# Generalizing input-driven languages: theoretical and practical benefits

## TL;DR

This paper explores the theoretical and practical advantages of generalizing input-driven languages, focusing on operator precedence languages, which combine the algebraic and logical properties of regular languages with enhanced parsing capabilities.

## Contribution

It demonstrates that operator precedence languages extend the properties of regular languages, enabling more effective parallel parsing and maintaining desirable algebraic and logical features.

## Key findings

- Operator precedence languages enable more effective parsing parallelization.
- They exhibit algebraic and logic properties similar to regular languages.
- These languages offer practical benefits for automatic verification and real-time recognition.

## Abstract

Regular languages (RL) are the simplest family in Chomsky's hierarchy. Thanks to their simplicity they enjoy various nice algebraic and logic properties that have been successfully exploited in many application fields. Practically all of their related problems are decidable, so that they support automatic verification algorithms. Also, they can be recognized in real-time. Context-free languages (CFL) are another major family well-suited to formalize programming, natural, and many other classes of languages; their increased generative power w.r.t. RL, however, causes the loss of several closure properties and of the decidability of important problems; furthermore they need complex parsing algorithms. Thus, various subclasses thereof have been defined with different goals, spanning from efficient, deterministic parsing to closure properties, logic characterization and automatic verification techniques. Among CFL subclasses, so-called structured ones, i.e., those where the typical tree-structure is visible in the sentences, exhibit many of the algebraic and logic properties of RL, whereas deterministic CFL have been thoroughly exploited in compiler construction and other application fields. After surveying and comparing the main properties of those various language families, we go back to operator precedence languages (OPL), an old family through which R. Floyd pioneered deterministic parsing, and we show that they offer unexpected properties in two fields so far investigated in totally independent ways: they enable parsing parallelization in a more effective way than traditional sequential parsers, and exhibit the same algebraic and logic properties so far obtained only for less expressive language families.