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### Decision problems for origin-close top-down tree transducers (full version) [article]

Sarah Winter
2021 arXiv   pre-print
origin-close non-deterministic top-down tree transducers.  ...  For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable.  ...  Decision problems for origin-close transducers We show that the decision problems become decidable for top-down tree transducers with bounded origin distance, see Theorem 16.  ...

### Decision Problems for Origin-Close Top-Down Tree Transducers

Sarah Winter, Filippo Bonchi, Simon J. Puglisi
2021
origin-close non-deterministic top-down tree transducers.  ...  For tree transductions defined by non-deterministic top-down tree transducers, inclusion, equivalence and synthesis problems are known to be undecidable.  ...  Decision problems for origin-close transducers We show that the decision problems become decidable for top-down tree transducers with bounded origin distance, see Theorem 16.  ...

### Decision problems of tree transducers with origin

Emmanuel Filiot, Sebastian Maneth, Pierre-Alain Reynier, Jean-Marc Talbot
2018 Information and Computation
For instance, equivalence of nondeterministic top-down and MSO transducers with origin is decidable. Both problems are undecidable without origin.  ...  With origin, we can decide if a deterministic macro tree transducer can be realized by a deterministic top-down tree transducer; without origin this is an open problem.  ...  We have shown that several important decision problems for tree transducers become decidable in the presence of origin information.  ...

### Decision Problems of Tree Transducers with Origin [chapter]

Emmanuel Filiot, Sebastian Maneth, Pierre-Alain Reynier, Jean-Marc Talbot
2015 Lecture Notes in Computer Science
For instance, equivalence of nondeterministic top-down and MSO transducers with origin is decidable. Both problems are undecidable without origin.  ...  With origin, we can decide if a deterministic macro tree transducer can be realized by a deterministic top-down tree transducer; without origin this is an open problem.  ...  We have shown that several important decision problems for tree transducers become decidable in the presence of origin information.  ...

### The Complexity of the Exponential Output Size Problem for Top-Down and Bottom-Up Tree Transducers,

Frank Drewes
2001 Information and Computation
It is shown to be NL-complete for total top-down tree transducers, DEXPTIME-complete for general top-down tree transducers, and P-complete for bottom-up tree transducers.  ...  The exponential output size problem is to determine whether the size of output trees of a tree transducer grows exponentially in the size of input trees.  ...  Acknowledgement I thank Joost Engelfriet, who told me where to nd the completeness results in 11] and pointed out the related work in 1], as well as Helmut Seidl and an anonymous referee for their careful  ...

### Equivalence Problems for Tree Transducers: A Brief Survey

Sebastian Maneth
2014 Electronic Proceedings in Theoretical Computer Science
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  ...  The decidability of equivalence for three important classes of tree transducers is discussed.  ...  For a top-down tree transducer M and trees s,t with t = M(s), it holds that each node v in the output tree t is produced by one particular node u in s. The latter is called v's origin.  ...

### A strict border for the decidability of E-unification for recursive functions [chapter]

Heinz Faßbender, Sebastian Maneth
1996 Lecture Notes in Computer Science
Acknowledgments We are thankful to Friedrich Otto for pointing out to us the possibility to improve our previous undecidability result by using the modified version of Post's correspondence problem.  ...  We also thank the referees for many helpful comments and suggestions.  ...  2 (Reduction Relation for Top-Down Tree Transducers) Let T = (F, ∆, R) be a top-down tree transducer.  ...

### Uniformization Problems for Tree-Automatic Relations and Top-Down Tree Transducers

Christof Löding, Sarah Winter, Marc Herbstritt
2016 International Symposium on Mathematical Foundations of Computer Science
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  ...  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.  ...  and Top-Down Tree Transducers uniformization problem for deterministic top-down tree relations was reduced to deciding the winner in a safety game.  ...

### A Survey on Decidable Equivalence Problems for Tree Transducers

Sebastian Maneth
2015 International Journal of Foundations of Computer Science
Top-down tree transducers generalize to trees the finite state (string) transducers (also known as "generalized sequential machines", or gsms, see [47, 9] ).  ...  transducer of Rounds and Thatcher [72, 81] . (1) In terms of the context-free tree grammar, the derivation of the grammar is (top-down) controlled by a given input tree (see [27] for the idea of grammars  ...  Acknowledgements I wish to thank Joost Engelfriet and the anonymous referee for many helpful comments on a previous version of this paper.  ...

### Symbolic Tree Transducers [chapter]

Margus Veanes, Nikolaj Bjørner
2012 Lecture Notes in Computer Science
We examine key closure properties of Symbolic Tree Transducers and we develop a composition algorithm and an equivalence decision procedure for linear single-valued transducers.  ...  Our notions regarding tree transducers are consistent with [15] . For finite state (string) transducers a brief introduction is given in [36] .  ...  However, a generalization to the finite-valued case is not expected to be straightforward, because the corresponding generalization of decidability of equivalence for finite-valued tree transducers [31  ...

### Synthesis of Deterministic Top-down Tree Transducers from Automatic Tree Relations

Christof Löding, Sarah Winter
2014 Electronic Proceedings in Theoretical Computer Science
We provide decision procedures for both bounded and arbitrary delay that yield deterministic top-down tree transducers which realize the specification for valid input trees.  ...  We consider the case of specifications that are deterministic top-down tree automatic, meaning the specification is recognizable by a deterministic top-down tree automaton that reads the two given trees  ...  If uniformization is possible, our decision procedure yields a top-down tree transducer that realizes the specification.  ...

### The Power of Extended Top-Down Tree Transducers

Andreas Maletti, Jonathan Graehl, Mark Hopkins, Kevin Knight
2009 SIAM journal on computing (Print)
In addition, it is shown that most interesting classes of transformations computed by extended top-down tree transducers are not closed under composition.  ...  Extended top-down tree transducers (transducteurs généralisés descendants [Arnold, Dauchet: Bi-transductions de forêts. ICALP'76.  ...  To address these drawbacks, a generalization of top-down tree transducers, called extended top-down tree transducers, was originally conceived by [25] and has been further pursued by [6, 1, 18, 21]  ...

### Capturing practical natural language transformations

Kevin Knight
2007 Machine Translation
For several variations of finite-state string and tree transducers, we survey answers to formal questions about their expressiveness, modularity, teachability, and generalization.  ...  We study automata for capturing the transformations in practical natural language processing systems, especially those that translate between human languages.  ...  The class of non-copying, non-deleting transducers is called LNT (L for linear, N for non-deleting, T for top-down).  ...

### Which DTDs are streaming bounded repairable?

Pierre Bourhis, Gabriele Puppis, Cristian Riveros
2013 Proceedings of the 16th International Conference on Database Theory - ICDT '13
In fact, we show the decidability of a more general problem, allowing a more general class of schemas than DTDs, and requiring a repair procedure that works only for documents that are already known to  ...  We show that this problem is decidable.  ...  We would like to thank Michael Benedikt for the many helpful remarks on the paper.  ...

### Automata for XML—A survey

Thomas Schwentick
2007 Journal of computer and system sciences (Print)
Automata play an important role for the theoretical foundations of XML data management, but also in tools for various XML processing tasks.  ...  Acknowledgments The author warmly thanks Joost Engelfriet, Christoph Koch, Sebastian Maneth, Wim Martens, Maarten Marx, Frank Neven, and Volker Weber and two anonymous for very many valuable suggestions  ...  They also produce output in a top-down fashion and, like top-down transducers, they traverse the input tree top-down.  ...
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