We prove that each element of a class of f,anctions (denoted by NPCtP), whose graphs can be accepted in nondeterministic polynomial time, can be evaluated in deterministic polynomial time if and only if '/-reducibility is equivalent to polynomial time many-one reducibility. We also modify the proof technique used to obtain part of this result to obtain the stronger result that if every ,/-reduc...

For f : [0, 1] → R, consider the relation Ef on [0, 1] defined by (xn)Ef (yn)⇔ P n<ω f(|yn−xn|) <∞. We study the Borel reducibility of Borel equivalence relations of the form Ef . Our results indicate that for every 1 ≤ p < q < ∞, the order ≤B of Borel reducibility on the set of equivalence relations {E : EIdp ≤B E ≤B EIdq} is more complicated than expected, e.g. consistently every linear order...

Many propositions are not known to be true or false, and many phenomena are not understood. What determines what propositions and phenomena are perceived as knowable or unknowable? We tested whether factors related to scientific methodology (a proposition’s reducibility and falsifiability), its intrinsic metaphysics (the materiality of the phenomena and its scope of applicability), and its rela...

We analyze the technique used by Adams and Kechris (2000) to obtain their results about Borel reducibility of countable Borel equivalence relations. Using this technique, we show that every Σ1 equivalence relation is Borel reducible to the Borel bi-reducibility of countable Borel equivalence relations. We also apply the technique to two other classes of essentially uncountable Borel equivalence...

The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic reduction. This concept — more precisely, the associated concept of reducibility — is a generalization of Turing reducibility from the traditional, input/output sor...

A set B is called EXPSPACE-avoiding, if every subset of B in EXPSPACE is sparse. For example, sets of high information density (called HIGH sets in 5]) are shown to be EXPSPACE-avoiding. Investigating the complexity of sets A in EXPSPACE that honestly reduce to EXPSPACE-avoiding sets, we show that if the reducibility used has a property, called range-constructibility, then A must also reduce to...

We establish necessary and sufficient conditions for a quadratic polynomial to be irre-ducible in the ring Z[[x]] of formal power series over the integers. In particular, for polynomials of the form p n + p m βx + αx 2 with n, m ≥ 1 and p prime, we show that reducibility in Z[[x]] is equivalent to reducibility in Zp[x], the ring of polynomials over the p-adic integers.

Hierarchies considered in computability theory and in complexity theory are related to some reducibilities in the sense that levels of the hierarchies are downward closed and have complete sets. In this paper we propose a reducibility having similar relationship to the Brzozowski’s dot-depth hierarchy and some its refinements. We prove some basic facts on the corresponding degree structure and ...

The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally in proofs in classical computability theory as well as in the recent work of Soare, Nabutovsky and Weinberger on applications of computability to differential geometry. We study the sw-degrees of c....

In response to a recent algorithm for counting the number of isomorphism classes of irreducible tropical curves through 3d+g-1 general points in the plane satisfying certain psi-class conditions by Hannah Markwig and Johannes Rau in [MR08], a method for determining the reducibility of a tropical cruve in terms of it’s dual Newton polytope is required. This paper provides a solution by giving an...