Related papers: Solving and Verifying the boolean Pythagorean Trip…
Tandem duplication in DNA is the process of inserting a copy of a segment of DNA adjacent to the original position. Motivated by applications that store data in living organisms, Jain {\em et al.} (2016) proposed the study of codes that…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
Given $\eta=\begin{pmatrix} a&b\\c&d \end{pmatrix}\in \text{GL}_2(\mathbb{Q})$, we consider the number of rational points on the genus one curve \[H_\eta:y^2=(a(1-x^2)+b(2x))^2+(c(1-x^2)+d(2x))^2.\] We prove that the set of $\eta$ for which…
We discover suprising connections between three seemingly different problems: finding right triangles with rational sides in a non-Euclidean geometry, finding three integers such that the difference of the squares of any two is a square,…
In this short paper we present a survey of some results concerning the random SAT problems. To elaborate, the Boolean Satisfiability (SAT) Problem refers to the problem of determining whether a given set of $m$ Boolean constraints over $n$…
Existing methods provide varying algorithms for different types of Boolean satisfiability problems (SAT), lacking a general solution framework. Accordingly, this study proposes a unified framework DCSAT based on integer programming and…
Satisfiability Testing (SAT) techniques are well-established in classical computing where they are used to solve a broad variety of problems, e.g., in the design of classical circuits and systems. Analogous to the classical realm, quantum…
In 1922, Mordell conjectured that the set of rational points on a smooth curve $C$ over $\mathbb{Q}$ with genus $g \ge 2$ is finite. This has been proved by Faltings in 1983. However, Coleman determined in 1985 an upper bound of…
In 1989, computer searches by Lam, Thiel, and Swiercz experimentally resolved Lam's problem from projective geometry$\unicode{x2014}$the long-standing problem of determining if a projective plane of order ten exists. Both the original…
In this paper, we consider different constrained partition problems for weighted trees and cactus graphs. We focus on the (l,u)-partition problem, which is the problem of partitioning a weighted graph into connected clusters such that each…
Many state-of-the-art Satisfiability Modulo Theories (SMT) solvers for the theory of fixed-size bit-vectors employ an approach called bit-blasting, where a given formula is translated into a Boolean satisfiability (SAT) problem and…
Two well-studied Diophantine equations are those of Pythagorean triples and elliptic curves; for the first, we have a parametrization through rational points on the unit circle, and for the second we have a structure theorem for the group…
We investigate the implementation of an oracle for the Subset Sum problem for quantum search using Grover's algorithm. Our work concerns reducing the number of qubits, gates, and multi-controlled gates required by the oracle. We describe…
In this paper, by constructing extremely hard examples of CSP (with large domains) and SAT (with long clauses), we prove that such examples cannot be solved without exhaustive search, which is stronger than P $\neq$ NP. This constructive…
By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$, i.e., a conjunctive normal form ($\textit{CNF}$) formula. We will seek a truth assignment to maximize the number of satisfied…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Boolean Satisfiability Problem (SAT) is one of the core problems in computer science. As one of the fundamental NP-complete problems, it can be used - by known reductions - to represent instances of variety of hard decision problems.…
We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture…
A new quantum algorithm is proposed to solve Satisfiability(SAT) problems by taking advantage of non-unitary transformation in ground state quantum computer. The energy gap scale of the ground state quantum computer is analyzed for 3-bit…
Schaefer's theorem is a complexity classification result for so-called Boolean constraint satisfaction problems: it states that every Boolean constraint satisfaction problem is either contained in one out of six classes and can be solved in…