Two-Way Visibly Pushdown Automata and Transducers

Automata-logic connections are pillars of the theory of regular languages. Such connections are harder to obtain for transducers, but important results have been obtained recently for word-to-word transformations, showing that the three following models are equivalent: deterministic two-way transducers, monadic second-order (MSO) transducers, and deterministic one-way automata equipped with a finite number of registers. Nested words are words with a nesting structure, allowing to model unranked trees as their depth-first-search linearisations. In this paper, we consider transformations from nested words to words, allowing in particular to produce unranked trees if output words have a nesting structure. The model of visibly pushdown transducers allows to describe such transformations, and we propose a simple deterministic extension of this model with two-way moves that has the following properties: i) it is a simple computational model, that naturally has a good evaluation complexity; ii) it is expressive: it subsumes nested word-to-word MSO transducers, and the exact expressiveness of MSO transducers is recovered using a simple syntactic restriction; iii) it has good algorithmic/closure properties: the model is closed under composition with a unambiguous one-way letter-to-letter transducer which gives closure under regular look-around, and has a decidable equivalence problem

Equivalence Problems for Tree Transducers: A Brief Survey

The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, (2) linear size increase, i.e., MSO definable tree transducers, and (3) monadic input and output ranked alphabets. For the full class of MTTs, decidability of equivalence remains a long-standing open problem.Comment: In Proceedings AFL 2014, arXiv:1405.527

Visibly pushdown transducers with look-ahead

Visibly Pushdown Transducers (VPT) form a subclass of pushdown transducers. In this paper, we investigate the extension of VPT with visibly pushdown look-ahead (VPT la). Their transitions are guarded by visibly pushdown automata that can check whether the well-nested subword starting at the current position belongs to the language they define. First, we show that VPT la are not more expressive than VPT, but are exponentially more succinct. Second, we show that the class of deterministic VPT la corresponds exactly to the class of functional VPT, yielding a simple characterization of functional VPT. Finally, we show that while VPT la are exponentially more succinct than VPT, checking equivalence of functional VPT la is, as for VPT, ExpT-C. As a consequence, we show that any functional VPT is equivalent to an unambiguous one. © 2012 Springer-Verlag.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

Look-ahead removal for total deterministic top-down tree transducers

Algorithms and the Foundations of Software technolog