The Roles of Advice to One-Tape Linear-Time Turing Machines and Finite Automata

TL;DR

This paper explores how different types of advice, especially randomized advice, can significantly enhance the computational power of weak models like one-tape linear-time Turing machines and finite automata.

Contribution

It analyzes the impact of deterministic versus randomized advice on the computational capabilities of weak automata and Turing machines, highlighting the power of randomness.

Findings

Randomized advice greatly increases computational power.

Weak machines with randomized advice surpass those with deterministic advice.

Insights into advice types for computational complexity.

Abstract

We discuss the power and limitation of various "advice," when it is given particularly to weak computational models of one-tape linear-time Turing machines and one-way finite (state) automata. Of various advice types, we consider deterministically-chosen advice (not necessarily algorithmically determined) and randomly-chosen advice (according to certain probability distributions). In particular, we show that certain weak machines can be significantly enhanced in computational power when randomized advice is provided in place of deterministic advice.