Abstract
The origin semantics for transducers was proposed in 2014, and it led to various characterizations and decidability results that are in contrast with the classical semantics. In this paper we add a further decidability result for characterizing transducers that are close to one-way transducers in the origin semantics. We show that it is decidable whether a non-deterministic two-way word transducer can be resynchronized by a bounded, regular resynchronizer into an origin-equivalent one-way transducer. The result is in contrast with the usual semantics, where it is undecidable to know if a non-deterministic two-way transducer is equivalent to some one-way transducer.
Work supported by ANR DeLTA (ANR-16-CE40-0007) and ReLaX.
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Rajeev Alur and Pavel Cerný. Expressiveness of streaming string transducer. In IARCS Annual Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS’10), volume 8 of LIPIcs, pages 1–12. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2010.
Félix Baschenis, Olivier Gauwin, Anca Muscholl, and Gabriele Puppis. One-way definability of sweeping transducers. In IARCS Annual Conference on Foundation of Software Technologyand Theoretical Computer Science (FSTTCS’15), volume 45 of LIPIcs, pages 178–191. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2015.
Félix Baschenis, Olivier Gauwin, Anca Muscholl, and Gabriele Puppis. One-way definability of two-way word transducers. Logical Methods in Computer Science, 14(4):1–54, 2018.
Mikolaj Bojańczyk. Transducers with origin information. In International Colloquium on Automata, Languages and Programming (ICALP’14), number 8572 in LNCS, pages 26–37. Springer, 2014.
Mikolaj Bojańczyk, Laure Daviaud, Bruno Guillon, and Vincent Penelle. Which classes of origin graphs are generated by transducers? In International Colloquium on Automata, Languages and Programming (ICALP’17), volume 80 of LIPIcs, pages 114:1–114:13. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2017.
Sougata Bose, Shankara Narayanan Krishna, Anca Muscholl, Vincent Penelle, and Gabriele Puppis. On synthesis of resynchronizers for transducers. In International Symposium on Mathematical Foundations of Computer Science (MFCS’19), volume 138 of LIPIcs, pages 69:1–69:14. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019.
Sougata Bose, Anca Muscholl, Vincent Penelle, and Gabriele Puppis. Origin-equivalence of two-way word transducers is in PSPACE. In IARCS Annual Conference on Foundations of Software Technologyand Theoretical Computer Science (FSTTCS’18), volume 122 of LIPIcs, pages 1–18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2018.
Thomas Colcombet. Factorisation forests for infinite words. In Fundamentals of Computation Theory (FCT), volume 4639 of LNCS, pages 226–237. Springer, 2007.
Bruno Courcelle and Joost Engelfriet. Graph Structure and Monadic Second-Order Logic - A Language-Theoretic Approach, volume 138 of Encyclopedia of mathematics and its applications. Cambridge University Press, 2012.
Luc Dartois, Ismaël Jecker, and Pierre-Alain Reynier. Aperiodic string transducers. Int. J. Found. Comput. Sci., 29(5):801–824, 2018.
Joost Engelfriet and Hendrik Jan Hoogeboom. MSO definable string transductions and two-way finite-statetransducers. ACM Trans. Comput. Log., 2(2):216–254, 2001.
Joost Engelfriet and Hendrik Jan Hoogeboom. Finitary compositions of two-way finite-state transductions. Fundamenta Informaticae, 80:111–123, 2007.
Emmanuel Filiot, Olivier Gauwin, and Nathan Lhote. Logical and algebraic characterizations of rational transductions. Logical Methods in Computer Science, 15(4), 2019.
Emmanuel Filiot, Olivier Gauwin, Pierre-Alain Reynier, and Frédéric Servais. From two-way to one-way finite state transducers. In ACM/IEEE Symposium on Logic in Computer Science (LICS’13), pages 468–477, 2013.
Emmanuel Filiot, Ismaël Jecker, Christof Löding, and Sarah Winter. On equivalence and uniformisation problems for finite transducers. In Proc. of nternational Colloquium on Automata, Languages, and Programming (ICALP’16), number 125 in LIPIcs, pages 1–14. Schloss Dagstuhl- Leibniz-Zentrum für Informatik, 2016.
Emmanuel Filiot, Shankara Narayanan Krishna, and Ashutosh Trivedi. First-order definable string transformations. In IARCS Annual Conference on Foundations of Software Technologyand Theoretical Computer Science (FSTTCS’14), LIPIcs, pages 147–159. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014.
Emmanuel Filiot, Sebastian Maneth, Pierre-Alain Reynier, and Jean-Marc Talbot. Decision problems of tree transducers with origin. Inf. Comput., 261(Part):311–335, 2018.
T. V. Griffiths. The unsolvability of the equivalence problem for lambda-free non-deterministic generalized machines. J. ACM, 15(3):409–413, 1968.
Oscar H. Ibarra. The unsolvability of the equivalence problem for e-free NGSM’s with unary input (output) alphabet and applications. SIAM J. of Comput., 7(4):524–532, 1978.
Ismael Jecker. Personal communication.
Denis Kuperberg and Jan Martens. Regular resynchronizability of origin transducers is undecidable. In International Symposium on Mathematical Foundations of Computer Science (MFCS’20), volume 170 of LIPIcs, pages 1–14. SchlossDagstuhl - Leibniz-Zentrum für Informatik, 2020.
John C. Shepherdson. The reduction of two-way automata to one-way automata. IBM Journal of Research and Development, 3(2):198–200, 1959.
Imre Simon. Factorization forests of finite height. Theoretical Computer Science, 72(1):65–94, 1990.
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Bose, S., Krishna, S.N., Muscholl, A., Puppis, G. (2021). One-way Resynchronizability of Word Transducers. In: Kiefer, S., Tasson, C. (eds) Foundations of Software Science and Computation Structures. FOSSACS 2021. Lecture Notes in Computer Science(), vol 12650. Springer, Cham. https://doi.org/10.1007/978-3-030-71995-1_7
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