Inkdots as advice for finite automata

TL;DR

This paper explores the use of inkdots as advice for finite automata, revealing an infinite hierarchy of language classes, effects on machine succinctness, and advantages of randomness and extended memory.

Contribution

It introduces inkdots as advice, establishes a hierarchy of recognized languages, and compares deterministic and probabilistic models with extended memory.

Findings

Infinite hierarchy of language classes with increasing inkdots

Random inkdots outperform deterministic advice in probabilistic automata

Small space with secondary memory becomes significantly useful

Abstract

We examine inkdots placed on the input string as a way of providing advice to finite automata, and establish the relations between this model and the previously studied models of advised finite automata. The existence of an infinite hierarchy of classes of languages that can be recognized with the help of increasing numbers of inkdots as advice is shown. The effects of different forms of advice on the succinctness of the advised machines are examined. We also study randomly placed inkdots as advice to probabilistic finite automata, and demonstrate the superiority of this model over its deterministic version. Even very slowly growing amounts of space can become a resource of meaningful use if the underlying advised model is extended with access to secondary memory, while it is famously known that such small amounts of space are not useful for unadvised one-way Turing machines.