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The complexity of probabilistic versus deterministic finite automata

Andris Ambainis

subject

Discrete mathematicsNested wordDeterministic finite automatonDFA minimizationDeterministic automatonQuantum finite automataTwo-way deterministic finite automatonNondeterministic finite automatonω-automatonNonlinear Sciences::Cellular Automata and Lattice GasesComputer Science::Formal Languages and Automata TheoryMathematics

description

We show that there exists probabilistic finite automata with an isolated cutpoint and n states such that the smallest equivalent deterministic finite automaton contains \(\Omega \left( {2^{n\tfrac{{\log \log n}}{{\log n}}} } \right)\) states.

https://doi.org/10.1007/bfb0009499