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This study evaluates Direct Preference Optimization (DPO) and its variants for aligning Large Language Models (LLMs) with human preferences, testing three configurations: (1) with Supervised Fine Tuning (SFT), (2) without SFT, and (3)…
Planning under uncertainty is a central problem in the study of automated sequential decision making, and has been addressed by researchers in many different fields, including AI planning, decision analysis, operations research, control…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
The structure of satisfiability problems is used to improve search algorithms for quantum computers and reduce their required coherence times by using only a single coherent evaluation of problem properties. The structure of random k-SAT…
Adversarial Training (AT) is one of the most effective methods for developing robust deep neural networks (DNNs). However, AT faces a trade-off problem between clean accuracy and adversarial robustness. In this work, we reveal a surprising…
The Model-Constructing Satisfiability Calculus (MCSAT) framework has been applied to SMT problems over various arithmetic theories. NLSAT, an implementation using cylindrical algebraic decomposition (CAD) for explanation, is especially…
Applying deep learning to solve real-life instances of hard combinatorial problems has tremendous potential. Research in this direction has focused on the Boolean satisfiability (SAT) problem, both because of its theoretical centrality and…
In this paper we present a new approach to solve the satisfiability problem (SAT), based on boolean networks (BN). We define a mapping between a SAT instance and a BN, and we solve SAT problem by simulating the BN dynamics. We prove that BN…
It has become standard that, when a SAT solver decides that a CNF $\Gamma$ is unsatisfiable, it produces a certificate of unsatisfiability in the form of a refutation of $\Gamma$ in some proof system. The system typically used is DRAT,…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
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…
Propositional satisfiability (SAT) is one of the most fundamental problems in computer science. The worst-case hardness of SAT lies at the core of computational complexity theory. The average-case analysis of SAT has triggered the…
Design Structure Matrix (DSM) modularization, the task of partitioning system elements into cohesive modules, is a fundamental combinatorial challenge in engineering design. Traditional methods treat modularization as a pure graph…
Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically,…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
In 2000, I published a relatively comprehensive study of mappings between propositional satisfiability (SAT) and constraint satisfaction problems (CSPs) [Wal00]. I analysed four different mappings of SAT problems into CSPs, and two of CSPs…
Recent works have explored using language models for planning problems. One approach examines translating natural language descriptions of planning tasks into structured planning languages, such as the planning domain definition language…
We investigate connections between SAT (the propositional satisfiability problem) and combinatorics, around the minimum degree (number of occurrences) of variables in various forms of redundancy-free boolean conjunctive normal forms…