Nominal Automata with Name Deallocation

2026-03-25

AI Summary

This work addresses the challenge of modeling non-nested scoping in programming languages such as C that support explicit memory allocation and deallocation. It proposes a novel nominal automaton model that, for the first time, incorporates name-deallocation transitions. This model precisely captures data-word languages featuring explicit name allocation and deallocation, and admits effective manipulation via a finite NFA-like representation. The main contributions include establishing the equivalence between the proposed automata and their corresponding regular expressions—thereby proving a Kleene theorem—and demonstrating that the nondeterministic variant is determinizable. These results overcome a fundamental limitation of traditional nominal automata, which cannot handle name deallocation, and provide a new formal framework for static analysis of stateful programming languages.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Cognitive Modeling & Cognitive Systems: Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• nominal automata
• name deallocation
• data words
• memory allocation
• register automata

Innovation

• nominal automata
• name deallocation
• data words with binders
• determinization
• Kleene theorem