Exact Affine Counter Automata

Abstract

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.Comment: In Proceedings AFL 2017, arXiv:1708.0622

Computational limitations of affine automata and generalized affine automata

“…AfAs and their certain generalizations have been investigated in a series of works by Díaz-Caro and Yakaryılmaz (2016), Villagra and Yakaryılmaz (2018), Belovs et al (2017), Hirvensalo et al (2017), Nakanish et al (2017), Ibrahimov et al (2018). In most of the cases, affine models (e.g., bounded-error and unbouded-error AfAs, zero-error affine OBDDs, zero-error affine counter automata, etc.)…”