On multiply-exponential write-once Turing machines

TL;DR

This paper investigates the computational complexity of write-once Turing machines with multiply-exponential bounds, establishing equivalences between space, time, and nondeterministic classes, and analyzing the impact of alternation on these classes.

Contribution

It provides a detailed complexity classification of multiply-exponential write-once Turing machines, including equivalences between various complexity measures and the effects of alternation.

Findings

$k$-DExpWOSpace = $k$-DExpWOTime = $k$-ExpTime

Nondeterministic classes are equivalent to deterministic ones in this setting

Alternating machines have reduced space complexity to $k-1$-ExpSpace

Abstract

In this work we analyze the multiply-exponential complexity classes for write-once Turing machines, i.e. machines that can write to a given tape cell at most once. We show that $k$-DExpWOSpace = $k$-DExpWOTime = $k$-ExpTime and the nondeterministic counterpart. For alternating machines we show that $k$-AExpWOTime = $k$-AExpTime = $k-1$-ExpSpace.