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Definability Results for Top-Down Tree Transducers [article]

Sebastian Maneth, Helmut Seidl, Martin Vu
2021 arXiv   pre-print
We prove that for a given deterministic top-down transducer with look-ahead it is decidable whether or not its translation is definable (1)~by a linear top-down tree transducer or (2)~by a tree homomorphism  ...  We present algorithms that construct equivalent such transducers if they exist.  ...  Note that the result of Engelfriet [4] shows that for any composition of nondeterministic top-down and bottom-up transducers that is functional, an equivalent deterministic top-down tree transducer with  ... 
arXiv:2105.14860v1 fatcat:47eg2yn5drc5pmxugmowdwtngy

Undecidable properties of deterministic top-down tree transducers

Z. Fülöp
1994 Theoretical Computer Science  
Decidability questions concerning ranges of deterministic top-down tree transducers are considered.  ...  It is shown that the following nine problems are undecidable, for ranges L1 a of arbitrary two deterministic, nondeleting and finite copying top-down tree transducers: I Correspondence to: Z. Fiiliip,  ...  Acknowledgement The author is grateful to the referee for his careful reviewing, valuable comments and especially for discovering a flaw in the first version of Theorem 5.2.  ... 
doi:10.1016/0304-3975(94)90241-0 fatcat:2r7kg7caibcfddv7gzbvqlsczq

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.  ...  We define the top-down tree transducer M 1 = ({q 0 , . . . , q n }, Σ, Σ ∪ {δ (n) }, q 0 , R).  ... 
doi:10.4204/eptcs.151.5 fatcat:bso3z5x5tjgy5fnx5anekyudei

A Survey on Decidable Equivalence Problems for Tree Transducers

Sebastian Maneth
2015 International Journal of Foundations of 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  ...  Top-down tree transducers generalize to trees the finite state (string) transducers (also known as "generalized sequential machines", or gsms, see [47, 9] ).  ...  Acknowledgements I wish to thank Joost Engelfriet and the anonymous referee for many helpful comments on a previous version of this paper.  ... 
doi:10.1142/s0129054115400134 fatcat:5wxybcc6xjbvdg43rgst5c4r5a

Tree transductions and families of tree languages

Brenda S. Baker
1973 Proceedings of the fifth annual ACM symposium on Theory of computing - STOC '73  
The rule-schemes in R generate a set of r%les S. defined as follows. If M is a top- down transducer, then define Range(X) -Z,. If is a bottom-up transducer~ define Range(X) - A,.  ...  bottom-up transducer which cannot be done by any top-down transducer, and vice versa.  ... 
doi:10.1145/800125.804051 dblp:conf/stoc/Baker73 fatcat:ddfwro7lnjdmjb7aw3vmxonu4y

Decision problems of tree transducers with origin

Emmanuel Filiot, Sebastian Maneth, Pierre-Alain Reynier, Jean-Marc Talbot
2018 Information and Computation  
[24, 23] , top-down tree-to-string transducers [11] , and mso definable tree-to-string transducers (see, e.g., [10] ).  ...  For instance, equivalence of nondeterministic top-down and MSO transducers with origin is decidable. Both problems are undecidable without origin.  ...  Tree-to-String Translations with Origin A top-down tree-to-string transducer (ytop for short) M is a tuple (Q, Σ, ∆, q 0 , R) where Q, q 0 , Σ are defined as for top-down tree transducers, ∆ is an alphabet  ... 
doi:10.1016/j.ic.2018.02.011 fatcat:umcrctauyzd6xgqyb2jfsse3ba

Decision Problems of Tree Transducers with Origin [chapter]

Emmanuel Filiot, Sebastian Maneth, Pierre-Alain Reynier, Jean-Marc Talbot
2015 Lecture Notes in Computer Science  
[24, 23] , top-down tree-to-string transducers [11] , and mso definable tree-to-string transducers (see, e.g., [10] ).  ...  For instance, equivalence of nondeterministic top-down and MSO transducers with origin is decidable. Both problems are undecidable without origin.  ...  Tree-to-String Translations with Origin A top-down tree-to-string transducer (ytop for short) M is a tuple (Q, Σ, ∆, q 0 , R) where Q, q 0 , Σ are defined as for top-down tree transducers, ∆ is an alphabet  ... 
doi:10.1007/978-3-662-47666-6_17 fatcat:bpl3ttlxmzdpxmbbpes3i6fiwm

