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Superiority of one-way and realtime quantum machines∗∗∗

Published online by Cambridge University Press:  08 October 2012

Abuzer Yakaryılmaz
Abuzer Yakaryılmaz*
Affiliation:
University of Latvia, Faculty of Computing, Raina bulv. 19, LV-1586 Rīga, Latvia. abuzer@lu.lv
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Abstract

In automata theory, quantum computation has been widely examined for finite statemachines, known as quantum finite automata (QFAs), and less attention has been given toQFAs augmented with counters or stacks. In this paper, we focus on such generalizations ofQFAs where the input head operates in one-way or realtime mode, and present some newresults regarding their superiority over their classical counterparts. Our first result isabout the nondeterministic acceptance mode: Each quantum model architecturallyintermediate between realtime finite state automaton and one-way pushdown automaton(one-way finite automaton, realtime and one-way finite automata with one-counter, andrealtime pushdown automaton) is superior to its classical counterpart. The second andthird results are about bounded error language recognition: for anyk > 0, QFAs with k blind counters outperform theirdeterministic counterparts; and, a one-way QFA with a single head recognizes an infinitefamily of languages, which can be recognized by one-way probabilistic finite automata withat least two heads. Lastly, we compare the nondeterminictic and deterministic acceptancemodes for classical finite automata with k blind counter(s), and we showthat for any k > 0, the nondeterministic models outperform thedeterministic ones.

Keywords

Quantum computationquantum automatablind counter automatamultihead finite automatanondeterminismbounded error
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 4: Special Issue: Non-Classical Models ofAutomata and Applications III (NCMA-2011) , October 2012 , pp. 615 - 641
Copyright
© EDP Sciences 2012

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