Temporal Logic and Model Checking for Operator Precedence Languages

TL;DR

This paper introduces a new temporal logic tailored for operator precedence languages, enabling automatic verification of properties in a broader class of context-free languages beyond visible-structure languages.

Contribution

It presents a novel temporal logic for operator precedence languages and a procedure to construct automata for property verification, surpassing the expressiveness of existing logics for visible pushdown languages.

Findings

Logic is as expressive as those for visible pushdown languages

Automaton construction is exponential in formula length

Supports verification of more powerful language families

Abstract

In the last decades much research effort has been devoted to extending the success of model checking from the traditional field of finite state machines and various versions of temporal logics to suitable subclasses of context-free languages and appropriate extensions of temporal logics. To the best of our knowledge such attempts only covered structured languages, i.e. languages whose structure is immediately "visible" in their sentences, such as tree-languages or visibly pushdown ones. In this paper we present a new temporal logic suitable to express and automatically verify properties of operator precedence languages. This "historical" language family has been recently proved to enjoy fundamental algebraic and logic properties that make it suitable for model checking applications yet breaking the barrier of visible-structure languages (in fact the original motivation of its inventor Floyd was just to support efficient parsing, i.e. building the "hidden syntax tree" of language sentences). We prove that our logic is at least as expressive as analogous logics defined for visible pushdown languages yet covering a much more powerful family; we design a procedure that, given a formula in our logic builds an automaton recognizing the sentences satisfying the formula, whose size is at most exponential in the length of the formula.