Representation of (Left) Ideal Regular Languages by Synchronizing Automata

  title={Representation of (Left) Ideal Regular Languages by Synchronizing Automata},
  author={Marina I. Maslennikova and Emanuele Rodaro},
We follow language theoretic approach to synchronizing automata and Cerný’s conjecture initiated in a series of recent papers. We find a precise lower bound for the reset complexity of a principal ideal language. Also we show a strict connection between principal left ideals and synchronizing automata. Actually, it is proved that all strongly connected synchronizing automata are homomorphic images of automata recognizing languages which are left quotients of principal left ideal languages. This… 
1 Citations
Synchronizing automata and the language of minimal reset words
  • E. Rodaro
  • Computer Science, Mathematics
    Adv. Appl. Math.
  • 2018


Regular Ideal Languages and Synchronizing Automata
It is shown that each ideal regular language has at least a reset left regular decomposition and this one-to-one correspondence allows Cerný's conjecture in a pure language theoretic framework to be formulated.
Synchronizing automata with finitely many minimal synchronizing words
Recognizing Synchronizing Automata with Finitely Many Minimal Synchronizing Words is PSPACE-Complete
Here it is proved that recognizing synchronizing automata whose language of synchronizing words is finitely generated as a two-sided ideal in Σ*.
Complexity of Checking Whether Two Automata Are Synchronized by the Same Language
It is proved that it is a PSPACE-complete problem to check whether the language of reset words for a given automaton coincides with the language that brings all states of the automaton Open image in new window to a particular one.
Finitely Generated Ideal Languages and Synchronizing Automata
For every finitely generated ideal language L, this work constructs an automaton with at most 2 n states, where n is the maximal length of words in L, based on the De Bruijn graph.
Finite Automata
  • D. Perrin
  • Computer Science
    Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
  • 1990
Synchronizing Automata Preserving a Chain of Partial Orders
Testing for Synchronization
It is shown that an automaton is synchronizing with probability 1 O( 1 n0.5k ) and presented an algorithm with linear in n expected time, while the best known algorithm is quadratic on each instance.
Principal Ideal Languages and Synchronizing Automata
An algorithm to construct a strongly connected synchronizing automaton for which such a language serves as the language of synchronizing words and a compact formula to calculate the syntactic complexity of this language is presented.