6533b862fe1ef96bd12c74f8
RESEARCH PRODUCT
Artin’s Conjecture and Size of Finite Probabilistic Automata
Rūsiņš Freivaldssubject
Discrete mathematicsNested wordDeterministic finite automatonDFA minimizationDeterministic automatonAutomata theoryQuantum finite automataNondeterministic finite automatonω-automatonNonlinear Sciences::Cellular Automata and Lattice GasesComputer Science::Formal Languages and Automata TheoryMathematicsdescription
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
year | journal | country | edition | language |
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2008-02-07 |