Operator Precedence \omega-languages

TL;DR

This paper introduces operator precedence -languages ( OPLs) for -languages, extending their analysis to infinite words, exploring acceptance criteria, closure properties, and demonstrating their increased expressiveness and utility in verification.

Contribution

The paper defines  OPLs for -languages, investigates their properties, and shows their advantages over smaller classes in expressiveness and verification.

Findings

 OPLs strictly include VPLs.

 OPLs have robust closure properties.

Application examples demonstrate enhanced expressiveness.

Abstract

\omega-languages are becoming more and more relevant nowadays when most applications are 'ever-running'. Recent literature, mainly under the motivation of widening the application of model checking techniques, extended the analysis of these languages from the simple regular ones to various classes of languages with 'visible syntax structure', such as visibly pushdown languages (VPLs). Operator precedence languages (OPLs), instead, were originally defined to support deterministic parsing and, though seemingly unrelated, exhibit interesting relations with these classes of languages: OPLs strictly include VPLs, enjoy all relevant closure properties and have been characterized by a suitable automata family and a logic notation. In this paper we introduce operator precedence \omega-languages (\omega OPLs), investigating various acceptance criteria and their closure properties. Whereas some properties are natural extensions of those holding for regular languages, others required novel investigation techniques. Application-oriented examples show the gain in expressiveness and verifiability offered by \omega OPLs w.r.t. smaller classes.