相关论文: Satisfiability and computing van der Waerden numbe…

We show that the emptiness (unsatisfiability) problem is undecidable and $\mathrm{\Pi}^{0}_{1}$-complete for deterministic propositional while programs with (graph) loop. To this end, we introduce a hypothesis elimination using loops. Using…

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,…

This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…

Propositional satisfiability (SAT) is at the nucleus of state-of-the-art approaches to a variety of computationally hard problems, one of which is cryptanalysis. Moreover, a number of practical applications of SAT can only be tackled…

Finding a quantum computing method to solve nondeterministic polynomial time (NP)-complete problems is currently of paramount importance in quantum information science. Here an experiment is presented to demonstrate the use of Rydberg atoms…

A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…

Conformal prediction is a powerful framework for constructing prediction sets with valid coverage guarantees in multi-class classification. However, existing methods often rely on a single score function, which can limit their efficiency…

We explore the properties of non-piecewise syndetic sets with positive upper density, which we call "discordant", in countably infinite amenable (semi)groups. Sets of this kind are involved in many questions of Ramsey theory and manifest…

Accepting a proposition means that our confidence in this proposition is strictly greater than the confidence in its negation. This paper investigates the subclass of uncertainty measures, expressing confidence, that capture the idea of…

#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…

Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…

Vacillating tableaux are sequences of integer partitions that satisfy specific conditions. The concept of vacillating tableaux stems from the representation theory of the partition algebra and the combinatorial theory of crossings and…

SMT solvers use sophisticated techniques for polynomial (linear or non-linear) integer arithmetic. In contrast, non-polynomial integer arithmetic has mostly been neglected so far. However, in the context of program verification, polynomials…

We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…

This paper gives a dichotomy theorem for the complexity of computing the partition function of an instance of a weighted Boolean constraint satisfaction problem. The problem is parameterised by a finite set F of non-negative functions that…

We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the…

In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…

One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…

We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…

This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…