Related papers: Covered Clause Elimination
Second-order quantifier elimination is the problem of finding, given a formula with second-order quantifiers, a logically equivalent first-order formula. While such formulas are not computable in general, there are practical algorithms and…
State-of-the-art SAT solvers are nowadays able to handle huge real-world instances. The key to this success is the so-called Conflict-Driven Clause-Learning (CDCL) scheme, which encompasses a number of techniques that exploit the conflicts…
In this paper we propose a structural parameter of CNF formulas and use it to identify instances of weighted MaxSAT and #SAT that can be solved in polynomial time. Given a CNF formula we say that a set of clauses is precisely satisfiable if…
Unsupervised sentence embedding representation has become a hot research topic in natural language processing. As a tensor, sentence embedding has two critical properties: direction and norm. Existing works have been limited to constraining…
We call a CNF formula linear if any two clauses have at most one variable in common. We show that there exist unsatisfiable linear k-CNF formulas with at most 4k^2 4^k clauses, and on the other hand, any linear k-CNF formula with at most…
This system report presents our approaches and results for the Chinese Essay Fluency Evaluation (CEFE) task at CCL-2024. For Track 1, we optimized predictions for challenging fine-grained error types using binary classification models and…
In many speech recording applications, noise and acoustic echo corrupt the desired speech. Consequently, combined noise reduction (NR) and acoustic echo cancellation (AEC) is required. Generally, a cascade approach is followed, i.e., the…
We study -- within the framework of propositional proof complexity -- the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where ``many'' stands for an…
There are two competing paradigms in successful SAT solvers: Conflict-driven clause learning (CDCL) and stochastic local search (SLS). CDCL uses systematic exploration of the search space and has the ability to learn new clauses. SLS…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
Unit propagation (which is called also Boolean Constraint Propagation) has been an important component of every modern CDCL SAT solver since the CDCL solver was developed. In general, unit propagation is implemented by scanning sequentially…
This note considers checking satisfiability of sets of propositional clauses (SAT instances). It shows that "unipolar sets" of clauses (containing no positive or no negative clauses) provide an "early sign" of satisfiability of SAT…
The PPSZ algorithm by Paturi, Pudl\'ak, Saks, and Zane (FOCS 1998) is the fastest known algorithm for (Promise) Unique k-SAT. We give an improved algorithm with exponentially faster bounds for Unique 3-SAT. For uniquely satisfiable 3-CNF…
The task of Emotion-Cause Pair Extraction (ECPE) aims to extract all potential clause-pairs of emotions and their corresponding causes in a document. Unlike the more well-studied task of Emotion Cause Extraction (ECE), ECPE does not require…
We prove that conflict-driven clause learning SAT-solvers with the ordered decision strategy and the DECISION learning scheme are equivalent to ordered resolution. We also prove that, by replacing this learning scheme with its opposite that…
A basic algorithm for enumerating disjoint propositional models (disjoint AllSAT) is based on adding blocking clauses incrementally, ruling out previously found models. On the one hand, blocking clauses have the potential to reduce the…
Cutting planes are frequently used for solving integer programs. A common strategy is to derive cutting planes from building blocks or a substructure of the integer program. In this paper, we focus on knapsack constraints that arise from…
Given a CNF formula and a weight for each assignment of values to variables, two natural problems are weighted model counting and distribution-aware sampling of satisfying assignments. Both problems have a wide variety of important…
Automated deduction lies at the core of Artificial Intelligence (AI), underpinning theorem proving, formal verification, and logical reasoning. Despite decades of progress, reconciling deductive completeness with computational efficiency…
Dead code introduces several challenges in software development, such as increased binary size and maintenance difficulties. It can also obscure logical errors and be exploited for obfuscation in malware. For LLM-based code-related tasks,…