Languages Recognizable by Quantum Finite Automata with cut-point 0

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Languages Recognizable by Quantum Finite Automata
with cut-point 0
Lelde Lace Oksana Scegulnaja-DubrovskaSupervisor
Rusins FreivaldsUniversity of Latvia
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Definition MM-QFA
States Q , q0?Q, Qacc ? Q, Qrej ?Q, Qacc ?
Qrej0 Halting states Qacc Qrej , Non halting
states Qnon Q( Qacc? Qrej)
Input alphabet ?, Working alphabet - ? ? ?
,
State of M superposition of states in Q ?
?qi?Q aiqi? ?qi?Qacc ?iqi? ?qj?Qrej ?jqj?
?qk?Qnon ?kqk?
Transition function V ? ?l2(Q)? l2(Q) ?a ?
?, Va(x) unitary transformation
Word acceptance with cut-point 0 ?w ?L,
probaccgt0, ?w ?L, probacc0
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PALINDROMES
PALINDROMES x x ?0,1 and x xrev
Input word coding x x1x2x3...xn k1 (n)
0.0nx1x2x3...xn k2 (n)
0.0nxnxn-1xn-2...x1
ki (n1) ki (n)c1c2(n) ?w ?L,
k1 k2 , ?w ? L, k1? k2
Hadamard operation
Co-PALINDROMES can be recognized by finite
automata
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Postselection
MM-QFA postselection set of states and state q
? ?qi?Qpost ?iqi? ?qj?Q-Qpost ?jqj?
Co-PALINDROMES can be recognized with probability
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Complement of language can be recognized with
probability 1
PALINDROMES can be recognized with probability 1