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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…
Operators of Earth observation satellites need justifications for scheduling decisions: why a request was selected, rejected, or what changes would make it schedulable. Existing approaches construct post-hoc reasoning layers independent of…
Modern high-performance SAT solvers quickly solve large satisfiability instances that occur in practice. If the instance is satisfiable, then the SAT solver can provide a witness which can be checked independently in the form of a…
This manuscript describes the notions of blocker and interdiction applied to well-known optimization problems. The main interest of these two concepts is the capability to analyze the existence of a combinatorial structure after some…
Large language models often improve reasoning by sampling multiple outputs and aggregating their final answers, but precise and efficient control of error levels remains a challenging task. In particular, deciding when to stop sampling…
In the context of Answer Set Programming, this paper investigates symmetry-breaking to eliminate symmetric parts of the search space and, thereby, simplify the solution process. We propose a reduction of disjunctive logic programs to a…
It was shown before that the NP-hard problem of deterministic finite automata (DFA) identification can be effectively translated to Boolean satisfiability (SAT). Modern SAT-solvers can tackle hard DFA identification instances efficiently.…
In a previous paper, we proposed a unique physically implemented type simulator for combinatorial optimization problems, called the spontaneous symmetry breaking machine (SSBM). In this paper, we first report the results of experimental…
The use of Boolean Satisfiability (SAT) solver for hardware verification incurs exponential run-time in several instances. In this work we have proposed an efficient quantum SAT (qSAT) solver for equivalence checking of Boolean circuits…
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 study of combinatorial optimization problems with a submodular objective has attracted much attention in recent years. Such problems are important in both theory and practice because their objective functions are very general. Obtaining…
The practical success of Boolean Satisfiability (SAT) solvers stems from the CDCL (Conflict-Driven Clause Learning) approach to SAT solving. However, from a propositional proof complexity perspective, CDCL is no more powerful than the…
We focus on rational solutions or nearly-feasible rational solutions that serve as certificates of feasibility for polynomial optimization problems. We show that, under some separability conditions, certain cubic polynomially constrained…
If supersymmetric particles are discovered, an important problem will be to determine how supersymmetry has been broken. At collider energies, supersymmetry breaking can be parameterised by soft supersymmetry breaking parameters. Several…
We examine three different algorithms that enable the collision certificate method from [Bialkowski, et al.] to handle the case of a centralized multi-robot team. By taking advantage of symmetries in the configuration space of multi-robot…
We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
Convexification is a core technique in global polynomial optimization. Currently, there are two main approaches competing in theory and practice: the approach of nonlinear programming and the approach based on positivity certificates from…
There are many complex combinatorial problems which involve searching for an undirected graph satisfying given constraints. Such problems are often highly challenging because of the large number of isomorphic representations of their…
Artificial Neural Networks (ANN) comprise important symmetry properties, which can influence the performance of Monte Carlo methods in Neuroevolution. The problem of the symmetries is also known as the competing conventions problem or…