Affine computation and affine automaton

TL;DR

This paper introduces affine computation, a classical model inspired by quantum mechanics, and demonstrates its superior power over existing probabilistic and quantum automata in various language recognition modes.

Contribution

It defines affine finite automata and compares their computational power with quantum and probabilistic automata, showing their advantages in certain error modes.

Findings

AfAs outperform QFAs and PFAs with bounded and unbounded error.

AfAs are more powerful than PFAs in nondeterministic mode.

AfAs are equivalent to QFAs in nondeterministic computation.

Abstract

We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it with quantum and probabilistic finite automata (QFA and PFA, respectively) with respect to three basic language recognition modes. We show that, in the cases of bounded and unbounded error, AfAs are more powerful than QFAs and PFAs, and, in the case of nondeterministic computation, AfAs are more powerful than PFAs but equivalent to QFAs.