Finding Attractors in Biological Models Based on Boolean Dynamical Systems Using Hitting Set Boolean networks are discretetime dynamic systems that have been used as a model for a wide range of applications in different areas, especially in Systems Biology. The analysis of Boolean networks includes the search for attractors, which may represent important biological conditions such as gene expression patterns in models of gene regulatory networks, among others. Attractors can be found through exploring the network paths by achieving the solution to the SAT problem, which is known to be NPcomplete. In this paper, we propose an approach to find all attractors by first transforming the corresponding instance of the SAT problem to a Hitting Set instance in linear time through a new direct linear reduction. Finally, the instance of the Hitting Set problem is solved by applying a fast parallel algorithm implemented in GPU. As a proof of principle, we tested the method for Boolean networks with 3 and 4 variables, returning the result in about 3 seconds and 9 hours respectively. However, for larger networks the execution time grows substantially due to the algorithm used in the Hitting Set problem solver. But the result achieved for networks with 3 and 4 variables encourages improvements in the method for dealing with largescale Boolean networks, specially by incorporating some parameter restrictions based on prior information about the state diagram transition graphs structure and optimizing the method by means of dynamic programming and parallelism.

Synthesis of Boolean Networks from Biological Dynamical Constraints using AnswerSet Programming Boolean networks model finite discrete dynamical systems with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging dynamical properties of the resulting network. The dynamical properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on AnswerSet Programming with a parametrized complexity, and leads to a complete nonredundant characterization of the set of solutions. Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scalefree structures up to 100 to 1,000 nodes depending on the type of constraints.