Beyond Language Equivalence on Visibly Pushdown Automata

TL;DR

This paper investigates the computational complexity of various simulation and equivalence relations on visibly pushdown automata and its subclasses, establishing tight bounds and polynomial-time decidability results.

Contribution

It provides generic methods for complexity analysis and precisely characterizes the complexity of multiple relations on these automata classes, including new lower bounds.

Findings

All relations are EXPTIME-complete on visibly pushdown automata.

Relations are PSPACE-complete on visibly one-counter automata.

Relations are P-complete on visibly BPA.

Abstract

We study (bi)simulation-like preorder/equivalence checking on the class of visibly pushdown automata and its natural subclasses visibly BPA (Basic Process Algebra) and visibly one-counter automata. We describe generic methods for proving complexity upper and lower bounds for a number of studied preorders and equivalences like simulation, completed simulation, ready simulation, 2-nested simulation preorders/equivalences and bisimulation equivalence. Our main results are that all the mentioned equivalences and preorders are EXPTIME-complete on visibly pushdown automata, PSPACE-complete on visibly one-counter automata and P-complete on visibly BPA. Our PSPACE lower bound for visibly one-counter automata improves also the previously known DP-hardness results for ordinary one-counter automata and one-counter nets. Finally, we study regularity checking problems for visibly pushdown automata and show that they can be decided in polynomial time.