---
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 $ {\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.'
author:
- Masaki Nakanishi
- Kamil Khadiev
- 'Krišjānis Prūsis Jevgēnijs Vihrovs Abuzer Yakary[i]{}lmaz'
bibliography:
- 'tcs.bib'
title: 'Exact Affine Counter Automata[^1]'
---

Introduction
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Quantum computation models can be more powerful than their classical counterparts. This is mainly because quantum models are allowed to use negative amplitudes, by which interference can occur between configurations. In order to mimic quantum interference classically, recently a new 