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The paper briefly describes a basic set of special combinatorial engineering frameworks for solving complex problems in the field of hierarchical modular systems. The frameworks consist of combinatorial problems (and corresponding models),…
Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the…
Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gau{\ss}-Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Graph generation and enumeration problems often require handling equivalent graphs -- those that differ only in vertex labeling. We study how to extend SAT Modulo Symmetries (SMS), a framework for eliminating such redundant graphs, to…
Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…
This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…
Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith…
We introduce novel methods for encoding acyclicity and s-t-reachability constraints for propositional formulas with underlying directed graphs. They are based on vertex elimination graphs, which makes them suitable for cases where the…
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…
In computational complexity theory, a decision problem is NP-complete when it is both in NP and NP-hard. Although a solution to a NP-complete can be verified quickly, there is no known algorithm to solve it in polynomial time. There exists…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
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…
Emerging low-powered architectures like Coarse-Grain Reconfigurable Arrays (CGRAs) are becoming more common. Often included as co-processors, they are used to accelerate compute-intensive workloads like loops. The speedup obtained is…
Satellite mission planning for Earth observation satellites is a combinatorial optimization problem that consists of selecting the optimal subset of imaging requests, subject to constraints, to be fulfilled during an orbit pass of a…
Modern SAT solvers have experienced a remarkable progress on solving industrial instances. Most of the techniques have been developed after an intensive experimental testing process. Recently, there have been some attempts to analyze the…
This paper introduces AlphaMapleSAT, a Cube-and-Conquer (CnC) parallel SAT solver that integrates Monte Carlo Tree Search (MCTS) with deductive feedback to efficiently solve challenging combinatorial SAT problems. Traditional lookahead…
Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
A simple yet successful approach to parallel satisfiability (SAT) solving is to run several different (a portfolio of) SAT solvers on the input problem at the same time until one solver finds a solution. The SAT solvers in the portfolio can…