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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…
SATNet is a differentiable constraint solver with a custom backpropagation algorithm, which can be used as a layer in a deep-learning system. It is a promising proposal for bridging deep learning and logical reasoning. In fact, SATNet has…
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…
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise landscape of predictions has been…
Classic AI planning problems have been revisited in the Large Language Model (LLM) era, with a focus of recent benchmarks on success rates rather than plan efficiency. We examine the degree to which frontier models reason optimally versus…
While static symmetry breaking has been explored in the SAT community for decades, only as of 2010 research has focused on exploiting the same discovered symmetry dynamically, during the run of the SAT solver, by learning extra clauses. The…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly…
It is well known in the literature that the problem of learning the structure of Bayesian networks is very hard to tackle: its computational complexity is super-exponential in the number of nodes in the worst case and polynomial in most…
Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and…
Large Language Models (LLMs) have achieved remarkable performance across a wide range of mathematical benchmarks. However, concerns remain as to whether these successes reflect genuine reasoning or superficial pattern recognition. Existing…
A variational approach to finite connectivity spin-glass-like models is developed and applied to describe the structure of optimal solutions in random satisfiability problems. Our variational scheme accurately reproduces the known replica…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
With the aggressive scaling of VLSI technology, the explosion of layout patterns creates a critical bottleneck for DFM applications like OPC. Pattern clustering is essential to reduce data complexity, yet existing methods struggle with…
The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the…
Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) are widely used in automated verification, but there is a lack of interactive tools designed for educational purposes in this field. To address this gap, we present…
Abductive reasoning (or Abduction, for short) is among the most fundamental AI reasoning methods, with a broad range of applications, including fault diagnosis, belief revision, and automated planning. Unfortunately, Abduction is of high…
Constraint Satisfaction Problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value…
In the 1970s and 1980s, searches performed by L. Carter, C. Lam, L. Thiel, and S. Swiercz showed that projective planes of order ten with weight 16 codewords do not exist. These searches required highly specialized and optimized computer…
Large language models are increasingly applied to operational decision-making where the underlying structure is constrained optimization. Existing benchmarks evaluate whether LLMs can formulate optimization problems as solver code, but…