Model Checking Parse Trees

TL;DR

This paper explores the use of propositional dynamic logic (PDL) for model-checking parse trees in linguistics and compiler construction, analyzing complexity under various restrictions to improve practical applicability.

Contribution

It demonstrates the suitability of PDL for parse tree model-checking and characterizes the complexity of the problem under natural restrictions.

Findings

Complexity ranges from nondeterministic polynomial time to polynomial space.

Natural restrictions on grammars reduce complexity.

PDL is adequate for model-checking parse trees in applications.

Abstract

Parse trees are fundamental syntactic structures in both computational linguistics and compilers construction. We argue in this paper that, in both fields, there are good incentives for model-checking sets of parse trees for some word according to a context-free grammar. We put forward the adequacy of propositional dynamic logic (PDL) on trees in these applications, and study as a sanity check the complexity of the corresponding model-checking problem: although complete for exponential time in the general case, we find natural restrictions on grammars for our applications and establish complexities ranging from nondeterministic polynomial time to polynomial space in the relevant cases.