Weak and Nested Class Memory Automata

TL;DR

This paper introduces a restriction called weakness to Class Memory Automata (CMA), making the emptiness problem equivalent to Petri Net Coverability, and extends CMA to nested data with decidable emptiness under this restriction.

Contribution

It identifies the weakness restriction in CMA, establishes its computational properties, and extends CMA to nested data with decidability results.

Findings

Weak CMA emptiness is equivalent to Petri Net Coverability.

Deterministic weak CMA are closed under all Boolean operations.

Weakness constraint recovers decidability for nested data CMA.

Abstract

Automata over infinite alphabets have recently come to be studied extensively as potentially useful tools for solving problems in verification and database theory. One popular model of automata studied is the Class Memory Automata (CMA), for which the emptiness problem is equivalent to Petri Net Reachability. We identify a restriction - which we call weakness - of CMA, and show that their emptiness problem is equivalent to Petri Net Coverability. Further, we show that in the deterministic case they are closed under all Boolean operations. We clarify the connections between weak CMA and existing automata over data languages. We also extend CMA to operate over multiple levels of nested data values, and show that while these have undecidable emptiness in general, adding the weakness constraint recovers decidability of emptiness, via reduction to coverability in well-structured transition systems. We also examine connections with existing automata over nested data.