The asymptotic number of acyclic diagraphs, II
Journal of Combinatorial Theory Series A
Minimisation of acyclic deterministic automata in linear time
Theoretical Computer Science - Selected papers of the Combinatorial Pattern Matching School
Theoretical Computer Science - Special issue on implementing automata
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
On the number of distinct languages accepted by finite automata with n states
Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Incremental construction of minimal acyclic finite-state automata
Computational Linguistics - Special issue on finite-state methods in NLP
Improved bounds on the number of automata accepting finite languages
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Enumeration and generation with a string automata representation
Theoretical Computer Science
| Hi-index | 0.05 |
A linear recurrence relation is derived for the number of unlabelled initially connected acyclic automata. The coefficients of this relation are determined by another, alternating, recurrence relation. The latter determines, in particular, the number of acyclic automata with labelled states. Certain simple enumerative techniques developed by the author for counting initially connected automata and acyclic digraphs are combined and applied. Calculations show that the results obtained in this paper improve recent upper bounds for the number of minimal deterministic automata (with accepting states) recognizing finite languages. Various related questions are also discussed.