Abstract. Transforming deterministic ω-automata into deterministic parity automata is traditionally done using variants of appearance records. We present a more efficient variant of this approach, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and find out that our method produces smaller automata than previous approaches. Moreover, the experiments demonstrate the potential of our method for LTL synthesis, using LTL-to-Rabin translators. It leads to significantly smaller parity automata when compared to state-of-the-art approaches on complex formulae.

The k disjoint shortest paths problem (k-DSPP) on a graph with k source-sink pairs (s i , t i ) asks for the existence of k pairwise edge-or vertex-disjoint shortest s i -t i -paths. It is known to be NP-complete if k is part of the input. Restricting to 2-DSPP with strictly positive lengths, it becomes solvable in polynomial time. We extend this result by allowing zero edge lengths and give a polynomial time algorithm based on dynamic programming for 2-DSPP on undirected graphs with non-negative edge lengths.

ABSTRACT. In this paper we report on the full classification of Dirichlet-Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. We obtain a complete list of 110244 affine types (Ltypes) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet-Voronoi polyhedra. Using a refinement of corresponding secondary cones, we obtain 181394 contraction types. We report on details of our computer assisted enumeration, which we verified by three independent implementations and a topological mass formula check.

Transforming $$\omega $$ ω -automata into parity automata is traditionally done using appearance records. We present an efficient variant of this idea, tailored to Rabin automata, and several optimizations applicable to all appearance records. We compare the methods experimentally and show that our method produces significantly smaller automata than previous approaches.

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