On Domain and Range Tree Languages of Superlinear Deterministic Top-down Tree Transformations

Gábor Dányi
1996 Acta Cybernetica  
Denote by sl-DT the class of superlinear deterministic top-down tree transformations, by REC the class of recognizable tree languages, and by DREC the class of deterministic recognizable tree languages  ...  The class dom(sl-DT) is exactly the class of tree languages recognized by semi-universal deterministic top-down tree recognizers, which are introduced in this paper.  ...  The author is grateful to Zoltán Fülöp for his valuable suggestions regarding the result of Section 4.  ... 
dblp:journals/actaC/Danyi96 fatcat:exmjg3yfgnfmpd4y2ojl6uhmcu

The Power of Tree Series Transducers of Type I and II [chapter]

Andreas Maletti
2005 Lecture Notes in Computer Science  
On the other hand, polynomial OI tree series transducers of type I and II and top-down OI tree series transducers are equally powerful.  ...  The power of tree series transducers of type I and II is studied for IO as well as OI tree series substitution.  ...  One referee raised the question of effectiveness of the constructions when the involved tree representations are not polynomial.  ... 
doi:10.1007/11505877_30 fatcat:2s3oq5lbwnhlbnjq37gsdxakwy

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.  ...  The class of relations definable by ↓TTs is called the class of top-down tree transformations. We consider two restricted types of top-down tree transducers.  ... 
doi:10.4230/lipics.mfcs.2016.65 dblp:conf/mfcs/LodingW16 fatcat:its6yse2xnccresnpn3uu4ihce

Page 1062 of Mathematical Reviews Vol. , Issue 91B [page]

1991 Mathematical Reviews  
In this paper we consider iterated deterministic top- down look-ahead for deterministic top-down tree transducers in the following sense.  ...  In Section 4, we define the concept of the iterated deterministic top-down look-ahead for deterministic top-down tree transducers and prove that the iteration hierarchy is strict with re- spect to recognizing  ... 

Page 3770 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
Summary: “We generalize bottom-up tree transducers and top- down tree transducers to the concept of bottom-up tree series transducer and top-down tree series transducer, respectively, by allowing formal  ...  Moreover, we show that certain fundamental constructions and re- sults concerning bottom-up and top-down tree transducers can be generalized for the corresponding tree series transducers.  ... 

On the Expressiveness of Deterministic Transducers over Infinite Trees [chapter]

Thomas Colcombet, Christof Löding
2004 Lecture Notes in Computer Science  
We introduce top-down deterministic transducers with rational lookahead (transducer for short) working on infinite terms.  ...  We show that for such a transducer e T , there exists an MSO-transduction T such that for any graph G, unfold(T (G)) = e T (unfold (G)).  ...  We describe in the present paper a similar theory for top-down tree transducers, but working on infinite terms.  ... 
doi:10.1007/978-3-540-24749-4_38 fatcat:4onayeweibgp7mo7py7cimzrdu

Checking Time Linearity of Regular Expression Matching Based on Backtracking

Satoshi Sugiyama, Yasuhiko Minamide
2014 IPSJ Online Transactions  
We construct a top-down tree transducer with regular lookahead that translates the input string into a tree corresponding to the execution steps of matching based on backtracking.  ...  The regular expression matching then runs in linear time if the tree transducer is of linear size increase. To check this property of the tree transducer, we apply a result of Engelfriet and Maneth.  ...  In this paper, we use an extension of top-down tree transducers, called top-down tree transducers with regular lookahead (or T R for short).  ... 
doi:10.2197/ipsjtrans.7.82 fatcat:e55skq5uerempaioci36ns6owa

Determinacy and Rewriting of Top-Down and MSO Tree Transformations [chapter]

Michael Benedikt, Joost Engelfriet, Sebastian Maneth
2013 Lecture Notes in Computer Science  
by deterministic top-down tree transducers with regular lookahead or by MSO tree transducers.  ...  For a large class of non-copying views, namely compositions of functional extended linear top-down tree transducers with regular look-ahead, we show that determinacy is decidable, where queries are given  ...  Ordinary Top-Down Tree Transducers.  ... 
doi:10.1007/978-3-642-40313-2_15 fatcat:argb3c3fjvcrjc6kfaiqyrazye
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