Nominal Automata with Name Deallocation
This work addresses formal modeling of memory management in programming languages, but it is incremental as it extends existing nominal automata models.
The authors tackled the problem of modeling data words with explicit memory allocation and deallocation, common in stateful languages like C, by introducing a nominal automaton model with deallocating transitions. They established a Kleene theorem for equivalence with an expression language and showed that their non-deterministic model allows for determinization, which is unusual in this domain.
Data words with binders formalize concurrently allocated memory. Most name-binding mechanisms in formal languages, such as the $λ$-calculus, adhere to properly nested scoping. In contrast, stateful programming languages with explicit memory allocation and deallocation, such as C, commonly interleave the scopes of allocated memory regions. This phenomenon is captured in dedicated formalisms such as dynamic sequences and bracket algebra, which similarly feature explicit allocation and deallocation of letters. One of the classical formalisms for data languages are register automata, which have been shown to be equivalent to automata models over nominal sets. In the present work, we introduce a nominal automaton model for languages of data words with explicit allocation and deallocation that strongly resemble dynamic sequences, extending existing nominal automata models by adding deallocating transitions. Using a finite NFA-type representation of the model, we establish a Kleene theorem that shows equivalence with a natural expression language. Moreover, we show that our non-deterministic model allows for determinization, a quite unusual phenomenon in the realm of nominal and register automata.