Abstract
We consider a graph-based model for the process of gene assembly in ciliates, as proposed in [A. Ehrenfeucht, T. Harju, I. Petre, D. M. Prescott, G. Rozenberg, Computation in Living Cells: Gene Assembly in Ciliates, Springer, 2003]. The model consists of three operations, each reducing the order of the signed graph. Reducing the graph to the empty graph through a sequence of operations corresponds to assembling a gene. We investigate parallel reductions of a given signed graph, where the graph is reduced through a sequence of parallel steps. A parallel step consists of operations such that any of their sequential compositions are applicable to the current graph. We improve the basic exhaustive search algorithm reported in [A. Alhazov, C. Li, I. Petre, Computing the graph-based parallel complexity of gene assembly, Theoretical Computer Science, 2008 (in press)] to compute the parallel complexity of signed graphs. On the one hand, we reduce the number of sets of operations which should be checked for parallel applicability. On the other hand, we speed up the parallel applicability check procedure. We prove also that deciding whether a given parallel composition of operations is applicable to a given signed graph is a coNP problem. Deciding whether the parallel complexity (the length of a shortest parallel reduction) of a signed graph is bounded by a given constant is in NP NP .
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