Related papers: PolySAT: Word-level Bit-vector Reasoning in Z3
Discrete variables are common in many applications, such as probabilistic reasoning, planning and explainable AI. When symbolic reasoning techniques are brought in to bear on these applications, a standard technique for handling discrete…
The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…
This is a commentary on, and critique of, Latif Salum's paper titled "Tractability of One-in-three $\mathrm{3SAT}$: $\mathrm{P} = \mathrm{NP}$." Salum purports to give a polynomial-time algorithm that solves the $\mathrm{NP}$-complete…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
Recent years have witnessed a wide array of results in software testing, exploring different approaches and methodologies ranging from fuzzers to symbolic engines, with a full spectrum of instances in between such as concolic execution and…
Abstract geometrical computation can solve hard combinatorial problems efficiently: we showed previously how Q-SAT can be solved in bounded space and time using instance-specific signal machines and fractal parallelization. In this article,…
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…
Vision-Language Models (vLLMs) have emerged as powerful architectures for joint reasoning over visual and textual inputs, enabling breakthroughs in image captioning, cross modal retrieval, and multimodal dialogue. However, as these models…
State-of-the-art answer set programming (ASP) solvers rely on a program called a grounder to convert non-ground programs containing variables into variable-free, propositional programs. The size of this grounding depends heavily on the size…
What is the minimum amount of information and time needed to solve 2SAT? When the instance is known, it can be solved in polynomial time, but is this also possible without knowing the instance? Bei, Chen and Zhang (STOC '13) considered a…
Complex logical reasoning tasks require a long sequence of reasoning, which a large language model (LLM) with chain-of-thought prompting still falls short. To alleviate this issue, neurosymbolic approaches incorporate a symbolic solver.…
Non-linear polynomial systems over finite fields are used to model functional behavior of cryptosystems, with applications in system security, computer cryptography, and post-quantum cryptography. Solving polynomial systems is also one of…
The capabilities of large language models (LLMs) have been enhanced by training on data that reflects human thought processes, such as the Chain-of-Thought format. However, evidence suggests that the conventional scheme of next-word…
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…
Despite the significant improvements achieved by large language models (LLMs) in English reasoning tasks, these models continue to struggle with multilingual reasoning. Recent studies leverage a full-parameter and two-stage training…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
We formally study the logical reasoning capabilities of decoder-only Transformers in the context of the boolean satisfiability (SAT) problem. First, we prove by construction that decoder-only Transformers can decide 3-SAT, in a non-uniform…
Existing methods provide varying algorithms for different types of Boolean satisfiability problems (SAT), lacking a general solution framework. Accordingly, this study proposes a unified framework DCSAT based on integer programming and…
The dramatic improvements in combinatorial optimization algorithms over the last decades have had a major impact in artificial intelligence, operations research, and beyond, but the output of current state-of-the-art solvers is often hard…
Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…