Homing Vector Automata

TL;DR

This paper introduces homing vector automata, a new computational model combining finite automata with vector transformations, analyzing their capabilities and comparing different variants, along with a generalized string encoding method.

Contribution

The paper presents the concept of homing vector automata, explores their computational properties, and develops a generalized Stern-Brocot encoding for arbitrary alphabets.

Findings

Homing vector automata have distinct computational powers based on their variants.

Deterministic and nondeterministic versions exhibit different acceptance capabilities.

A generalized encoding method extends string representation to arbitrary alphabets.

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 and properties of deterministic, nondeterministic, blind, non-blind, real-time and one-way versions of these 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.