Related papers: The Parameterized Complexity of Reasoning Problems…
We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
Graph Neural Networks (GNNs) have been recently leveraged to solve several logical reasoning tasks. Nevertheless, counting problems such as propositional model counting (#SAT) are still mostly approached with traditional solvers. Here we…
Motivated by recent progress in quantum technologies and in particular quantum software, research and industrial communities have been trying to discover new applications of quantum algorithms such as quantum optimization and machine…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular. There has been many efforts to extend stable model semantics so that answer set programs can use…
The purpose of this article is to examine and limit the conditions in which the P complexity class could be equivalent to the NP complexity class. Proof is provided by demonstrating that as the number of clauses in a NP-complete problem…
In this manuscript, we derive the principle of conservation of computational complexity. We measure computational complexity as the number of binary computations (decisions) required to solve a problem. Every problem then defines a unique…
The Strong Exponential Time Hypothesis (SETH) asserts that for every $\varepsilon>0$ there exists $k$ such that $k$-SAT requires time $(2-\varepsilon)^n$. The field of fine-grained complexity has leveraged SETH to prove quite tight…
The framework of Pearl's Causal Hierarchy (PCH) formalizes three types of reasoning: probabilistic (i.e. purely observational), interventional, and counterfactual, that reflect the progressive sophistication of human thought regarding…
Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. The…
This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…
Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
As a seemingly self-explanatory task, problem-solving has been a significant component of science and engineering. However, a general yet concrete formulation of problem-solving itself is missing. With the recent development of AI-based…
We carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the {\sc Test Cover} problem we are given a set $[n]=\{1,...,n\}$ of items together…
Answer-set programming (ASP) paradigm is a way of using logic to solve search problems. Given a search problem, to solve it one designs a theory in the logic so that models of this theory represent problem solutions. To compute a solution…
We analyse how the standard reductions between constraint satisfaction problems affect their proof complexity. We show that, for the most studied propositional, algebraic, and semi-algebraic proof systems, the classical constructions of…
Constraint satisfaction problems (CSPs) models many important intractable NP-hard problems such as propositional satisfiability problem (SAT). Algorithms with non-trivial upper bounds on running time for restricted SAT with bounded clause…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…