Synchronizing word

For synchronizing words in the theory of synchronized codes, see Self-synchronizing code § Synchronizing word.
This drawing represents a DFA with eight states and two input symbols, red and blue. The word blue-red-red-blue-red-red-blue-red-red is a synchronizing word that sends all states to the yellow state; the word blue-blue-red-blue-blue-red-blue-blue-red is another synchronizing word that sends all states to the green state.

In computer science, more precisely, in the theory of deterministic finite automata (DFA), a synchronizing word or reset sequence is a word in the input alphabet of the DFA that sends any state of the DFA to one and the same state.[1] That is, if an ensemble of copies of the DFA are each started in different states, and all of the copies process the synchronizing word, they will all end up in the same state. Not every DFA has a synchronizing word; for instance, a DFA with two states, one for words of even length and one for words of odd length, can never be synchronized.

  1. ^ Avraham Trakhtman: Synchronizing automata, algorithms, Cerny Conjecture. Accessed May 15, 2010.