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Questions tagged [synchronization]

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8
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1answer
136 views

A conjecture related to the Cerny conjecture - counterexample/reference request

The Cerny conjecture is the statement that any synchronizing automaton with $n$ states has a synchronizing word of length at most $(n-1)^2$. The best current upper bound for the length of a ...
3
votes
1answer
116 views

Under what conditions is the Dining Philosophers Problem unsolvable?

The wikipedia article for the Dining Philosophers Problem lists some solutions which are dependent on external information, i.e.: Numbering of forks A waiter to act as mutex Messaging between ...
3
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0answers
73 views

Communication complexity of edit resilient synchronization

Supposing we have two strings $A$ and $B$ that are both edit distance $\tau$ from each other at two different sites is there a communication complexity model where synchronizing such strings have been ...
10
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2answers
250 views

The number of states of local automata

A deterministic automaton $\mathcal A = (X, Q, q_0, F, \delta)$ is called $k$-local for $k > 0$ if for every $w \in X^k$ the set $\{ \delta(q,w) : q \in Q \}$ contains at most one element. ...
19
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2answers
1k views

Status of Cerny Conjecture?

A DFA has a synchronizing word if there is a string that sends any state of the DFA to a single state. In ‘The Cerny Conjecture for Aperiodic Automata” by A. N. Trahtman (Discrete Mathematics and ...