Minimization of visibly pushdown automata is NP-complete

TL;DR

This paper proves that minimizing visibly pushdown automata is an NP-complete problem by introducing immersions, a concept that recognizes multiple languages with shared transition structures, and reducing the problem to automata minimization.

Contribution

It introduces immersions as a new concept and establishes the NP-completeness of the minimization problem for visibly pushdown automata.

Findings

Minimization of visibly pushdown automata is NP-complete.

Immersions can recognize multiple languages using a shared transition graph.

Reduction from immersions minimization to automata minimization proves NP-completeness.

Abstract

We show that the minimization of visibly pushdown automata is NP-complete. This result is obtained by introducing immersions, that recognize multiple languages (over a usual, non-visible alphabet) using a common deterministic transition graph, such that each language is associated with an initial state and a set of final states. We show that minimizing immersions is NP-complete, and reduce this problem to the minimization of visibly pushdown automata.