Real-Time Vector Automata

TL;DR

This paper investigates the computational capabilities of real-time vector automata, which are finite automata enhanced with a vector that is multiplied by matrices at each step, and compares their language recognition power with related automata models.

Contribution

It introduces and analyzes the classes of languages recognized by deterministic, nondeterministic, and blind real-time vector automata, establishing their relationships with multicounter and multiplication automata.

Findings

Deterministic and nondeterministic vector automata recognize distinct language classes.

Blind vector automata have different computational power compared to non-blind versions.

The paper compares these classes with multicounter automata and generalized finite automata.

Abstract

We study the computational power of real-time finite automata that have been augmented with a vector of dimension k, and programmed to multiply this vector at each step by an appropriately selected $k \times k$ matrix. Only one entry of the vector can be tested for equality to 1 at any time. Classes of languages recognized by deterministic, nondeterministic, and "blind" versions of these machines are studied and compared with each other, and the associated classes for multicounter automata, automata with multiplication, and generalized finite automata.