Reset sequences for monotonic automata
SIAM Journal on Computing
Composition sequences for functions over a finite domain
Theoretical Computer Science
Synchronizing finite automata on Eulerian digraphs
Theoretical Computer Science - Mathematical foundations of computer science
Synchronizing monotonic automata
Theoretical Computer Science - Developments in language theory
Synchronizing generalized monotonic automata
Theoretical Computer Science - Insightful theory
A series of slowly synchronizing automata with a zero state over a small alphabet
Information and Computation
The mortality threshold for partially monotonic automata
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
Complexity of problems concerning reset words for cyclic and Eulerian automata
CIAA'11 Proceedings of the 16th international conference on Implementation and application of automata
Complexity of problems concerning reset words for cyclic and Eulerian automata
Theoretical Computer Science
Approximating the Minimum Length of Synchronizing Words Is Hard
Theory of Computing Systems
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A word w is called a reset word for a deterministic finite automaton A if it maps all states of A to one state. A word w is called a compressing to M states for a deterministic finite automaton A if it maps all states of A to at most M states. We consider several subclasses of automata: aperiodic, D- trivial, monotonic, partially monotonic automata and automata with a zero state. For these subclasses we study the computational complexity of the following problems. Does there exist a reset word for a given automaton? Does there exist a reset word of given length for a given automaton? What is the length of the shortest reset word for a given automaton? Moreover, we consider complexity of the same problems for compressing words.