Quantum and probabilistic finite multitape automata

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Quantum and probabilistic finite multitape
automata

• Ginta Garkaje and Rusins Freivalds
• Riga, Latvia

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First, we discuss the following 2-tape
language L1 (0n1m,2k) nmk
Theorem. The language L1 can be recognized with
arbitrary probability 1-e by a probabilistic
2-tape finite automaton.
2n 3m 5k 3n 6m 9k 2n 9m 11k
SOFSEM 2009
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Theorem. There exists no quantum finite 2-tape
automaton which recognizes the language L41 with
bounded error. For arbitrary positive e, there
exists a probabilistic finite 2-tape automaton
recognizing the language L41 with a probability
1-e.
are binary words and either
xy or yz but not both of them.
There exists no probabilistic finite 2-tape
automaton which recognizes language L42 with a
bounded error. There exists a quantum finite
2-tape automaton recognizing the language L42
with a probability 1-e.
SOFSEM 2009
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Theorem. For arbitrary r, there exists a quantum
finite 2-tape automaton recognizing the language
L43 with the probability 1. For arbitrary r,
there exists no quantum finite 2-tape automaton
with 2 O(r/log r) states which recognizes the
language L43 with abounded error. For arbitrary
r, and for arbitrary positive e there exists a
probabilistic finite 2-tape automaton with const.
r states recognizing the language L43 with
probability 1- e.
Theorem. For arbitrary r, there exists quantum
finite 2-tape automaton with 2 O(r/log r) states
which recognizes the language L44 with the
probability 1. For arbitrary r, there exists no
probabilistic finite 2-tape automaton with 2
O(r/log r) states which recognizes the language
L44 with the probability 1.
SOFSEM 2009