Related papers: Ramsey Quantifiers in Linear Arithmetics
The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…
Satisfiability Modulo Theories (SMT) and SAT solvers are critical components in many formal software tools, primarily due to the fact that they are able to easily solve logical problem instances with millions of variables and clauses. This…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
Constraint satisfaction problems form a nicely behaved class of problems that lends itself to complexity classification results. From the point of view of parameterized complexity, a natural task is to classify the parameterized complexity…
A semilinear relation is a finite union of finite intersections of open and closed half-spaces over, for instance, the reals, the rationals, or the integers. Semilinear relations have been studied in connection with algebraic geometry,…
A graph is called Rank-Ramsey if (i) Its clique number is small, and (ii) The adjacency matrix of its complement has small rank. We initiate a systematic study of such graphs. Our main motivation is that their constructions, as well as…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
In this paper we consider a fragment of the first-order theory of the real numbers that includes systems of equations of continuous functions in bounded domains, and for which all functions are computable in the sense that it is possible to…
The SMT (Satisfiability Modulo Theories) theory of arrays is well-established and widely used, with variousdecision procedures and extensions developed for it. However, recent works suggest that developing tailoredreasoning for some…
This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of…
We complete a 40-year old program on the computability-theoretic analysis of Ramsey's theorem, starting with Jockusch in 1972, and improving a result of Chong, Slaman and Yang in 2014. Given a set $X$, let $[X]^n$ be the collection of all…
Nowhere dense classes of graphs are classes of sparse graphs with rich structural and algorithmic properties, however, they fail to capture even simple classes of dense graphs. Monadically stable classes, originating from model theory,…
Until recently, techniques for obtaining lower bounds for kernelization were one of the most sought after tools in the field of parameterized complexity. Now, after a strong influx of techniques, we are in the fortunate situation of having…
Disjunctive Linear Arithmetic (DLA) is a major decidable theory that is supported by almost all existing theorem provers. The theory consists of Boolean combinations of predicates of the form $\Sigma_{j=1}^{n}a_j\cdot x_j \le b$, where the…
The exploration of network structures through the lens of graph theory has become a cornerstone in understanding complex systems across diverse fields. Identifying densely connected subgraphs within larger networks is crucial for uncovering…
Ramsey Theorem [6] for pairs is intuitionistically but not classically provable: it is equivalent to a subclassical principle [2]. In this note we show that Ramsey may be restated in an intuitionistically provable form, which is informative…
Quantization, a commonly used technique to reduce the memory footprint of a neural network for edge computing, entails reducing the precision of the floating-point representation used for the parameters of the network. The impact of such…
We present an SMT-based symbolic model checking algorithm for safety verification of recursive programs. The algorithm is modular and analyzes procedures individually. Unlike other SMT-based approaches, it maintains both "over-" and…
Satisfiability modulo theories (SMT) is a core tool in formal verification. While the SMT-LIB specification language can be used to interact with theorem proving software, a high-level interface allows for faster and easier specifications…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…