On Functionality of Visibly Pushdown Transducers

TL;DR

This paper proves that checking whether visibly pushdown transducers produce a unique output for each input is decidable in polynomial space, and establishes the complexity of their equivalence problem.

Contribution

It introduces a PSpace decision procedure for functionality and shows that equivalence of functional transducers is Exptime-Complete.

Findings

Functionality is decidable in PSpace.

Equivalence of functional visibly pushdown transducers is Exptime-Complete.

Uses pumping arguments and word combinatorics techniques.

Abstract

Visibly pushdown transducers form a subclass of pushdown transducers that (strictly) extends finite state transducers with a stack. Like visibly pushdown automata, the input symbols determine the stack operations. In this paper, we prove that functionality is decidable in PSpace for visibly pushdown transducers. The proof is done via a pumping argument: if a word with two outputs has a sufficiently large nesting depth, there exists a nested word with two outputs whose nesting depth is strictly smaller. The proof uses technics of word combinatorics. As a consequence of decidability of functionality, we also show that equivalence of functional visibly pushdown transducers is Exptime-Complete.