Behaviours of Unary Quantum Automata

Decision problems on unary probabilistic and quantum automata

It is well known that the emptiness problem for binary probabilistic automata and so for quantum automata is undecidable. We present the current status of the emptiness problems for unary probabilistic and quantum automata with connections with Skolem’s and positivity problems. We also introduce the concept of linear recurrence automata in order to show the connection naturally. Then, we also g...

Classical and quantum realtime alternating automata

We present some new results on realtime classical and quantum alternating models. Firstly, we show that the emptiness problem for alternating one-counter automata on unary alphabets is undecidable. Then, we define realtime private alternating finite automata (PAFAs) and show that they can recognize some non-regular unary languages, and the emptiness problem is undecidable for them. Moreover, PA...

Unary Probabilistic and Quantum Automata on Promise Problems

We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present ...

On the Succinctness of Deterministic, Nondeterministic, Probabilistic and Quantum Finite Automata

We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family {Lm} of cyclic languages, where Lm = {a | k ∈ N}. In particular, we show that, for any m, the number of states necessary and sufficient for accepting the unary language Lm with isolated cut point on one-way probabilistic finite automata is p1 1 +p α2 2 + · · ·+ps s , wit...

Events and Languages on Unary Quantum Automata