One-way finite automata with quantum and classical states
| Authors | |
|---|---|
| Year of publication | 2012 |
| Type | Article in Proceedings |
| Conference | Languages Alive Essays Dedicated to Jürgen Dassow on the Occasion of His 65th Birthday |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.doi.org/10.1007/978-3-642-31644-9_19 |
| Field | Informatics |
| Keywords | One-way finite automata |
| Description | In this paper, we introduce and explore a new model of quantum finite automata (QFA). Namely, one-way finite automata with quantum and classical states (1QCFA), a one way version of two-way finite automata with quantum and classical states (2QCFA) introduced by Ambainis and Watrous in 2002. First, we prove that one-way probabilistic finite automata (1PFA) and one-way quantum finite automata with control language (1QFACL), as well as several other models of QFA, can be simulated by 1QCFA. Afterwards, we explore several closure properties for the family of languages accepted by 1QCFA. Finally, the state complexity of 1QCFA is explored and the main succinctness result is derived. Namely, for any prime m and any \epsilon_{1} > 0, there exists a language L_{m} that cannot be recognized by any measure-many one-way quantum finite automata (MM-1QFA) with bounded error 7/9+\epsilon_{1}, and any 1PFA recognizing it has at last m states, but L_{m} can be recognized by a 1QCFA for any error bound \epsilon > 0 with O(log(m)$ quantum states and 12 classical states. |
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