Cyril Nicaud

On the Average Complexity of Moore's State Minimization Algorithm

We prove that, for any arbitrary finite alphabet and for the uniform distribution over deterministic and accessible automata with

On the Average Size of Glushkov's Automata

n

REGAL: a library to randomly and exhaustively generate automata

states, the average complexity of Moores state minimization algorithm is in

The standard factorization of Lyndon words: an average point of view

\mathcal{O}(n \log n)

Fast Synchronization of Random Automata.

. Moreover this bound is tight in the case of unary automata.

Average Case Analysis of Moore’s State Minimization Algorithm

Glushkovs algorithm builds an *** -free nondeterministic automaton from a given regular expression. In the worst case, its number of states is linear and its number of transitions is quadratic in the size of the expression. We show in this paper that in average, the number of transitions is linear.

Seed: An Easy-to-Use Random Generator of Recursive Data Structures for Testing

The C++ library REGAL is devoted to the random and exhaustive generation of finite deterministic automata. The random generation of automata can be used for example to test properties of automata, to experimentally study average complexities of algorithms dealing with automata or to compare different implementations of the same algorithm. The exhaustive generation allows one to check conjectures on small automata.

RANDOM GENERATION OF FINITELY GENERATED SUBGROUPS OF A FREE GROUP

A non-empty word w is a Lyndon word if and only if it is strictly smaller for the lexicographical order than any of its proper suffixes. Such a word w is either a letter or admits a standard factorization uv where v is its smallest proper suffix. For any Lyndon word v, we show that the set of Lyndon words having v as right factor of the standard factorization is regular and compute explicitly the associated generating function. Next, considering the Lyndon words of length n over a twoletter alphabet, we establish that, for the uniform distribution, the average length of the right factor v of the standard factorization is asymptotically 3n/4.

The Average State Complexity of Rational Operations on Finite Languages

A synchronizing word for an automaton is a word that brings that automaton into one and the same state, regardless of the starting position. Cerny conjectured in 1964 that if a n-state deterministic automaton has a synchronizing word, then it has a synchronizing word of size at most (n-1)^2. Berlinkov recently made a breakthrough in the probabilistic analysis of synchronization by proving that with high probability, an automaton has a synchronizing word. In this article, we prove that with high probability an automaton admits a synchronizing word of length smaller than n^(1+\epsilon), and therefore that the Cerny conjecture holds with high probability.

Brzozowski Algorithm Is Generically Super-Polynomial for Deterministic Automata

We prove that the average complexity of Moore’s state minimization algorithm is