Related papers: Approximate-At-Most-k Encoding of SAT for Soft Con…
The Simple Assembly Line Balancing Problem with Power Peak Minimization (SALBP-3PM) minimizes maximum instantaneous power usage while assigning $n$ tasks to $m$ workstations and determining execution schedules within given cycle time…
The quantum approximate optimization algorithm is commonly used to solve combinatorial optimization problems. While unconstrained problems map naturally into the algorithm, incorporating constraints typically requires penalizing constraint…
The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT,…
We present an approach to propagation-based SAT encoding of combinatorial problems, Boolean equi-propagation, where constraints are modeled as Boolean functions which propagate information about equalities between Boolean literals. This…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…
Local consistency techniques such as k-consistency are a key component of specialised solvers for constraint satisfaction problems. In this paper we show that the power of using k-consistency techniques on a constraint satisfaction problem…
The Boolean satisfiability (SAT) problem lies at the core of many applications in combinatorial optimization, software verification, cryptography, and machine learning. While state-of-the-art solvers have demonstrated high efficiency in…
Constraint satisfaction problems (or CSPs) have been extensively studied in, for instance, artificial intelligence, database theory, graph theory, and statistical physics. From a practical viewpoint, it is beneficial to approximately solve…
The problem of counting the number of models of a given Boolean formula has numerous applications, including computing the leakage of deterministic programs in Quantitative Information Flow. Model counting is a hard, #P-complete problem.…
Given $k$ collections of 2SAT clauses on the same set of variables $V$, can we find one assignment that satisfies a large fraction of clauses from each collection? We consider such simultaneous constraint satisfaction problems, and design…
Boolean Satisfiability (SAT) problems are critical in fields such as artificial intelligence and cryptography, where efficient solutions are essential. Conventional probabilistic solvers often encounter scalability issues due to complex…
The At-Most-One (AMO) constraint is a special case of cardinality constraint that requires at most one variable from a set of Boolean variables to be set to TRUE. AMO is important for modeling problems as Boolean satisfiability (SAT) from…
To study the question under which circumstances small solutions can be found faster than by exhaustive search (and by how much), we study the fine-grained complexity of Boolean constraint satisfaction with size constraint exactly $k$. More…
We study a family of problems, called \prob{Maximum Solution}, where the objective is to maximise a linear goal function over the feasible integer assignments to a set of variables subject to a set of constraints. When the domain is Boolean…
Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…
We study the counting version of the Boolean satisfiability problem #SAT using the ZH-calculus, a graphical language originally introduced to reason about quantum circuits. Using this, we generalize #SAT to a weighted variant we call…
Determining the evolutionary history of a given biological data is an important task in biological sciences. Given a set of quartet topologies over a set of taxa, the Maximum Quartet Consistency (MQC) problem consists of computing a global…
We present an approach to propagation based solving, Boolean equi-propagation, where constraints are modelled as propagators of information about equalities between Boolean literals. Propagation based solving applies this information as a…
The random $k$-SAT problem serves as a model that represents the 'typical' $k$-SAT instances. This model is thought to undergo a phase transition as the clause density changes, and it is believed that the random $k$-SAT problem is primarily…
Satisfiability Modulo Counting (SMC) is a recently proposed general language to reason about problems integrating statistical and symbolic Artificial Intelligence. An SMC problem is an extended SAT problem in which the truth values of a few…