Abstract | ||
---|---|---|
We approach the problem of finding strongly connected synchronizing automata with a given ideal I that serves as the set of reset words, by studying the set of minimal words M of the ideal I (no proper factor is a reset word). We first show the existence of an infinite strongly connected synchronizing automaton A having I as the set of reset words and such that every other strongly connected synchronizing automaton having I as the set of reset words is an homomorphic image of A. Finally, we show that for any non-unary regular ideal I there is a strongly connected synchronizing automaton having I as the set of reset words with at most (kmk)2kmkn states, where k is the dimension of the alphabet, m is twice the length of a shortest word in I, and n is the number of states of the smallest automaton recognizing M. This synchronizing automaton is computable and we exhibit an algorithm to compute it in time O((k2mk)2kmkn). |
Year | DOI | Venue |
---|---|---|
2018 | 10.1016/j.aam.2018.04.006 | Advances in Applied Mathematics |
Keywords | Field | DocType |
68Q70,68Q45,20M30,16D25,68R15 | Homomorphic encryption,Combinatorics,Synchronizing automaton,Regular ideal,Automaton,Strongly connected component,Mathematics,Alphabet | Journal |
Volume | ISSN | Citations |
99 | 0196-8858 | 0 |
PageRank | References | Authors |
0.34 | 11 | 1 |
Name | Order | Citations | PageRank |
---|---|---|---|
Emanuele Rodaro | 1 | 55 | 15.63 |