相关论文: Considerations on P vs NP

In a seminal paper from 1985, Sistla and Clarke showed that satisfiability for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of propositional…

We provide a parameterized polynomial algorithm for the propositional model counting problem #SAT, the runtime of which is single-exponential in the rank-width of a formula. Previously, analogous algorithms have been known -- e.g.~[Fischer,…

We remark that the AKS primality testing algorithm [Annals of Mathematics 160 (2), 2004] needs about 1,000,000,000 G (gigabyte) storage space for a number of 1024 bits. The requirement is very hard to meet. The complexity class P which…

The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $\tau$-Conjecture for polynomials implies that…

Article presents the compatibility matrix method and illustrates it with the application to P vs NP problem. The method is a generalization of descriptive geometry: in the method, we draft problems and solve them utilizing the image…

We consider a committee voting setting in which each voter approves of a subset of candidates and based on the approvals, a target number of candidates are selected. Aziz et al. (2015) proposed two representation axioms called justified…

It is well known that modal satisfiability is PSPACE-complete (Ladner 1977). However, the complexity may decrease if we restrict the set of propositional operators used. Note that there exist an infinite number of propositional operators,…

A polynomial algorithm is obtained for the NP-complete linear ordering problem.

A P-matrix is a square matrix $X$ such that all principal submatrices of $X$ have positive determinant. Such matrices appear naturally in instances of the linear complementarity problem, where these are precisely the matrices for which the…

This work explores the relationship between solution space and time complexity in the context of the $\textbf{P}$ vs. $\textbf{NP}$ problem, particularly through the lens of the sliding tile puzzle and root finding algorithms. We focus on…

We show that the affirmation $P\subseteq NP$ (in computer science) erroneously and we prove the justice of the hypotesis J.Edmonds's $P\neq NP$. We show further that all the $NP$-complete problems is not polynomial and we give the…

In a previous paper, we have shown that any Boolean formula can be encoded as a linear programming problem in the framework of Bayesian probability theory. When applied to NP-complete algorithms, this leads to the fundamental conclusion…

We investigate the computational complexity of deciding whether a given univariate integer polynomial p(x) has a factor q(x) satisfying specific additional constraints. When the only constraint imposed on q(x) is to have a degree smaller…

In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…

We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic.…

It is well-known (cf. K.-Pudl\'ak 1989) that a polynomial time algorithm finding tautologies hard for a propositional proof system $P$ exists iff $P$ is not optimal. Such an algorithm takes $1^{(k)}$ and outputs a tautology $\tau_k$ of size…

We connect learning algorithms and algorithms automating proof search in propositional proof systems: for every sufficiently strong, well-behaved propositional proof system $P$, we prove that the following statements are equivalent, 1.…

This paper depicts algorithms for solving the decision Boolean Satisfiability Problem. An extreme problem is formulated to analyze the complexity of algorithms and the complexity for solving it. A novel and easy reformulation as a lottery…

In connection with machine arithmetic, we are interested in systems of constraints of the form x + k \leq y + k'. Over integers, the satisfiability problem for such systems is polynomial time. The problem becomes NP complete if we restrict…

We investigate the class of regular-ordered word equations. In such equations, each variable occurs at most once in each side and the order of the variables occurring in both sides is the preserved (the variables can be, however, separated…