Exact affine counter automata

© F. Blanchet-Sadri & S. Osborne. 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 language that can be recognized by exact realtime affine counter automata but by neither 1-way deterministic pushdown automata nor realtime deterministic k-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. Lastly, we show that how a counter helps for affine finite automata by showing that the language 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

Error-free affine, unitary, and probabilistic OBDDS

© IFIP International Federation for Information Processing 2018. We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata versions of these models

On the computational power of affine automata

International audienceWe investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case. Moreover, we address to the question of [4] by showing that any affine language can be recognized by an AfA with certain limitation on the entries of affine states and transition matrices. Lastly, we present the first languages shown to be not recognized by AfAs with bounded-error