Weak and Nested Class Memory Automata

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 they are equivalent to three existing forms of automata over data languages. Further, we show that in the deterministic case they are closed under all Boolean operations, and hence have an ExpSpace-complete equivalence problem. 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.