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Glass piecewise linear ODE models are frequently used for simulation of neural and gene regulatory networks. Efficient computational 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 propose to encode the identification of models with periodic orbits along cyclic attractors as a propositional formula, and solving it using stateof-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 runtime of our algorithm increases slower than the size of the search space of the problem.

Abstract. Induced (chord-free) cycles in binary hypercubes have many applications in computer science. The state of the art for computing such cycles relies on genetic algorithms, which are, however, unable to perform a complete search. In this paper, we propose an approach to finding a special class of induced cycles we call lean, based on an efficient propositional SAT encoding. Lean induced cycles dominate a minimum number of hypercube nodes. Such cycles have been identified in Systems Biology as candidates for stable trajectories of gene regulatory networks. The encoding enabled us to compute lean induced cycles for hypercubes up to dimension 7. We also classify the induced cycles by the number of nodes they fail to dominate, using a custom-built All-SAT solver. We demonstrate how clause filtering can reduce the number of blocking clauses by two orders of magnitude.

Abstract-Glass models are frequently used as models for gene regulatory networks. This paper proposes algorithmic methods for the synthesis of Glass networks with specific dynamics, including periodic orbits and equilibrium states. In contrast to existing work, bi-periodic networks and networks possessing both stable equilibria and periodic trajectories are considered. The robustness of the attractor is also addressed, which gives rise to hypercube paths with non-dominated nodes and double coils. These paths correspond to novel combinatorial problems, for which initial experimental results are presented. Finally, a classification of Glass networks with respect to their corresponding gene interaction graphs for the case of graphs with three edges is presented.

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