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We analyze how symmetries can be used to compress structures (also known as interpretations) onto a smaller domain without loss of information. This analysis suggests the possibility to solve satisfiability problems in the compressed domain…
We present algorithms based on satisfiability problem (SAT) solving, as well as answer set programming (ASP), for solving the problem of determining inconsistency degrees in propositional knowledge bases. We consider six different…
Optimal path planning is the problem of finding a valid sequence of states between a start and goal that optimizes an objective. Informed path planning algorithms order their search with problem-specific knowledge expressed as heuristics…
We provide a dual fitting technique on a semidefinite program yielding simple proofs of tight bounds for the robust price of anarchy of several congestion and scheduling games under the sum of weighted completion times objective. The same…
In 2006, Biere, Jussila, and Sinz made the key observation that the underlying logic behind algorithms for constructing Reduced, Ordered Binary Decision Diagrams (BDDs) can be encoded as steps in a proof in the extended resolution logical…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
In this project, we aimed to improve the runtime of Minisat, a Conflict-Driven Clause Learning (CDCL) solver that solves the Propositional Boolean Satisfiability (SAT) problem. We first used a logistic regression model to predict the…
Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…
Large Reasoning Models (LRMs) have revolutionized complex problem-solving, yet they exhibit a pervasive "overthinking", generating unnecessarily long reasoning chains. While current solutions improve token efficiency, they often sacrifice…
A new framework for presenting and analyzing the functionality of a modern DLL-based SAT solver is proposed. Our approach exploits the inherent relation between backtracking and resolution. We show how to derive the algorithm of a modern…
Governance theory has quietly relied on a rough cognitive comparability between governors and governed. The assumption is load-bearing, and this paper tries to show why by making it testable. The vehicle is a six-dimension evaluation…
Finding asymptotically-optimal paths in multi-robot motion planning problems could be achieved, in principle, using sampling-based planners in the composite configuration space of all of the robots in the space. The dimensionality of this…
Large language models (LLMs) have exhibited impressive reasoning abilities on a wide range of complex tasks. However, enhancing these capabilities through post-training remains resource intensive, particularly in terms of data and…
Conflict-Driven Clause Learning (CDCL) is the mainstream framework for solving the Satisfiability problem (SAT), and CDCL solvers typically rely on various heuristics, which have a significant impact on their performance. Modern CDCL…
Recent large language models (LLMs) achieve near-saturation accuracy on many established mathematical reasoning benchmarks, raising concerns about their ability to diagnose genuine reasoning competence. This saturation largely stems from…
Discrete facility layout design involves placing physical entities to minimize handling costs while adhering to strict safety and spatial constraints. This combinatorial problem is typically addressed using Mixed Integer Linear Programming…
State-of-the-art techniques for simultaneous localization and mapping (SLAM) employ iterative nonlinear optimization methods to compute an estimate for robot poses. While these techniques often work well in practice, they do not provide…
In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories…
The structural phase transitions and computational complexity of random 3-SAT instances are traditionally described using thermodynamic analogies from statistical physics, such as Replica Symmetry Breaking and energy landscapes. While…
Modern conflict-driven clause-learning (CDCL) Boolean SAT solvers provide efficient automatic analysis of real-world feature models (FM) of systems ranging from cars to operating systems. It is well-known that solver-based analysis of…