Solving Sudoku with Membrane Computing

Sudoku is a very popular puzzle which consists on placing several numbers in a squared grid according to some simple rules. In this paper we present an efficient family of P systems which solve sudokus of any order verifying a specific property. The solution is searched by using a simple human-style method. If the sudoku cannot be solved by using this strategy, the P system detects this drawback and then the computations stops and returns No. Otherwise, the P system encodes the solution and returns Yes in the last computation step.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08-TIC-0420

A Cellular Sudoku Solver

Sudoku is a very popular puzzle which consists on placing several numbers in a squared grid according to some simple rules. In this paper we present an efficient family of P systems which solve sudoku puzzles of any order verifying a specific property. The solution is searched by using a simple human-style method. If the sudoku cannot be solved by using this strategy, the P system detects this drawback and then the computations stops and returns No. Otherwise, the P system encodes the solution and returns Yes in the last computation step.Ministerio de Ciencia e Innovación TIN2008-04487-EMinisterio de Ciencia e Innovación TIN-2009-13192Junta de Andalucía P08-TIC-0420

A sublinear Sudoku solution in cP Systems and its formal verification

Sudoku is known as a NP-complete combinatorial number-placement puzzle. In this study, we propose the first cP system solution to generalised Sudoku puzzles with m×m cells grouped in m blocks. By using a fixed constant number of rules, our cP system can solve all Sudoku puzzles in sublinear steps. We evaluate the cP system and discuss its formal verification

Comparing Neuromorphic Systems by Solving Sudoku Problems

Ostrau C, Klarhorst C, Thies M, Rückert U. Comparing Neuromorphic Systems by Solving Sudoku Problems. In: Conference Proceedings: 2019 International Conference on High Performance Computing & Simulation (HPCS). Piscataway, NJ: IEEE; Accepted.In the field of neuromorphic computing several hardware accelerators for spiking neural networks have been introduced, but few studies actually compare different systems. These comparative studies reveal difficulties in porting an existing network to a specific system and in predicting its performance indicators. Finding a common network architecture that is suited for all target platforms and at the same time yields decent results is a major challenge. In this contribution, we show that a winner-takes-all inspired network structure can be employed to solve Sudoku puzzles on three diverse hardware accelerators. By exploring several network implementations, we measured the number of solved puzzles in a set of 100 assorted Sudokus, as well as time and energy to solution. Concerning the last two indicators, our measurements indicate that it can be beneficial to port a network to an analogue hardware system

Spectral graph theory : from practice to theory

Graph theory is the area of mathematics that studies networks, or graphs. It arose from the need to analyse many diverse network-like structures like road networks, molecules, the Internet, social networks and electrical networks. In spectral graph theory, which is a branch of graph theory, matrices are constructed from such graphs and analysed from the point of view of their so-called eigenvalues and eigenvectors. The first practical need for studying graph eigenvalues was in quantum chemistry in the thirties, forties and fifties, specifically to describe the Hückel molecular orbital theory for unsaturated conjugated hydrocarbons. This study led to the field which nowadays is called chemical graph theory. A few years later, during the late fifties and sixties, graph eigenvalues also proved to be important in physics, particularly in the solution of the membrane vibration problem via the discrete approximation of the membrane as a graph. This paper delves into the journey of how the practical needs of quantum chemistry and vibrating membranes compelled the creation of the more abstract spectral graph theory. Important, yet basic, mathematical results stemming from spectral graph theory shall be mentioned in this paper. Later, areas of study that make full use of these mathematical results, thus benefitting greatly from spectral graph theory, shall be described. These fields of study include the P versus NP problem in the field of computational complexity, Internet search, network centrality measures and control theory.peer-reviewe

Sudoku solver based on human strategies an application in VBA

Mestrado Bolonha em Métodos Quantitativos para a Decisão Económica e EmpresariaO Sudoku é um puzzle popularmente conhecido, com aplicações em diversas áreas que se estendem desde a Criptografia à Medicina. Por ser um problema NP-completo, a maior parte dos esforços para o resolver focam-se em heurísticas e não em métodos exatos. Exemplo destes últimos são as estratégias humanas. A proposta deste Trabalho Final de Mestrado (TFM) consiste no desenvolvimento de um Sudoku Solver, em VBA. O solver desenvolvido é um algoritmo de duas fases que incorpora estratégias humanas (Fase 1) e backtracking (Fase 2). A Fase 2 só é executada se, terminada a Fase 1, não for encontrada uma solução admissível. Foi conduzida uma experiência computacional para testar a performance do solver para puzzles 9×9 de três níveis de dificuldade: fácil, moderado e difícil. Das 230 instâncias testadas, aproximadamente 55% foram resolvidas. O tempo máximo de resolução foi de 6,813 segundos, o tempo mínimo foi de 0,309 e a média do tempo total foi de 2,525 segundos.Sudoku is a popular puzzle, with applications in several areas ranging from Cryptography to Medicine. Because it is an NP-complete problem, most efforts to solve it focus on heuristics and not on exact methods. Examples of the latter are human strategies. The proposal of this Master’s Final Work (MFW) is the development of a Sudoku Solver, in VBA. The developed solver is a two-phase algorithm that incorporates human strategies (Phase 1) and a backtracking procedure (Phase 2). Phase 2 is only executed if a feasible solution has not been found after Phase 1 ends. It was conducted a computational experience to test the solver performance for 9×9 puzzles with three difficulty levels: easy, moderate, and hard. Among the 230 instances tested, approximately 55% were solved. The maximum running time was 6.813 seconds, the minimum time was 0.309, and the average total time was 2.525 seconds.info:eu-repo/semantics/publishedVersio