Quantum and probabilistic finite multitape automata Ginta Garkaje and Rusins Freivalds Riga, Latvia

First, we discuss the following 2-tape language L 1 = {(0 n 1 m,2 k )| n=m=k } Theorem. The language L 1 can be recognized with arbitrary probability 1-ε by a probabilistic 2-tape finite automaton. 2n + 3m = 5k 3n + 6m = 9k 2n + 9m = 11k SOFSEM 2009

Theorem. There exists no quantum finite 2-tape automaton which recognizes the language L 41 with bounded error. For arbitrary positive ε, there exists a probabilistic finite 2-tape automaton recognizing the language L 41 with a probability 1-ε. There exists no probabilistic finite 2-tape automaton which recognizes language L 42 with a bounded error. There exists a quantum finite 2-tape automaton recognizing the language L 42 with a probability 1-ε. SOFSEM 2009 } are binary words and either x=y or y=z but not both of them.}

Theorem. For arbitrary r, there exists a quantum finite 2-tape automaton recognizing the language L 43 with the probability 1. For arbitrary r, there exists no quantum finite 2-tape automaton with 2 Ω(r/log r) states which recognizes the language L 43 with abounded error. For arbitrary r, and for arbitrary positive ε there exists a probabilistic finite 2-tape automaton with const. r states recognizing the language L 43 with probability 1- ε. Theorem. For arbitrary r, there exists quantum finite 2-tape automaton with 2 Ω(r/log r) states which recognizes the language L 44 with the probability 1. For arbitrary r, there exists no probabilistic finite 2-tape automaton with 2 Ω(r/log r) states which recognizes the language L 44 with the probability 1. SOFSEM 2009 }