Related papers: AlphaMapleSAT: An MCTS-based Cube-and-Conquer SAT …

We analyze to what extent the random SAT and Max-SAT problems differ in their properties. Our findings suggest that for random $k$-CNF with ratio in a certain range, Max-SAT can be solved by any SAT algorithm with subexponential slowdown,…

Many problems in interprocedural program analysis can be modeled as the context-free language (CFL) reachability problem on graphs and can be solved in cubic time. Despite years of efforts, there are no known truly sub-cubic algorithms for…

The one of the most interesting problem of discrete mathematics is the SAT (satisfiability) problem. Good way in SAT solver developing is to transform the SAT problem to the problem of continuous search of global minimums of the functional…

We discuss an approach for solving sparse or dense banded linear systems ${\bf A} {\bf x} = {\bf b}$ on a Graphics Processing Unit (GPU) card. The matrix ${\bf A} \in {\mathbb{R}}^{N \times N}$ is possibly nonsymmetric and moderately large;…

Due to the adoption of horizontal business models following the globalization of semiconductor manufacturing, the overproduction of integrated circuits (ICs) and the piracy of intellectual properties (IPs) can lead to significant damage to…

We consider semidefinite programming (SDP) approaches for solving the maximum satisfiability problem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suited to approximate the (MAX-)2-SAT. Our work shows the…

The search of hardware-compatible strategies for solving NP-hard combinatorial optimization problems (COPs) is an important challenge of today s computing research because of their wide range of applications in real world optimization…

One-shot neural architecture search (NAS) methods significantly reduce the search cost by considering the whole search space as one network, which only needs to be trained once. However, current methods select each operation independently…

Complex sequential decision-making planning problems, covering infinite states' space have been shown to be solvable by AlphaZero type of algorithms. Such an approach that trains a neural model while simulating projection of futures with a…

Recent advancements in Large Language Models (LLMs) have successfully employed search-based strategies to enhance code generation. However, existing methods typically rely on static, sparse public test cases for verification, leading to…

Circuit Satisfiability (CSAT) plays a pivotal role in Electronic Design Automation. The standard workflow for solving CSAT problems converts circuits into Conjunctive Normal Form (CNF) and employs generic SAT solvers powered by…

This work presents the first study of using the popular Monte Carlo Tree Search (MCTS) method combined with dedicated heuristics for solving the Weighted Vertex Coloring Problem. Starting with the basic MCTS algorithm, we gradually…

Monte Carlo Tree Search (MCTS) is an immensely popular search-based framework used for decision making. It is traditionally applied to domains where a perfect simulation model of the environment is available. We study and improve MCTS in…

AlphaZero in 2017 was able to master chess and other games without human knowledge by playing millions of games against itself (self-play), with a computation budget running in the tens of millions of dollars. It used a variant of the Monte…

The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties,…

This paper has three main contributions to our understanding of fixed-depth minimax search: (A) A new formulation for Stockman's SSS* algorithm, based on Alpha-Beta, is presented. It solves all the perceived drawbacks of SSS*, finally…

One of the most important AI research questions is to trade off computation versus performance since ``perfect rationality" exists in theory but is impossible to achieve in practice. Recently, Monte-Carlo tree search (MCTS) has attracted…

In the application of IC design for microprocessors, there are often demands for optimizing the implementation of datapath circuits, on which various arithmetic operations are performed. Combinational equivalence checking (CEC) plays an…

This paper introduces a novel method for compact representation of sets of n-dimensional binary sequences in a form of compact triplets structures (CTS), supposing both logic and arithmetic interpretations of data. Suitable illustration of…

We propose a resource-constrained heuristic for instances of Max-SAT that iteratively decomposes a larger problem into smaller subcomponents that can be solved by optimized solvers and hardware. The unconstrained outer loop maintains the…