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The Copying Power of One-State Tree Transducers

Joost Engelfriet
1978 DAIMI Report Series  
One-state deterministic top-down transducers (or tree homomorphisms) cannot handle "prime copying", i.e. their class of output (string) languages is not closed under the operation L ( -> { (w)^f(n)  ...  The exact amount of nonclosure under these copying operations is established for several classes of input (tree) languages.  ...  In this paper we investigate the copying power of one-state top-down tree transducers and (multi-state) bottom-up tree transducers with respect to these copying operations.  ... 
doi:10.7146/dpb.v7i91.6507 fatcat:bibexwgy4vayhocpgoy3e7h5vi

The copying power of one-state tree transducers

Joost Engelfriet, Sven Skyum
1982 Journal of computer and system sciences (Print)  
One-state deterministic top-down tree transducers (or, tree homomorphisms) cannot handle "prime copying," i.e., their class of output (string) languages is not closed under the operation L --) {$(w%~'"  ...  The exact amount of nonclosure under these copying operations is established for several classes of input (tree) languages.  ...  In this paper we investigate the copying power of one-state top-down tree transducers and (multi-state) bottom-up tree transducers with respect to these copying operations.  ... 
doi:10.1016/0022-0000(82)90019-8 fatcat:4756bt2l5rbzpawech2ntieavq

Page 392 of Computational Linguistics Vol. 34, Issue 3 [page]

2008 Computational Linguistics  
Many of these composition results are first found in Engelfriet (1975). The power of T to change the structure of an input tree is surprising.  ...  At each point in the top-down traversal, the transducer chooses a produc- tion to apply, based only on the current state and the current root symbol.  ... 

An Overview of Probabilistic Tree Transducers for Natural Language Processing [chapter]

Kevin Knight, Jonathan Graehl
2005 Lecture Notes in Computer Science  
Trees Despite the attractive computational properties of finite-state tools, no one is particularly fond of their representational power for natural language.  ...  The statistical machine translation model of [9] implemented with a cascade of standard finite-state transducers [8].  ...  -D: Deterministic transducer, with a maximum of one production per <state, sym-bol> pair. -T: Total transducer, with a minimum of one production per <state, symbol> pair.  ... 
doi:10.1007/978-3-540-30586-6_1 fatcat:opmc54t5uzbnllkwhyh5hqeyta

Tree transducers, L systems, and two-way machines

Joost Engelfriet, Grzegorz Rozenberg, Giora Slutzki
1980 Journal of computer and system sciences (Print)  
Restrictions on the "copying power" of these devices endow them with rich structuring and give insight into the issues of determinism, parallelism, and copying.  ...  automaton, the two-way finite-state transducer, and (generalizations of) the one-way checking stack automaton.  ...  It should be clear that the number of states of a topdown tree transducer (the number of "active" symbols of an ETOL system) is directly related to its "copying power."  ... 
doi:10.1016/0022-0000(80)90058-6 fatcat:ldgh73slincnfpvowc6mfqrbp4

Linear deterministic multi bottom-up tree transducers

Zoltán Fülöp, Armin Kühnemann, Heiko Vogler
2005 Theoretical Computer Science  
In this paper we focus on the class ld-MBOT of tree transformations which are computed by linear deterministic multi bottom-up tree transducers.  ...  If deterministic top-down tree transducers are extended by the capability to recognize regular tree properties and deterministic bottom-up tree transducers are generalized by allowing states with arbitrary  ...  Acknowledgements We would like to thank the referees for their helpful comments; in particular, one of the referees indicated how to shorten the paper considerably.  ... 
doi:10.1016/j.tcs.2005.07.025 fatcat:asc5e7xmyjcq7p6u5sug7fpgq4

Tiburon: A Weighted Tree Automata Toolkit [chapter]

Jonathan May, Kevin Knight
2006 Lecture Notes in Computer Science  
The availability of weighted finite-state string automata toolkits made possible great advances in natural language processing.  ...  To combat this problem, we introduce a weighted finite-state tree automata toolkit, which incorporates recent developments in weighted tree automata theory and is useful for natural language applications  ...  As seen above, the image of a tree onto a tree-to-tree transducer is a wRTG. The image of a tree onto a tree-to-string transducer is a wCFG, currently represented in Tiburon as a one-state wRTG.  ... 
doi:10.1007/11812128_11 fatcat:pfdxcnllmfdepotrv2hn2bmar4

