On Direct Product and Quotient of Strongly Connected Automata
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2011
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| _version_ | 1866911865430343680 |
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| author | Hu, Zino H. |
| author_facet | Hu, Zino H. |
| contents | Let $A \ \times \ B$ be the direct product of a strongly connected permutation automaton $A$ and a strongly connected synchronizing (reset) automaton $B$, then $A \ \times \ B$ is strongly connected and $$\boldsymbol{A \cong (A \times B)/π}$$ $$\boldsymbol{B \cong (A \times B)/ρ}$$ $$\boldsymbol{(A \times B) \ \cong \ (A \times B)/π\ \times \ (A \times B)/ρ}$$ where $π$ and $ρ$ are automaton congruence relations defined in this paper, $(A \times B)/π$ and $(A \times B)/ρ$ are quotient automata constructed by $π$ and $ρ$ respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1104_3314 |
| institution | arXiv |
| publishDate | 2011 |
| record_format | arxiv |
| spellingShingle | On Direct Product and Quotient of Strongly Connected Automata Hu, Zino H. Formal Languages and Automata Theory Group Theory F.1.1 Let $A \ \times \ B$ be the direct product of a strongly connected permutation automaton $A$ and a strongly connected synchronizing (reset) automaton $B$, then $A \ \times \ B$ is strongly connected and $$\boldsymbol{A \cong (A \times B)/π}$$ $$\boldsymbol{B \cong (A \times B)/ρ}$$ $$\boldsymbol{(A \times B) \ \cong \ (A \times B)/π\ \times \ (A \times B)/ρ}$$ where $π$ and $ρ$ are automaton congruence relations defined in this paper, $(A \times B)/π$ and $(A \times B)/ρ$ are quotient automata constructed by $π$ and $ρ$ respectively. |
| title | On Direct Product and Quotient of Strongly Connected Automata |
| topic | Formal Languages and Automata Theory Group Theory F.1.1 |
| url | https://arxiv.org/abs/1104.3314 |