Quantum automata and quantum grammars

To study quantum computation, it might be helpful to generalize structures from language and automata theory to the quantum case. To that end, we prop ose quantum versions of finite-state and push-down automata, and regular an d contest-free grammars. We find analogs of several classical theorems, inc luding pumping lemmas, closure properties, rational and algebraic generatin g functions, and Greibach normal form. We also show that there are quantum context-free languages that are not context-free, so QCFL not equal CFL. (C ) 2000 Elsevier Science B.V. All rights reserved.