Compositions of extended top-down tree transducers

Andreas Maletti
2008 Information and Computation  
More precisely, it constitutes the composition closure of the class of transformations computed by finite-copying top-down tree transducers.  ...  The class of transformations computed by the latter device is shown to be closed under composition, and to be included in the composition of the class of transformations computed by top-down tree transducers  ...  Acknowledgments The author is grateful to the anonymous referees for their insightful remarks on the draft version of the paper. Especially one referee improved the presentation dramatically.  ... 
doi:10.1016/j.ic.2008.03.019 fatcat:5x3hertfc5b3nkerfryyorrjve

Typechecking Top-Down Uniform Unranked Tree Transducers [chapter]

Wim Martens, Frank Neven
2002 Lecture Notes in Computer Science  
We focus on simple top-down recursive transformations motivated by XSLT and structural recursion on trees.  ...  As typechecking quickly turns undecidable for query languages capable of testing equality of data values, we return to the limited framework where we abstract XML documents as labeled ordered trees.  ...  In the construction, we exploit the copying power of transducers to make n copies of the input tree: one for each A i .  ... 
doi:10.1007/3-540-36285-1_5 fatcat:tqikbk5yrrdsxl6g7ow44ejtgy

Three hierarchies of transducers

Joost Engelfriet
1981 Mathematical Systems Theory  
Composition of top-down tree transducers yields a proper hierarchy of transductions and of output languages.  ...  The same is true for ETOL systems (viewed as transducers) and for two-way generalized sequential machines.  ...  Acknowledgments I wish to thank Giora Slutzki for many days of stimulating discussions. I thank the referee for careful reading of the paper and for helpful suggestions.  ... 
doi:10.1007/bf01786975 fatcat:adpmfrqjajbkbcteugtaluvolu

Frontiers of tractability for typechecking simple XML transformations

Wim Martens, Frank Neven
2007 Journal of computer and system sciences (Print)  
Typechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type.  ...  We focus on complete algorithms which always produce the correct answer.  ...  Acknowledgment We thank Giorgio Ghelli for raising the question about the complexity of typechecking in the setting of a fixed output schema. We thank Dirk Leinders, Thomas Schwentick, and  ... 
doi:10.1016/j.jcss.2006.10.005 fatcat:svotzzqmfjcbnpae3mjbyaiicu

Frontiers of tractability for typechecking simple XML transformations

Wim Martens, Frank Neven
2004 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '04  
Typechecking consists of statically verifying whether the output of an XML transformation is always conform to an output type for documents satisfying a given input type.  ...  We focus on complete algorithms which always produce the correct answer.  ...  Acknowledgment We thank Giorgio Ghelli for raising the question about the complexity of typechecking in the setting of a fixed output schema. We thank Dirk Leinders, Thomas Schwentick, and  ... 
doi:10.1145/1055558.1055563 dblp:conf/pods/MartensN04 fatcat:zt4zz55nirdo3ltg5wff3rvgsi

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.  ...  For example, it appears that bottom-up transducers are not expressive, even with copying and deleting power.  ... 
doi:10.1007/s10590-008-9039-0 fatcat:vdaipnawzjhoxeuv5pzegujjma

XML transformation by tree-walking transducers with invisible pebbles

Joost Engelfriet, Hendrik Jan Hoogeboom, Bart Samwel
2007 Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS '07  
The pebble tree automaton and the pebble tree transducer are enhanced by additionally allowing an unbounded number of 'invisible' pebbles (as opposed to the usual 'visible' ones).  ...  The resulting pebble tree transducers can apply arbitrary MSO definable tests to (the observable part of) their configurations, they (still) have a decidable typechecking problem, and they can model the  ...  transducer starts a copy in state q in every node v that satisfies ψ(u, v), see the construction in the proof of Lemma 19.  ... 
doi:10.1145/1265530.1265540 dblp:conf/pods/EngelfrietHS07 fatcat:lmeteupkabb65h5zpqnzbhvsbi

Tree Transducers and Tree Compressions [chapter]

Sebastian Maneth, Giorgio Busatto
2004 Lecture Notes in Computer Science  
A more powerful way of tree compression is to allow the sharing of tree patterns, i.e., internal parts of the tree.  ...  The resulting "sharing graph" is at most double-exponentially smaller than the original tree. Consider a macro tree transducer and an input tree s.  ...  The first author is grateful to Markus Lohrey for providing many useful references, and in particular for the introduction to the concept of sharing graphs.  ... 
doi:10.1007/978-3-540-24727-2_26 fatcat:7tzr7rrdyjf5lny7i2pdzilyqq
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