相关论文: On the questions P ?= NP $\cap$ co-NP and NP ?= co…

In the early 1980s, Selman's seminal work on positive Turing reductions showed that positive Turing reduction to NP yields no greater computational power than NP itself. Thus, positive Turing and Turing reducibility to NP differ sharply…

One way of suggesting that an NP problem may not be NP-complete is to show that it is in the class UP. We suggest an analogous new approach---weaker in strength of evidence but more broadly applicable---to suggesting that concrete~NP…

Adleman, DeMarrais, and Huang introduced the nondeterministic quantum polynomial-time complexity class NQP as an analogue of NP. Fortnow and Rogers implicitly showed that, when the amplitudes are rational numbers, NQP is contained in the…

We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…

The paper contains a proof for the P != NP hypothesis with the help of the two "natural" postulates. The postulates restrict capacity of the Turing machines and state that each independent and necessary condition of the problem should be…

Complexity classes such as $\#\mathbf{P}$, $\oplus\mathbf{P}$, $\mathbf{GapP}$, $\mathbf{OptP}$, $\mathbf{NPMV}$, or the class of fuzzy languages realised by polynomial-time fuzzy nondeterministic Turing machines, can all be described in…

Let ${\mathbf P}$ be the class of polynomial-time decision problems and $\mathbf{NP}$ be the class of nondeterministic polynomial time decision problems. We prove the following: Theorem 3. The classes ${\mathbf P}$ and $\mathbf{NP}$ are…

This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…

An artificially designed Turing Machine algorithm $\mathbf{M}_{}^{o}$ generates the instances of the satisfiability problem, and check their satisfiability. Under the assumption $\mathcal{P}=\mathcal{NP}$, we show that $\mathbf{M}_{}^{o}$…

A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…

This article presents counter examples for three articles claiming that P=NP. Articles for which it applies are: Moustapha Diaby "P = NP: Linear programming formulation of the traveling salesman problem" and "Equality of complexity classes…

Using nonstandard analysis, we will extend the classical Turing machines into the internal Turing machines. The internal Turing machines have the capability to work with infinite ($*$-finite) number of bits while keeping the finite…

Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…

For a fixed marked surface $S$, we construct polynomial bounds on the periodic and preperiodic lengths of the maximal splitting sequences of a projectively invariant measured train track. We give two consequences of these bounds. Firstly,…

The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…

We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…

In this paper, we study the relationship of parametrised enumeration complexity classes defined by Creignou et al. (MFCS 2013). Specifically, we introduce two hierarchies (IncFPTa and CapIncFPTa) of enumeration complexity classes for…

Nonuniformity is a central concept in computational complexity with powerful connections to circuit complexity and randomness. Nonuniform reductions have been used to study the isomorphism conjecture for NP and completeness for larger…

The present paper presents and proves a proposition concerning the time complexity of finite languages. It is shown herein, that for any finite language (a language for which the set of words composing it is finite) there is a Turing…

Subclasses of TFNP (total functional NP) are usually defined by specifying a complete problem, which is necessarily in TFNP, and including all problems many-one reducible to it. We study two notions of how a TFNP problem can be reducible to…