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Quantum Automata and Quantum Grammars

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Abstract

To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we propose quantum versions of finite-state and push-down automata, and regular and context-free grammars. We find analogs of several classical theorems, including pumping lemmas, closure properties, rational and algebraic generating functions, and Greibach normal form. We also show that there are quantum context-free languages that are not context-free.

Suggested Citation

  • Cristopher Moore & James P. Crutchfield, 1997. "Quantum Automata and Quantum Grammars," Working Papers 97-07-062, Santa Fe Institute.
    • Handle: RePEc:wop:safiwp:97-07-062
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