Related papers: Scheme-Theoretic Approach to Computational Complex…

A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…

The rigorous theoretical analyses of algorithms for #SAT have been proposed in the literature. As we know, previous algorithms for solving #SAT have been analyzed only regarding the number of variables as the parameter. However, the time…

New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…

We present a new algorithm for deciding formula entailment in orthologic (a sound approximation of classical logic) that avoids the costly preprocessing phase of prior implementations while retaining the same $\mathcal{O}(n^2(1+|A|))$…

We focus on the random generation of SAT instances that have properties similar to real-world instances. It is known that many industrial instances, even with a great number of variables, can be solved by a clever solver in a reasonable…

Let $Z(F)$ be the number of solutions of a random $k$-satisfiability formula $F$ with $n$ variables and clause density $\alpha$. Assume that the probability that $F$ is unsatisfiable is $O(1/\log(n)^{1+\e})$ for $\e>0$. We show that…

Let f(n)=1 if n=1, 2^(2^(n-2)) if n \in {2,3,4,5}, (2+2^(2^(n-4)))^(2^(n-4)) if n \in {6,7,8,...}. We conjecture that if a system T \subseteq {x_i+1=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in positive…

We propose a new algorithm, call Sam to determinate the existence of the solutions for the equation $x^3+y^3+z^3=n$ for a fixed value $n > 0$ unknown.

We show that for all integers $2\le s\le t$, any $K_{s,t}$-free subset of $[N]$ with size $\Omega(n^{1-1/s})$ must contain a nontrivial solution to every fixed translation-invariant linear equation in at least five variables. This extends…

Partly on the basis of heuristic arguments from physics it has been suggested that the performance of certain types of algorithms on random $k$-SAT formulas is linked to phase transitions that affect the geometry of the set of satisfying…

We consider weighted counting of independent sets using a rational weight x: Given a graph with n vertices, count its independent sets such that each set of size k contributes x^k. This is equivalent to computation of the partition function…

We present an improvement on Thurley's recent randomized approximation scheme for #k-SAT where the task is to count the number of satisfying truth assignments of a Boolean function {\Phi} given as an n-variable k-CNF. We introduce a novel…

A challenging problem is to find an algorithm to decide whether a morphism is k-power-free. We provide such an algorithm when k >= 3 for uniform morphisms showing that in such a case, contrarily to the general case, there exist finite…

For k>=3 let A \subset [1,N] be a set not containing a solution to a_1 x_1+...+a_k x_k=a_1 x_{k+1}+...+a_k x_{2k} in distinct integers. We prove that there is an epsilon>0 depending on the coefficients of the equation such that every such A…

Shallit and Wang showed that the automatic complexity $A(x)$ satisfies $A(x)\ge n/13$ for almost all $x\in{\{\mathtt{0},\mathtt{1}\}}^n$. They also stated that Holger Petersen had informed them that the constant 13 can be reduced to 7. Here…

We propose an algorithm of generating hard instances for the Satisfying Assignment Search Problem (in short, SAT). The algorithm transforms instances of the integer factorization problem into SAT instances efficiently by using the Chinese…

We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical…

The problem of identifying a planted assignment given a random $k$-SAT formula consistent with the assignment exhibits a large algorithmic gap: while the planted solution becomes unique and can be identified given a formula with $O(n\log…

Using elementary rigorous methods we prove the existence of a clustered phase in the random $K$-SAT problem, for $K\geq 8$. In this phase the solutions are grouped into clusters which are far away from each other. The results are in…

The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT)…