Related papers: A SAT Encoding for the $n$-Fractions Problem
In the present paper, we propose a technology for translating algorithmic descriptions of discrete functions to SAT. The proposed technology is aimed at applications in algebraic cryptanalysis. We describe how cryptanalysis problems are…
We contemplate the notion of ambiguity in mathematical discourse. We consider a general method of resolving ambiguity and semantic options for sustaining a resolution. The general discussion is applied to the case of `fraction' which is…
Given a CNF formula F on n variables, the problem of model counting or #SAT is to compute the number of satisfying assignments of F . Model counting is a fundamental but hard problem in computer science with varied applications. Recent…
Constraint satisfaction problems (CSPs) are about finding values of variables that satisfy the given constraints. We show that Transformer extended with recurrence is a viable approach to learning to solve CSPs in an end-to-end manner,…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we…
Regular signed SAT is a variant of the well-known satisfiability problem in which the variables can take values in a fixed set V \subset [0,1], and the `literals' have the form "x \le a" or "x \ge a". We answer some open question regarding…
We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
The question of whether the complexity class P is equal to the complexity class NP has been a seemingly intractable problem for over 4 decades. It has been clear that if an algorithm existed that would solve the problems in the NP class in…
Case split is a core proof rule in current decision procedures for the theory of string constraints. Its use is the primary cause of the state space explosion in string constraint solving, since it is the only rule that creates branches in…
In this paper we consider the following problems: how many different subsets of Sigma^n can occur as set of all length-n factors of a finite word? If a subset is representable, how long a word do we need to represent it? How many such…
This paper aims to introduce high school students to the intriguing world of continued fractions, a mathematical concept that provides a unique representation of numbers. The study focuses on the exploration and development of the…
We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…
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…
In this paper, we investigate the strength of six different SAT solvers in attacking various obfuscation schemes. Our investigation revealed that Glucose and Lingeling SAT solvers are generally suited for attacking small-to-midsize…
Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
Calculating the probability of an individual solution being selected under lexicase selection is an important problem in attempts to develop a deeper theoretical understanding of lexicase selection, a state-of-the art parent selection…
We derive closed formulas for the number of $k$-coloured partitions and the number of plane partitions of $n$ in terms of the Bell polynomials.