Axiomatizing physical experiments as oracles to algorithms.

We developed earlier a theory of combining algorithms with physical systems, on the basis of using physical experiments as oracles to algorithms. Although our concepts and methods are general, each physical oracle requires its own analysis, on the basis of some fragment of physical theory that specifies the equipment and its behaviour. For specific examples of physical systems (mechanical, opti...

Some separation axioms via modified θ-open sets

On bD-Sets and Associated Separation Axioms

Fragments of Bounded Arithmetic and Bounded Query Classes Jan

We characterize functions and predicates Z^+, -definable in S!¡ ■ In particular, predicates I^+1-definable in S^ are precisely those in bounded query Y? YP class .Pi[0(logn)] (which equals to Log Space • by [B-H,W]). This implies yP that Sj ^ T-\ unless P •[0(lo$n)] = Apj+X . Further we construct oracle A such that for all i > 1 : P^iA)lO(logn)] ¿ tf¡+x(A). It follows that S fa) ¿ Tfa) for all ...