Related papers: The Long, the Short and the Random
Here, we give an algorithm for deciding if the nonnegative rank of a matrix $M$ of dimension $m \times n$ is at most $r$ which runs in time $(nm)^{O(r^2)}$. This is the first exact algorithm that runs in time singly-exponential in $r$. This…
We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random…
We give the first efficient algorithm to approximately count the number of solutions in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previous counting algorithm for the permissive version…
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…
We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…
Given a CNF formula F on n variables, the problem of model counting or #SAT is to compute the number of satisfying assignments of F . Model counting is a fundamental but hard problem in computer science with varied applications. Recent…
We study the exponential time complexity of approximate counting satisfying assignments of CNFs. We reduce the problem to deciding satisfiability of a CNF. Our reduction preserves the number of variables of the input formula and thus also…
Propositional model enumeration, or All-SAT, is the task to record all models of a propositional formula. It is a key task in software and hardware verification, system engineering, and predicate abstraction, to mention a few. It also…
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
Let $\Phi$ be a random $k$-SAT formula in which every variable occurs precisely $d$ times positively and $d$ times negatively. Assuming that $k$ is sufficiently large and that $d$ is slightly below the critical degree where the formula…
We provide the first fully polynomial-time randomized approximation scheme for the following two counting problems: 1. Given a Context Free Grammar $G$ over alphabet $\Sigma$, count the number of words of length exactly $n$ generated by…
Let F be a uniformly distributed random k-SAT formula with n variables and m clauses. We present a polynomial time algorithm that finds a satisfying assignment of F with high probability for constraint densities m/n<(1-eps_k)2^k\ln(k)/k,…
We present a deterministic approximation algorithm to compute logarithm of the number of `good' truth assignments for a random k-satisfiability (k-SAT) formula in polynomial time (by `good' we mean that violate a small fraction of clauses).…
We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this…
This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…
(k,s)-SAT is the satisfiability problem restricted to instances where each clause has exactly k literals and every variable occurs at most s times. It is known that there exists a function f such that for s\leq f(k) all (k,s)-SAT instances…
In many decision-making processes, one may prefer multiple solutions to a single solution, which allows us to choose an appropriate solution from the set of promising solutions that are found by algorithms. Given this, finding a set of…
We prove that throughout the satisfiable phase, the logarithm of the number of satisfying assignments of a random 2-SAT formula satisfies a central limit theorem. This implies that the log of the number of satisfying assignments exhibits…