6533b826fe1ef96bd1284597

RESEARCH PRODUCT

Postselection Finite Quantum Automata

Rūsiņš FreivaldsOksana Scegulnaja-dubrovskaLelde Lāce

subject

Discrete mathematicsNested wordTheoretical computer scienceComputer Science::Computational Complexityω-automatonNonlinear Sciences::Cellular Automata and Lattice GasesDeterministic finite automatonDFA minimizationQuantum finite automataAutomata theoryNondeterministic finite automatonComputer Science::Formal Languages and Automata TheoryMathematicsQuantum cellular automaton

description

Postselection for quantum computing devices was introduced by S. Aaronson[2] as an excitingly efficient tool to solve long standing problems of computational complexity related to classical computing devices only. This was a surprising usage of notions of quantum computation. We introduce Aaronson's type postselection in quantum finite automata. There are several nonequivalent definitions of quantumfinite automata. Nearly all of them recognize only regular languages but not all regular languages. We prove that PALINDROMES can be recognized by MM-quantum finite automata with postselection. At first we prove by a direct construction that the complement of this language can be recognized this way. This result distinguishes quantum automata from probabilistic automata because probabilistic finite automata with non-isolated cut-point 0 can recognize only regular languages but PALINDROMES is not a regular language.

https://doi.org/10.1007/978-3-642-13523-1_14