Quantum automata and quantum grammars
Theoretical Computer Science
Introduction to the Theory of Computation
Introduction to the Theory of Computation
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
1-way quantum finite automata: strengths, weaknesses and generalizations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Quantum computing: 1-way quantum automata
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Hierarchy and equivalence of multi-letter quantum finite automata
Theoretical Computer Science
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The regular language (a+b)*a (the words in alphabet {a, b} having a as the last letter) is at the moment a classical example of a language not recognizable by a one-way quantum finite automaton (QFA). Up to now, there have been introduced many different models of QFAs, with increasing capabilities, but none of them can cope with this language. We introduce a new, quite simple modification of the QFA model (actually even a deterministic reversible FA model) which is able to recognize this language. We also completely characterise the set of languages recognizable by the new model FAs, by finding a "forbidden construction" whose presence or absence in the minimal deterministic (not necessarily reversible) finite automaton of the language decides the recognizability. Thus, the new model still cannot recognize the whole set of regular languages, however it enhances the understanding of what can be done in a finite-state real-time quantum process.