Related papers: Efficient Local Search for Nonlinear Real Arithmet…
Satisfiability Modulo Theories (SMT) has significant application in various domains. In this paper, we focus on quantifier-free Satisfiablity Modulo Real Arithmetic, referred to as SMT(RA), including both linear and non-linear real…
Satisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer…
The Model Constructing Satisfiability (MCSat) approach to the SMT problem extends the ideas of CDCL from the SAT level to the theory level. Like SAT, its search is driven by incrementally constructing a model by assigning concrete values to…
MaxSAT modulo theories (MaxSMT) is an important generalization of Satisfiability modulo theories (SMT) with various applications. In this paper, we focus on MaxSMT with the background theory of Linear Integer Arithmetic, denoted as…
Local search algorithms use the neighborhood relations among search states and often perform well for a variety of NP-hard combinatorial search problems. This paper shows how quantum computers can also use these neighborhood relations. An…
Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first order theories. In this paper, we focus on Satisfiablity Modulo Integer Arithmetic, which is…
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…
Stochastic local search (SLS) algorithms have exhibited great effectiveness in finding models of random instances of the Boolean satisfiability problem (SAT). As one of the most widely known and used SLS algorithm, WalkSAT plays a key role…
We present new refinement heuristics for the balanced graph partitioning problem that break with an age-old rule. Traditionally, local search only permits moves that keep the block sizes balanced (below a size constraint). In this work, we…
Satisfiability modulo nonlinear real arithmetic theory (SMT(NRA)) solving is essential to multiple applications, including program verification, program synthesis and software testing. In this context, recently model constructing…
In scheduling problems, deterministic task durations are often assumed. This usually does not capture reality and may lead to schedules that are not robust to (small) changes to these task lengths. The use of stochastic task durations…
The problem of finding global minima of nonlinear discrete functions arises in many fields of practical matters. In recent years, methods based on discrete filled functions become popular as ways of solving these sort of problems. However,…
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…
The class PLS (Polynomial Local Search) captures the complexity of finding a solution that is locally optimal and has proven to be an important concept in the theory of local search. It has been shown that local search versions of various…
The Boolean Satisfiability problem (SAT), as the prototypical $\mathsf{NP}$-complete problem, is crucial in both theoretical computer science and practical applications. To address this problem, stochastic local search (SLS) algorithms,…
In this paper, we propose a hybrid framework for Satisfiability Modulo the Theory of Nonlinear Real Arithmetic (SMT-NRA for short). First, we introduce a two-dimensional cell-jump move, called \emph{$2d$-cell-jump}, generalizing the key…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…
Solving nonlinear SMT problems over real numbers has wide applications in robotics and AI. While significant progress is made in solving quantifier-free SMT formulas in the domain, quantified formulas have been much less investigated. We…
Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear regression in which the predictor-response pairs are partially mismatched. We use an optimization…
We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…