24 research outputs found
Enumeration of finite automata
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33337/1/0000734.pd
Random Generation and Enumeration of Accessible Determinisitic Real-time Pushdown Automata
This papers presents a general framework for the uniform random generation of
deterministic real-time accessible pushdown automata. A polynomial time
algorithm to randomly generate a pushdown automaton having a fixed stack
operations total size is proposed. The influence of the accepting condition
(empty stack, final state) on the reachability of the generated automata is
investigated.Comment: Frank Drewes. CIAA 2015, Aug 2015, Umea, Sweden. Springer, 9223,
pp.12, 2015, Implementation and Application of Automata - 20th International
Conferenc
A large deviations principle for the Maki-Thompson rumour model
We consider the stochastic model for the propagation of a rumour within a
population which was formulated by Maki and Thompson. Sudbury established that,
as the population size tends to infinity, the proportion of the population
never hearing the rumour converges in probability to . Watson later
derived the asymptotic normality of a suitably scaled version of this
proportion. We prove a corresponding large deviations principle, with an
explicit formula for the rate function.Comment: 18 pages, 2 figure
Asymptotic enumeration of Minimal Automata
We determine the asymptotic proportion of minimal automata, within n-state
accessible deterministic complete automata over a k-letter alphabet, with the
uniform distribution over the possible transition structures, and a binomial
distribution over terminal states, with arbitrary parameter b. It turns out
that a fraction ~ 1-C(k,b) n^{-k+2} of automata is minimal, with C(k,b) a
function, explicitly determined, involving the solution of a transcendental
equation.Comment: 12+5 pages, 2 figures, submitted to STACS 201
Brzozowski Algorithm Is Generically Super-Polynomial Deterministic Automata
International audienceWe study the number of states of the minimal automaton of the mirror of a rational language recognized by a random deterministic automaton with n states. We prove that, for any d > 0, the probability that this number of states is greater than nd tends to 1 as n tends to infinity. As a consequence, the generic and average complexities of Brzozowski minimization algorithm are super-polynomial for the uniform distribution on deterministic automata
On the asymptotic enumeration of accessible automata
Automata, Logic and Semantic