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It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
Boolean satisfiability (SAT) problems are routinely solved by SAT solvers in real-life applications, yet solving time can vary drastically between solvers for the same instance. This has motivated research into machine learning models that…
Many constraint satisfaction problems involve synthesizing subgraphs that satisfy certain reachability constraints. This paper presents programs in Picat for four problems selected from the recent LP/CP programming competitions. The…
The Cyclic Antibandwidth Problem (CABP), a variant of the Antibandwidth Problem, is an NP-hard graph labeling problem with numerous applications. Despite significant research efforts, existing state-of-the-art approaches for CABP are…
Until now, Computer Scientists have concerned themselves with identifying efficient algorithms for solving the general case of some problem -- that is finding one which performs well when the size of the input tends to infinity. In this…
Answer set programming (ASP) is a popular nonmonotonic-logic based paradigm for knowledge representation and solving combinatorial problems. Computing the answer set of an ASP program is NP-hard in general, and researchers have been…
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been…
We present Graph-$Q$-SAT, a branching heuristic for a Boolean SAT solver trained with value-based reinforcement learning (RL) using Graph Neural Networks for function approximation. Solvers using Graph-$Q$-SAT are complete SAT solvers that…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…
The MaxClique problem, finding the largest complete subgraph in an Erd{\"o}s-R{\'e}nyi $G(N,p)$ random graph in the large $N$ limit, is a well-known example of a simple problem for which finding any approximate solution within a factor of…
We proposes a novel method that enables Graph Neural Networks (GNNs) to solve SAT problems by leveraging a technique developed for applying GNNs to Mixed Integer Linear Programming (MILP). Specifically, k-CNF formulae are mapped into MILP…
Reducing the cognitive complexity of a piece of code to a given threshold is not trivial. Recently, we modeled software cognitive complexity reduction as an optimization problem and we proposed an approach to assist developers on this task.…
We apply the splitting method to three well-known counting problems, namely 3-SAT, random graphs with prescribed degrees, and binary contingency tables. We present an enhanced version of the splitting method based on the capture-recapture…
Theorem provers has been used extensively in software engineering for software testing or verification. However, software is now so large and complex that additional architecture is needed to guide theorem provers as they try to generate…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Finding a maximum clique in a given graph is one of the fundamental NP-hard problems. We compare two multi-core thread-parallel adaptations of a state-of-the-art branch and bound algorithm for the maximum clique problem, and provide a novel…
Given a simple undirected graph $G$, the maximum $k$-club problem is to find a maximum-cardinality subset of nodes inducing a subgraph of diameter at most $k$ in $G$. This NP-hard generalization of clique, originally introduced to model low…
The Satisfiability (SAT) problem is a core challenge with significant applications in software engineering, including automated testing, configuration management, and program verification. This paper presents SolSearch, a novel framework…
Boolean satisfiability (SAT) has an extensive application domain in computer science, especially in electronic design automation applications. Circuit synthesis, optimization, and verification problems can be solved by transforming original…