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This paper gives a shortest path algorithm for CFG (context free grammar) labeled and
weighted digraphs where edge weights may be positive or negative,
but negative-weight cycles are not allowed in the underlying unlabeled graph.
These results build directly on an algorithm of Barrett et al. [SIAM J. Comput.30 (2000) 809–837].
In addition to many other results, they gave a shortest path algorithm for CFG labeled and
weighted digraphs where all edges are nonnegative.
Our algorithm is based closely...
The main focus of combinatorial dynamics is put on the structure of periodic points (and the corresponding orbits) of topological dynamical systems. The first result in this area is the famous Sharkovsky's theorem which completely describes the coexistence of periods of periodic points for a continuous map from the closed unit interval to itself. One feature of this theorem is that it can be proved using digraphs of a special type (the so-called periodic graphs). In this paper we use Markov graphs...
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