Related papers: PolySAT: Word-level Bit-vector Reasoning in Z3
Program-of-Thought (PoT), which aims to use programming language instead of natural language as an intermediate step in reasoning, is an important way for LLMs to solve mathematical problems. Since different programming languages excel in…
Polylab is a MATLAB toolbox for multivariate polynomial scalars and polynomial matrices with a unified symbolic-numeric interface across CPU and GPU-oriented backends. The software exposes three aligned classes: MPOLY for CPU execution,…
Recent advancements in Chain-of-Thoughts (CoT) and Program-of-Thoughts (PoT) methods have greatly enhanced language models' mathematical reasoning capabilities, facilitating their integration into instruction tuning datasets with LLMs.…
Despite significant advancements in the general capability of large language models (LLMs), they continue to struggle with consistent and accurate reasoning, especially in complex tasks such as mathematical and code reasoning. One key…
This paper analyzes to what extent it is possible to efficiently reduce the number of clauses in NP-hard satisfiability problems, without changing the answer. Upper and lower bounds are established using the concept of kernelization.…
In this paper, we present a novel algorithm to solve the Boolean Satisfiability (SAT) problem, using noise-based logic (NBL). Contrary to what the name may suggest, NBL is not a random/fuzzy logic system. In fact, it is a completely…
When a language model answers a table question, users have no way to verify which cells informed which reasoning steps. We introduce RSAT, a method that trains small language models (SLMs, 1-8B) to produce step-by-step reasoning with…
We study the complexity of Boolean constraint satisfaction problems (CSPs) when the assignment must have Hamming weight in some congruence class modulo M, for various choices of the modulus M. Due to the known classification of tractable…
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…
In this paper, we investigated the semantic segmentation of Polarimetric Synthetic Aperture Radar (PolSAR) using Complex-Valued Neural Network (CVNN). Although the coherency matrix is more widely used as the input of CVNN, the Pauli vector…
String constraint solving, and the underlying theory of word equations, are highly interesting research topics both for practitioners and theoreticians working in the wide area of satisfiability modulo theories. As string constraint solving…
This paper introduces the 2019 version of \us{}, a novel Constraint Programming framework for floating point verification problems expressed with the SMT language of SMTLIB. SMT solvers decompose their task by delegating to specific…
Quantum error correction (QEC) is essential for operating quantum computers in the presence of noise. Here, we accurately decode arbitrary Calderbank-Shor-Steane (CSS) codes via the maximum satisfiability (MaxSAT) problem. We show how to…
We demonstrate that any logical problem can be solved by Bayesian inference. In this approach, the distinction between complexity classes vanishes. The method is illustrated by solving the 3-SAT problem in polynomial time. Beyond this,…
This paper introduces SATFuL, a SAT solver for fuzzy logics. In contrast to the Boolean case, for which numerous SAT solvers exist, the SAT problem for fuzzy logics has attracted less attention, even though these tools have interesting…
On the one hand, Constraint Satisfaction Problems allow one to declaratively model problems. On the other hand, propositional satisfiability problem (SAT) solvers can handle huge SAT instances. We thus present a technique to declaratively…
Large language models exhibit strong reasoning capabilities, yet often rely on shortcuts such as surface pattern matching and answer memorization rather than genuine logical inference. We propose Shortcut-Aware Reasoning Training (SART), a…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…
While Multimodal Large Language Models (MLLMs) demonstrate proficiency in 2D scenes, extending their perceptual intelligence to 3D point cloud understanding remains a significant challenge. Current approaches focus primarily on aligning 3D…