Masaki Nakanishi, Abuzer Yakaryılmaz
We introduce an affine generalization of counter automata, and analyze their ability as well as affine finite automata. Our contributions are as follows. We show that there is a promise problem that can be solved by exact affine counter automata but cannot be solved by deterministic counter automata. We also show that a certain promise problem, which is conjectured not to be solved by two-way quantum finite automata in polynomial time, can be solved by Las-Vegas affine finite automata in linear time. Lastly, we show that how a counter helps for affine finite automata by showing that the language $ \mathtt{MANYTWINS} $, which is conjectured not to be recognized by affine, quantum or classical finite state models in polynomial time, can be recognized by affine counter automata with one-sided bounded-error in realtime.
arXiv:1703.04281•Jan 1, 2017•0 citations