349 research outputs found
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
Decision Problems for Origin-Close Top-Down Tree Transducers
Tree transductions are binary relations of finite trees. For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable. Adding origin semantics to tree transductions, i.e., tagging each output node with the input node it originates from, is a known way to recover decidability for inclusion and equivalence. The origin semantics is rather rigid, in this work, we introduce a similarity measure for transducers with origin semantics and show that we can decide inclusion, equivalence and synthesis problems for origin-close non-deterministic top-down tree transducers
Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers
For a given binary relation of finite trees, we consider the
synthesis problem of deciding whether there is a deterministic
top-down tree transducer that uniformizes the relation, and
constructing such a transducer if it exists. A uniformization of a
relation is a function that is contained in the relation and has the
same domain as the relation. It is known that this problem is
decidable if the relation is a deterministic top-down tree-automatic
relation. We show that it becomes undecidable for general
tree-automatic relations (specified by non-deterministic top-down
tree automata). We also exhibit two cases for which the problem
remains decidable. If we restrict the transducers to be
path-preserving, which is a subclass of linear transducers, then the
synthesis problem is decidable for general tree-automatic
relations. If we consider relations that are finite unions of
deterministic top-down tree-automatic relations, then the problem is
decidable for synchronous transducers, which produce exactly one
output symbol in each step (but can be non-linear)
Determinacy and rewriting of functional topâdown and MSO tree transformations
A query is determined by a view, if the result of the query can be reconstructed from the result of the view. We consider the problem of deciding for two given (functional) tree transformations, whether one is determined by the other. If the view transformation is induced by a tree transducer that may copy, then determinacy is undecidable. For a large class of noncopying views, namely compositions of extended linear topâdown tree transducers, we show that determinacy is decidable, where queries are either deterministic topâdown tree transducers (with regular look-ahead) or deterministic MSO tree transducers. We also show that if a query is determined by a view, then it can be rewritten into a query that works over the view and is in the same class of transducers as the query. The proof relies on the decidability of equivalence for the considered classes of queries, and on their composition closure
Streamability of nested word transductions
We consider the problem of evaluating in streaming (i.e., in a single
left-to-right pass) a nested word transduction with a limited amount of memory.
A transduction T is said to be height bounded memory (HBM) if it can be
evaluated with a memory that depends only on the size of T and on the height of
the input word. We show that it is decidable in coNPTime for a nested word
transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In
this case, the required amount of memory may depend exponentially on the height
of the word. We exhibit a sufficient, decidable condition for a VPT to be
evaluated with a memory that depends quadratically on the height of the word.
This condition defines a class of transductions that strictly contains all
determinizable VPTs
On Functionality of Visibly Pushdown Transducers
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.Comment: 20 page
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