Homing Vector Automata

TL;DR

This paper introduces homing vector automata, a new class of automata with vector transformations, analyzes their computational power, and develops a generalized string encoding method for arbitrary alphabets.

Contribution

It defines homing vector automata, compares their computational capabilities, and extends the Stern-Brocot encoding for broader alphabet representation.

Findings

Deterministic, nondeterministic, and blind versions are analyzed and compared.

Homing vector automata can recognize certain languages beyond traditional automata.

A generalized encoding method for arbitrary alphabets is developed.

Abstract

We introduce homing vector automata, which are finite automata augmented by a vector that is multiplied at each step by a matrix determined by the current transition, and have to return the vector to its original setting in order to accept the input. The computational power of the deterministic, nondeterministic and blind versions of these real-time machines are examined and compared to various related types of automata. A generalized version of the Stern-Brocot encoding method, suitable for representing strings on arbitrary alphabets, is also developed.