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The problem of model counting, also known as #SAT, is to compute the number of models or satisfying assignments of a given Boolean formula $F$. Model counting is a fundamental problem in computer science with a wide range of applications.…
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…
Low-rank matrix completion concerns the problem of estimating unobserved entries in a matrix using a sparse set of observed entries. We consider the non-uniform setting where the observed entries are sampled with highly varying…
We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…
Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is, providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of known…
Universal quantifiers occur frequently in proof obligations produced by program verifiers, for instance, to axiomatize uninterpreted functions and to express properties of arrays. SMT-based verifiers typically reason about them via…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
We give improved separations for the query complexity analogue of the log-approximate-rank conjecture i.e. we show that there are a plethora of total Boolean functions on $n$ input bits, each of which has approximate Fourier sparsity at…
The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner…
The Constraint Satisfaction Problem (CSP) is ubiquitous in various areas of mathematics and computer science. Many of its variations have been studied including the Counting CSP, where the goal is to find the number of solutions to a CSP…
Stochastic Multi-Objective Optimization (SMOO) is critical for decision-making trading off multiple potentially conflicting objectives in uncertain environments. SMOO aims at identifying the Pareto frontier, which contains all mutually…
Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…
Parity-SAT is the problem of determining whether a given CNF formula has an odd number of satisfying assignments. As a canonical $\oplus$P-complete problem, it represents a fundamental variant of the exact model counting problem (#SAT).…
Cryptographic problems can often be reduced to solving Boolean polynomial systems, whose equivalent logical formulas can be treated using SAT solvers. Given the algebraic nature of the problem, the use of the logical XOR operator is common…
We describe a method of model checking called Computing Range Reduction (CRR). The CRR method is based on derivation of clauses that reduce the set of traces of reachable states in such a way that at least one counterexample remains (if…