Related papers: A Local Search Algorithm for MaxSMT(LIA)
As we approach the physical limits predicted by Moore's law, a variety of specialized hardware is emerging to tackle specialized tasks in different domains. Within combinatorial optimization, adiabatic quantum computers, CMOS annealers, and…
We provide a formulation for Local Support Vector Machines (LSVMs) that generalizes previous formulations, and brings out the explicit connections to local polynomial learning used in nonparametric estimation literature. We investigate the…
Among sub-optimal MAPF solvers, rule-based algorithms are particularly appealing since they are complete. Even in crowded scenarios, they allow finding a feasible solution that brings each agent to its target, preventing deadlock…
The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for…
This paper introduces Local Learner (2L), an algorithm for providing a set of reference strategies to guide the search for programmatic strategies in two-player zero-sum games. Previous learning algorithms, such as Iterated Best Response…
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…
Large Language Models (LLMs) demonstrate strong capabilities in general coding tasks but encounter two key challenges when optimizing code: (i) the complexity of writing optimized code (such as performant CUDA kernels and competition-level…
We study techniques for solving the Maximum Satisfiability problem (MaxSAT). Our focus is on variables of degree 4. We identify cases for degree-4 variables and show how the resolution principle and the kernelization techniques can be…
Compilers for statically typed functional programming languages are notorious for generating confusing type error messages. When the compiler detects a type error, it typically reports the program location where the type checking failed as…
We suggest a direct algorithm for searching the Lax pairs for nonlinear integrable equations. It is effective for both continuous and discrete models. The first operator of the Lax pair corresponding to a given nonlinear equation is found…
We study a variation of the Stable Marriage problem, where every man and every woman express their preferences as preference lists which may be incomplete and contain ties. This problem is called the Stable Marriage problem with Ties and…
#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…
Despite the rapid development of large language models (LLMs), a fundamental challenge persists: the lack of high-quality optimization modeling datasets hampers LLMs' robust modeling of practical optimization problems from natural language…
The fine-tuning of open-source large language models (LLMs) for machine translation has recently received considerable attention, marking a shift towards data-centric research from traditional neural machine translation. However, the area…
The solution-space structure of the 3-Satisfiability Problem (3-SAT) is studied as a function of the control parameter alpha (ratio of number of clauses to the number of variables) using numerical simulations. For this purpose, one has to…
This paper presents an advanced mathematical problem-solving framework, LLaMA-Berry, for enhancing the mathematical reasoning ability of Large Language Models (LLMs). The framework combines Monte Carlo Tree Search (MCTS) with iterative…
A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms…
Since its introduction in 1957, Lloyd's algorithm for $k$-means clustering has been extensively studied and has undergone several improvements. While in its original form it does not guarantee any approximation factor at all, Arthur and…
The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many…
Local search preprocessing makes Conflict-Driven Clause Learning (CDCL) solvers faster by providing high-quality starting points and modern SAT solvers have incorporated this technique into their preprocessing steps. However, these tools…