Complexity of Membership and Non-Emptiness Problems in Unbounded Memory Automata

TL;DR

This paper compares the complexity of membership and non-emptiness problems across three unbounded memory automata models, revealing NP-completeness for membership and varying non-emptiness complexities.

Contribution

It establishes the NP-completeness of membership problems and determines the non-emptiness complexity classes for nu-automata, Layered Memory Automata, and History-Register Automata.

Findings

Membership problem is NP-complete for all models.

Non-emptiness is Ackermann-complete for HRA.

Non-emptiness is PSPACE-complete for nu-automata.

Abstract

We study the complexity relationship between three models of unbounded memory automata: nu-automata ($\nu$-A), Layered Memory Automata (LaMA)and History-Register Automata (HRA). These are all extensions of finite state automata with unbounded memory over infinite alphabets. We prove that the membership problem is NP-complete for all of them, while they fall into different classes for what concerns non-emptiness. The problem of non-emptiness is known to be Ackermann-complete for HRA, we prove that it is PSPACE-complete for $\nu$-A.