Related papers: CNFs and DNFs with Exactly $k$ Solutions
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
We present a way to create small yet difficult model counting instances. Our generator is highly parameterizable: the number of variables of the instances it produces, as well as their number of clauses and the number of literals in each…
A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or…
On the Semantic Web, metadata and ontologies are used to enable computers to read data. The Web Ontology Language (OWL) has been proposed as a standard ontological language, and various inference systems for this language have been studied.…
We consider the following problem. Given a 2-CNF formula, is it possible to remove at most $k$ clauses so that the resulting 2-CNF formula is satisfiable? This problem is known to different research communities in Theoretical Computer…
This paper presents a comprehensive approach for model-based diagnosis which includes proposals for characterizing and computing preferred diagnoses, assuming that the system description is augmented with a system structure (a directed…
A decision problem is called parameterized if its input is a pair of strings. One of these strings is referred to as a parameter. The problem: given a propositional logic program P and a non-negative integer k, decide whether P has a stable…
We demonstrate a family of propositional formulas in conjunctive normal form so that a formula of size $N$ requires size $2^{\Omega(\sqrt[7]{N/logN})}$ to refute using the tree-like OBDD refutation system of Atserias, Kolaitis and Vardi…
In 1992 Blum and Rudich [BR92] gave an algorithm that uses membership and equivalence queries to learn $k$-term DNF formulas over $\{0,1\}^n$ in time $\textsf{poly}(n,2^k)$, improving on the naive $O(n^k)$ running time that can be achieved…
We study the time complexity of the weighted first-order model counting (WFOMC) over the logical language with two variables and counting quantifiers. The problem is known to be solvable in time polynomial in the domain size. However, the…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
This paper explores the computational complexity of various natural one-variable fragments of first-order modal logics with the addition of counting quantifiers, over both constant and varying domains. The addition of counting quantifiers…
A property $\Pi$ on a finite set $U$ is \emph{monotone} if for every $X \subseteq U$ satisfying $\Pi$, every superset $Y \subseteq U$ of $X$ also satisfies $\Pi$. Many combinatorial properties can be seen as monotone properties. The problem…
By the MAXSAT problem, we are given a set $V$ of $m$ variables and a collection $C$ of $n$ clauses over $V$, i.e., a conjunctive normal form ($\textit{CNF}$) formula. We will seek a truth assignment to maximize the number of satisfied…
A prominent challenge to the safe and optimal operation of the modern power grid arises due to growing uncertainties in loads and renewables. Stochastic optimal power flow (SOPF) formulations provide a mechanism to handle these…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
In an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…
Propositional model counting is a fundamental problem in artificial intelligence with a wide variety of applications, such as probabilistic inference, decision making under uncertainty, and probabilistic databases. Consequently, the problem…
We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n^Omega(w). This shows that the simple counting argument that any formula refutable in width w must…
Neural networks have emerged as essential components in safety-critical applications -- these use cases demand complex, yet trustworthy computations. Binarized Neural Networks (BNNs) are a type of neural network where each neuron is…