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The equivalence of finite valued transducers (on HDT0L languages) is decidable

Karel Culik, Juhani Karhumäki
1986 Theoretical Computer Science  
This is the first time the equivalence problem is shown to be decidable for a larger class of multivalued transducers. decidability of the equivalence problem for k-valued finite transducers.  ...  Testing the equivalence of mappings which are realized by finite transducers on a regular language is a special case of the equivalence problem for finite transducers since a restriction of a finite transduction  ...  is decidable if and only if the problem of testing the equivalence of two finite substitutions on regular languages is decidable, cf  ... 
doi:10.1016/0304-3975(86)90134-9 fatcat:oo5w5wvy55chzl57d4537wromq

Equivalence of finite-valued streaming string transducers is decidable [article]

Anca Muscholl, Gabriele Puppis
2019 arXiv   pre-print
In this paper we provide a positive answer to a question left open by Alur and and Deshmukh in 2011 by showing that equivalence of finite-valued copyless streaming string transducers is decidable.  ...  Finite-valued transductions were intensively studied in the setting of one-way and twoway transducers. For one-way transducers, k-valuedness can be checked in Ptime [GI83] .  ...  The main result of this paper is a positive answer to the first question left open in [AD11] : Theorem 1. The equivalence problem for finite-valued SST is decidable.  ... 
arXiv:1902.06973v2 fatcat:sm7sgronmvaubibdfufy7zvxly

Equivalence of Finite-Valued Streaming String Transducers Is Decidable

Anca Muscholl, Gabriele Puppis, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
In this paper we provide a positive answer to a question left open by Alur and and Deshmukh in 2011 by showing that equivalence of finite-valued copyless streaming string transducers is decidable.  ...  Finite-valued transductions were intensively studied in the setting of one-way and twoway transducers. For one-way transducers, k-valuedness can be checked in Ptime [17] .  ...  I C A L P 2 0 1 9 122:8 Equivalence of Finite-Valued Streaming String Transducers Is Decidable Normalization of transitions We finally turn to studying a notion of equivalence on transitions that is  ... 
doi:10.4230/lipics.icalp.2019.122 dblp:conf/icalp/MuschollP19 fatcat:cfum7qabgjhmxlhgf3ivx6clfe

Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable [article]

Helmut Seidl, Sebastian Maneth, Gregor Kemper
2017 arXiv   pre-print
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory.  ...  This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence.  ...  The known algorithm for deciding equivalence of yDT transducers with monadic alphabet is based on a reduction to the HDT0L sequence equivalence problem.  ... 
arXiv:1503.09163v2 fatcat:b7xeqhx3q5ednpmskwubfvsfoe

Equivalence of Deterministic Top-Down Tree-to-String Transducers Is Decidable

Helmut Seidl, Sebastian Maneth, Gregor Kemper
2018 Journal of the ACM  
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory.  ...  This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence.  ...  We thank the anonymous referees for careful reading and for many helpful comments.  ... 
doi:10.1145/3182653 fatcat:ayyyao4j4ncfflbq6lboybjbru

Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable

Helmut Seidl, Sebastian Maneth, Gregor Kemper
2015 2015 IEEE 56th Annual Symposium on Foundations of Computer Science  
We show that equivalence of deterministic top-down tree-to-string transducers is decidable, thus solving a long standing open problem in formal language theory.  ...  This allows us to construct two semi-algorithms, one searching for a proof of equivalence, one for a witness of non-equivalence.  ...  We thank the anonymous referees for careful reading and for many helpful comments.  ... 
doi:10.1109/focs.2015.62 dblp:conf/focs/SeidlMK15 fatcat:grhs3xh6qfazhfyp5hwl64gt7a

Copyful Streaming String Transducers [chapter]

Emmanuel Filiot, Pierre-Alain Reynier
2017 Lecture Notes in Computer Science  
On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem.  ...  As a consequence, equivalence of deterministic SST is decidable, (iii) the functionality of non-deterministic copyful SST is decidable, (iv) determining whether a deterministic copyful SST can be transformed  ...  It states that the equivalence of finite-valued transducers over HDT0L languages is decidable, with unknown complexity.  ... 
doi:10.1007/978-3-319-67089-8_6 fatcat:idfknjkd2jcm7akfud65v55rmu

On Streaming String Transducers and HDT0L Systems [article]

