Context-Free Grammars with Storage

TL;DR

This paper introduces context-free grammars with storage, a unified framework that generalizes various formal systems by associating storage objects with nonterminals, and explores their equivalences and language transformations.

Contribution

It formalizes context-free grammars with arbitrary storage types, unifying multiple formalisms and establishing their equivalence to pushdown automata with storage.

Findings

Context-free S grammars generalize many known formalisms.

They are equivalent to pushdown automata with storage.

Deterministic one-way S automaton languages relate to context-free S languages via delta operations.

Abstract

Context-free S grammars are introduced, for arbitrary (storage) type S, as a uniform framework for recursion-based grammars, automata, and transducers, viewed as programs. To each occurrence of a nonterminal of a context-free S grammar an object of type S is associated, that can be acted upon by tests and operations, as indicated in the rules of the grammar. Taking particular storage types gives particular formalisms, such as indexed grammars, top-down tree transducers, attribute grammars, etc. Context-free S grammars are equivalent to pushdown S automata. The context-free S languages can be obtained from the deterministic one-way S automaton languages by way of the delta operations on languages, introduced in this paper.