376 research outputs found
Logical and Algebraic Characterizations of Rational Transductions
Rational word languages can be defined by several equivalent means: finite
state automata, rational expressions, finite congruences, or monadic
second-order (MSO) logic. The robust subclass of aperiodic languages is defined
by: counter-free automata, star-free expressions, aperiodic (finite)
congruences, or first-order (FO) logic. In particular, their algebraic
characterization by aperiodic congruences allows to decide whether a regular
language is aperiodic.
We lift this decidability result to rational transductions, i.e.,
word-to-word functions defined by finite state transducers. In this context,
logical and algebraic characterizations have also been proposed. Our main
result is that one can decide if a rational transduction (given as a
transducer) is in a given decidable congruence class. We also establish a
transfer result from logic-algebra equivalences over languages to equivalences
over transductions. As a consequence, it is decidable if a rational
transduction is first-order definable, and we show that this problem is
PSPACE-complete
The Equivalence Problem for Deterministic MSO Tree Transducers is Decidable
It is decidable for deterministic MSO definable graph-to-string or
graph-to-tree transducers whether they are equivalent on a context-free set of
graphs
Deciding Equivalence of Linear Tree-to-Word Transducers in Polynomial Time
We show that the equivalence of deterministic linear top-down tree-to-word
transducers is decidable in polynomial time. Linear tree-to-word transducers
are non-copying but not necessarily order-preserving and can be used to express
XML and other document transformations. The result is based on a partial normal
form that provides a basic characterization of the languages produced by linear
tree-to-word transducers.Comment: short version of this paper will be published in the proceedings of
the 20th Conference on Developments in Language Theory (DLT 2016), Montreal,
Canad
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 Equivalence and Uniformisation Problems for Finite Transducers
Transductions are binary relations of finite words. For rational transductions, i.e., transductions defined by finite transducers, the inclusion, equivalence and sequential uniformisation problems are known to be undecidable. In this paper, we investigate stronger variants of inclusion, equivalence and sequential uniformisation, based on a general notion of transducer resynchronisation, and show their decidability. We also investigate the classes of finite-valued rational transductions and deterministic rational transductions, which are known to have a decidable equivalence problem. We show that sequential uniformisation is also decidable for them
The many facets of string transducers
Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning. They were already considered in early papers of formal language theory, but turned out to be much more challenging. The last decade brought considerable research around various transducer models, aiming to achieve similar robustness as for automata and languages. In this paper we survey some older and more recent results on string transducers. We present classical connections between automata, logic and algebra extended to transducers, some genuine definability questions, and review approaches to the equivalence problem
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
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