An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
The Synchronization Problem for Strongly Transitive Automata
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Matrix Mortality and the Černý-Pin Conjecture
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
Decision version of the road coloring problem is NP-complete
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Slowly synchronizing automata and digraphs
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
An algorithm for road coloring
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
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A coloring of edges of a finite directed graph turns the graph into a finite-state automaton. A synchronizing word of a deterministic automaton is a word in the alphabet of colors of its edges (regarded as letters) which maps the automaton to a single state. A coloring of edges of a directed graph of uniform outdegree (constant outdegree of any vertex) is synchronizing if the corresponding deterministic finite automaton possesses a synchronizing word. The road coloring problem is the problem of synchronizing coloring of a directed finite strongly connected graph of uniform outdegree if the greatest common divisor of lengths of all its cycles is one. Posed in 1970, it has evoked noticeable interest among the specialists in the theory of graphs, automata, codes, symbolic dynamics, and well beyond these areas. We present an algorithm for the road coloring of cubic worst-case time complexity and quadratic time complexity in the majority of studied cases. It is based on the recent positive solution of the road coloring problem. The algorithm was implemented in the freeware package TESTAS.