Model Checking Parse Trees

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.

💡 Research Summary

The paper tackles a problem that lies at the intersection of formal language theory, compiler construction, and computational linguistics: given a context‑free grammar (CFG) G, a word w, and a property expressed in propositional dynamic logic on trees (PDL‑tree), decide whether every parse tree of w according to G satisfies the property. The authors begin by motivating the need for such a verification step. In compilers, certain safety or coding‑style constraints (e.g., every if must have an else) are naturally expressed as global tree properties rather than local grammar rules. In natural‑language processing, linguistic theories often postulate structural constraints (e.g., every noun phrase must dominate a verb phrase) that are not captured by the CFG alone. Yet, to the best of their knowledge, systematic model‑checking of the set of parse trees has not been explored.

To formalize the verification task, the authors adopt propositional dynamic logic on trees. In this setting, tree nodes are states, and the usual PDL modalities ⟨α⟩ and