13 research outputs found
Reset thresholds of automata with two cycle lengths
We present several series of synchronizing automata with multiple parameters,
generalizing previously known results. Let p and q be two arbitrary co-prime
positive integers, q > p. We describe reset thresholds of the colorings of
primitive digraphs with exactly one cycle of length p and one cycle of length
q. Also, we study reset thresholds of the colorings of primitive digraphs with
exactly one cycle of length q and two cycles of length p.Comment: 11 pages, 5 figures, submitted to CIAA 201
Synchronizing automata with random inputs
We study the problem of synchronization of automata with random inputs. We
present a series of automata such that the expected number of steps until
synchronization is exponential in the number of states. At the same time, we
show that the expected number of letters to synchronize any pair of the famous
Cerny automata is at most cubic in the number of states
Complexity of checking whether two automata are synchronized by the same language
A deterministic finite automaton is said to be synchronizing if it has a
reset word, i.e. a word that brings all states of the automaton to a particular
one. We prove that it is a PSPACE-complete problem to check whether the
language of reset words for a given automaton coincides with the language of
reset words for some particular automaton.Comment: 12 pages, 4 figure
Synchronizing automata with a letter of deficiency 2
AbstractWe present two infinite series of synchronizing automata with a letter of deficiency 2 whose shortest reset words are longer than those for synchronizing automata obtained by a straightforward modification of Černý’s construction
Slowly synchronizing automata and digraphs
We present several infinite series of synchronizing automata for which the
minimum length of reset words is close to the square of the number of states.
These automata are closely related to primitive digraphs with large exponent.Comment: 13 pages, 5 figure