New Size Hierarchies for Two Way Automata

TL;DR

This paper introduces a novel nonuniform two-way automaton model with input shuffling, establishing hierarchy and incomparability results for various deterministic, nondeterministic, and probabilistic automata based on state complexity.

Contribution

It presents a new automaton model with input shuffling and provides hierarchy and lower bound results for different automata types.

Findings

Hierarchy results for state complexity in automata models

Incomparability results between different automata classes

Lower bounds based on subfunction counts

Abstract

We introduce a new type of nonuniform two--way automaton that can use a different transition function for each tape square. We also enhance this model by allowing to shuffle the given input at the beginning of the computation. Then we present some hierarchy and incomparability results on the number of states for the types of deterministic, nondeterministic, and bounded-error probabilistic models. For this purpose, we provide some lower bounds for all three models based on the numbers of subfunctions and we define two witness functions.