Latvian Quantum Finite State Automata for Unary Languages

We design Latvian quantum finite state automata (LQFAs) recognizing unary regular languages with isolated cut point $\frac{1}{2}$. From an architectural viewpoint, we suitably combine two LQFAs recognizing with isolated cut point, respectively, the finite part and the ultimately periodic part any given unary regular language $L$ consists of. In particular, both these LQFAs incorporate a sub-module discriminating strings on the basis of their length.

Both the number of basis states and the isolation around the cut point of the resulting LQFAs for $L$ exponentially depend on the size of the minimal deterministic finite state automaton for $L$. Moreover, the recognition of $L$ tends to becoming deterministic as the number of the basis states employed in the length-discriminating sub-module grows.