Using evolutionary techniques to hunt for snakes and coils
ABSTRACT The snake-in-the-box problem is a difficult problem in mathematics and computer science that deals with finding the longest-possible constrained path that can be formed by following the edges of a multidimensional hypercube. This problem was first described by Kautz in the late 1950's (Kautz, 1958). Snake-in-the-box codes, or 'snakes,' are the node or transition sequences of constrained open paths through an n-dimensional hypercube. Coil-in-the-box codes, or 'coils,' are the node or transition sequences of constrained closed paths, or cycles, through an n-dimensional hypercube. Snakes and coils have many applications in electrical engineering, coding theory, and computer network topologies. Generally, the longer the snake or coil for a given dimension, the more useful it is in these applications (Klee, 1970). By applying a relatively recent evolutionary search algorithm known as a population-based stochastic hill-climber, new lower bounds were achieved for (1) the longest-known snake in each of the dimensions nine through twelve and (2) the longest-known coil in each of the dimensions nine through eleven.
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- "The search for snakes is motivated by the theory of error-correcting codes (as the vertices of a solution to the snake or coil in the box problems can be used as a Gray code that can detect singlebit errors), electrical engineering, computer network topologies , Systems Biology , etc. Approaches to find long snakes range from studies of mathematical constructions (e.g. binary necklaces ) and certain patterns in lower dimensions   to genetic algorithms   . R. C. Singleton generalized the concept of snakein-the-box codes to circuit codes with a parameter spread . "
Conference Paper: An efficient SAT encoding of circuit codes[Show abstract] [Hide abstract]
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ABSTRACT: Glass piecewise linear ODE models are frequently used for simulation of neural and gene regulatory networks. Efficient computa- tional tools for automatic synthesis of such models are highly desirable. However, the existing algorithms for the identification of desired models are limited to four-dimensional networks, and rely on numerical solutions of eigenvalue problems. We suggest a novel algebraic criterion to detect the type of the phase flow along network cyclic attractors that is based on a corollary of the Perron-Frobenius theorem. We show an application of the criterion to the analysis of bifurcations in the networks. We pro- pose to encode the identification of models with periodic orbits along cyclic attractors as a propositional formula, and solving it using state- of-the-art SAT-based tools for real linear arithmetic. New lower bounds for the number of equivalence classes are calculated for cyclic attractors in six-dimensional networks. Experimental results indicate that the run- time of our algorithm increases slower than the size of the search space of the problem.Algebraic Biology, Second International Conference, AB 2007, Castle of Hagenberg, Austria, July 2-4, 2007, Proceedings; 01/2007