Related papers: Model Counting for Dependency Quantified Boolean F…
The paper explores the correspondence between balanced incomplete block designs (BIBD) and certain linear CNF formulas by identifying the points of a block design with the clauses of the Boolean formula and blocks with Boolean variables.…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
In this paper we show that PSPACE is equal to 4th level in the polynomial hierarchy. We also deduce a lot of important consequences. True quantified Boolean formula is a generalisation of the Boolean Satisfiability Problem, where…
This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…
Given a CNF formula $F$, we present a new algorithm for deciding the satisfiability (SAT) of $F$ and computing all solutions of assignments. The algorithm is based on the concept of \emph{cofactors} known in the literature. This paper is a…
It follows from the famous Fagin's theorem that all problems in NP are expressible in existential second-order logic (ESO), and vice versa. Indeed, there are well-known ESO characterizations of NP-complete problems such as 3-colorability,…
Query evaluation in tuple-independent probabilistic databases is the problem of computing the probability of an answer to a query given independent probabilities of the individual tuples in a database instance. There are two main approaches…
QCTL extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as MSO). Several…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
Model counting is a fundamental task that involves determining the number of satisfying assignments to a logical formula, typically in conjunctive normal form (CNF). While CNF model counting has received extensive attention over recent…
Deterministic quantum computation with one quantum bit (DQC1) is a restricted model of quantum computing where the input state is the completely mixed state except for a single clean qubit, and only a single output qubit is measured at the…
Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model…
In this paper we investigate the problem of quantifying the contribution of each variable to the satisfying assignments of a Boolean function based on the Shapley value. Our main result is a polynomial-time equivalence between computing…
The Boolean satisfiability problem (SAT) holds a central place in computational complexity theory as the first shown NP-complete problem. Due to this role, SAT is often used as the benchmark for polynomial-time reductions: if a problem can…
We propose a fragment of many-sorted second order logic called EQSMT and show that checking satisfiability of sentences in this fragment is decidable. EQSMT formulae have an $\exists^*\forall^*$ quantifier prefix (over variables, functions…
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and characterize their computational complexity. In the quantum setting,…
Deterministic quantum computation with one quantum bit (DQC1) is a model of quantum computing where the input restricted to containing a single qubit in a pure state and with all other qubits in a completely-mixed state, with only a single…
We propose an approach for decomposing Boolean satisfiability problems while extending recent results of \cite{sul2} on solving Boolean systems of equations. Developments in \cite{sul2} were aimed at the expansion of functions $f$ in…
Combinatorial counting problems pervade artificial intelligence, statistics, and discrete mathematics. Whether the task is enumerating subsets, multisets, permutations, partitions, or compositions under structural and arithmetic…
Architectural imperatives due to the slowing of Moore's Law, the broad acceptance of relaxed semantics and the O(n!) worst case verification complexity of generating sequential histories motivate a new approach to concurrent correctness.…