On the number of non-isomorphic strongly connected finite automata
Journal of Information Processing and Cybernetics
A calculus for the random generation of labelled combinatorial structures
Theoretical Computer Science
Combinatorial Algorithms: For Computers and Hard Calculators
Combinatorial Algorithms: For Computers and Hard Calculators
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
Theoretical Computer Science - Descriptional complexity of formal systems
Enumeration and random generation of accessible automata
Theoretical Computer Science
Enumeration and generation with a string automata representation
Theoretical Computer Science
SWCT '64 Proceedings of the 1964 Proceedings of the Fifth Annual Symposium on Switching Circuit Theory and Logical Design
Generating random binary trees - A survey
Information Sciences: an International Journal
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In the last few decades, several techniques to randomly generate a deterministic finite automaton have been developed. These techniques have implications in the enumeration and random generation of automata of size n. One of the ways to generate a finite automaton is to generate a random tree and to complete it to a deterministic finite automaton, assuming that the tree will be the automaton's breadth-first spanning tree. In this paper we explore further this method, and the string representation of a tree, and use it to counting the number of automata having a tree as a breadth-first spanning subtrees. We introduce the notions of characteristic and difference sequence of a tree, and define the weight of a tree. We also present a recursive formula for this quantity in terms of the "derivative" of a tree. Finally, we analyze the implications of this formula in terms of exploring trees with the largest and smallest number of automata in the span of the tree and present simple applications for finding densities of subsets of DFAs.