# On Store Languages of Language Acceptors

## TL;DR

This paper investigates the store languages of various automata models, showing their regularity, exploring their properties, and applying these findings to prove closure properties and space complexity bounds.

## Contribution

It introduces a unified study of store languages across multiple automata models, identifies their regularity, and applies these results to prove closure properties and complexity bounds.

## Key findings

- Store languages of all examined automata models are regular.
- Connections between store languages of one-way and two-way machines are established.
- A technique for proving closure under right quotient with regular languages is developed.

## Abstract

It is well known that the "store language" of every pushdown automaton -- the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations -- is a regular language. Here many models of language acceptors with various data structures are examined, along with a study of their store languages. For each model, an attempt is made to find the simplest model that accepts their store languages. Some connections between store languages of one-way and two-way machines generally are demonstrated, as with connections between nondeterministic and deterministic machines. A nice application of these store language results is also presented, showing a general technique for proving families accepted by many deterministic models are closed under right quotient with regular languages, resolving some open questions (and significantly simplifying proofs for others that are known) in the literature. Lower bounds on the space complexity for recognizing store languages for the languages to be non-regular are obtained.