Emmanuel Filiot, Pierre-Alain Reynier
2014 arXiv   pre-print
The proof reduces to the HDT0L sequence equivalence problem, which is known to be decidable.  ...  Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Cerny in 2010 as a one-way deterministic automata model to define transformations of finite strings.  ...  In the rest of this section, we therefore focus on the diagonal problem for non-deterministic biSST, and show its decidability by reduction to the HDT0L equivalence problem.  ... 
arXiv:1412.0537v1 fatcat:nft4y7e7fnhmvdid63n6iz6b5a

Equivalence Problems for Tree Transducers: A Brief Survey

Sebastian Maneth
2014 Electronic Proceedings in Theoretical Computer Science  
The decidability of equivalence for three important classes of tree transducers is discussed.  ...  For the full class of MTTs, decidability of equivalence remains a long-standing open problem.  ...  The second one is solved by the decidability of equivalence for deterministic MSO tree transducers of Engelfriet and Maneth [25] .  ... 
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  
The decidability of equivalence for three important classes of tree transducers is discussed.  ...  The decidability of equivalence for this class follows through a relationship with L-systems [36]; in particular, with the sequence equivalence problem of hdt0l systems.  ...  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

Comparison-free polyregular functions [article]

Lê Thành Dũng Nguyên, Camille Noûs, Pierre Pradic
2021 arXiv   pre-print
Finally, we look at the recently introduced layered streaming string transducers (SSTs), or equivalently k-marble transducers.  ...  of (k+1)-layered HDT0L systems.  ...  The first example in [13, §5] shows that a n → a n×n is HDT0L (via the equivalent model of marble transducers), hence the necessity of |Σ| ≥ 2 above.  ... 
arXiv:2105.08358v1 fatcat:gh4unytebfardnodb53idksige

The Many Facets of String Transducers (Invited Talk)

Anca Muscholl, Gabriele Puppis, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
Regular word transductions extend the robust notion of regular languages from a qualitative to a quantitative reasoning.  ...  In this paper we survey some older and more recent results on string transducers.  ...  Walukiewicz, for their comments on a draft version of this paper.  ... 
doi:10.4230/lipics.stacs.2019.2 dblp:conf/stacs/MuschollP19 fatcat:ir6th7r24vfjhlz6clrybdsmfu

Reducing Transducer Equivalence to Register Automata Problems Solved by "Hilbert Method"

Adrien Boiret, Radoslaw Piórkowski, Janusz Schmude, Michael Wagner
2018 Foundations of Software Technology and Theoretical Computer Science  
In the past decades, classical results from algebra, including Hilbert's Basis Theorem, had various applications in formal languages, including a proof of the Ehrenfeucht Conjecture, decidability of HDT0L  ...  sequence equivalence, and decidability of the equivalence problem for functional treeto-string transducers.  ...  They provide decidability results on register automata on algebras with nontrivial structure properties like commutativity of operations (e.g. children in UCF) that make the usual methods to decide equivalence  ... 
doi:10.4230/lipics.fsttcs.2018.48 dblp:conf/fsttcs/BoiretPS18 fatcat:f7sym7vpo5gevae5lqvrwmerhe

Reducing Transducer Equivalence to Register Automata Problems Solved by "Hilbert Method" [article]

Adrien Boiret, Radosław Piórkowski, Janusz Schmude
2019 arXiv   pre-print
We provide two results, one positive, one negative. The positive result is that equivalence is decidable for MSO transformations on unordered forests.  ...  In the past decades, classical results from algebra, including Hilbert's Basis Theorem, had various applications in formal languages, including a proof of the Ehrenfeucht Conjecture, decidability of HDT0L  ...  Acknowledgments We would like to thank Miko laj Bojańczyk, from the University of Warsaw, for introducing us to the topic of using the Hilbert Method to decide equivalence of register automata, and for  ... 
arXiv:1806.04361v2 fatcat:ajtqdi2rizfm3dzcw6u6q4lfzm

Comparison-Free Polyregular Functions

Nguyễn, Lê Thành Dũng (Tito), Camille Noûs, Pierre Pradic, Nikhil Bansal, Emanuela Merelli, James Worrell
2021
On the broader topic of polynomial growth transductions, we also consider the recently introduced layered streaming string transducers (SSTs), or equivalently k-marble transducers.  ...  Several equivalent definitions are provided: a machine model which is a restricted variant of pebble transducers, and a few inductive definitions that close the class of regular functions under certain  ...  The first example in [13, §5] shows that a n → a n×n is HDT0L (via the equivalent model of marble transducers), hence the necessity of |Σ| ≥ 2 above.  ... 
doi:10.4230/lipics.icalp.2021.139 fatcat:vxlm5ruz5vgynlve7kkjvbxtnq
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