Skip to main content
SpringerLink
Log in

Logic-Automata Connections for Transformations

  • Conference paper
Logic and Its Applications (ICLA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8923))

Included in the following conference series:

Abstract

Pioneered by Büchi, Elgot and Trakhtenbrot, connections between automata and logics that define languages of words and trees are now well-established. During the last decade, some of these powerful connections have been extended to binary relations (transformations) of words and trees. This paper is a survey of known automata-logic connections for transformations.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alur, A., Černý, P.: Streaming transducers for algorithmic verification of single-pass list-processing programs. In: POPL, pp. 599–610 (2011)

    Google Scholar 

  2. Alur, R., Černý, P.: Expressiveness of streaming string transducers. In: FSTTCS, vol. 8, pp. 1–12 (2010)

    Google Scholar 

  3. Alur, R., Filiot, E., Trivedi, A.: Regular transformations of infinite strings. Technical Report MS-CIS-12-05, University of Pennsylvania (2012)

    Google Scholar 

  4. Alur, R., D’Antoni, L.: Streaming tree transducers. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 42–53. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  5. Alur, R., Deshmukh, J.V.: Nondeterministic streaming string transducers. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 1–20. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Alur, R., Durand-Gasselin, A., Trivedi, A.: From monadic second-order definable string transformations to transducers. In: LICS, pp. 458–467 (2013)

    Google Scholar 

  7. Béal, M.-P., Carton, O., Prieur, C., Sakarovitch, J.: Squaring transducers: an efficient procedure for deciding functionality and sequentiality. Theoretical Computer Science 292(1), 45–63 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bloem, R., Engelfriet, J.: A comparison of tree transductions defined by monadic second order logic and by attribute grammars. J. Comput. Syst. Sci. 61(1), 1–50 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  9. Bojańczyk, M.: Transducers with origin information. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014, Part II. LNCS, vol. 8573, pp. 26–37. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  10. Büchi, J.R.: Weak second-order arithmetic and finite automata. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 6(1-6), 66–92 (1960)

    Article  MATH  Google Scholar 

  11. Büchi, J.R.: On a decision method in restricted second-order arithmetic. In: Int. Congr. for Logic Methodology and Philosophy of Science, pp. 1–11. Standford University Press, Stanford (1962)

    Google Scholar 

  12. Church, A.: An unsolvable problem of elementary number theory. Amer. J. Math. 58, 345–363 (1936)

    Article  MathSciNet  Google Scholar 

  13. Comon-Lundh, H., Dauchet, M., Gilleron, R., Löding, C., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications (November 2007)

    Google Scholar 

  14. Courcelle, B.: Monadic second-order definable graph transductions: A survey. Theoretical Computer Science 126(1), 53–75 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  15. Courcelle, B., Engelfriet, J.: Graph Structure and Monadic Second-Order Logic - A Language-Theoretic Approach. Encyclopedia of mathematics and its applications, vol. 138. Cambridge University Press (2012)

    Google Scholar 

  16. Culik II, K., Karhumäki, J.: The equivalence problem for single-valued two-way transducers (on NPDTOL languages) is decidable. SIAM J. Comput. 16(2), 221–230 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  17. Curry, H.B.: Functionality in Combinatory Logic. Proceedings of the National Academy of Sciences of the United States of America 20, 584–590 (1934)

    Article  Google Scholar 

  18. Diekert, V., Gastin, P.: First-order definable languages. In: Logic and Automata: History and Perspectives, Texts in Logic and Games, pp. 261–306. Amsterdam University Press (2008)

    Google Scholar 

  19. Ebbinghaus, H.D., Flum, J.: Finite Model Theory. Springer, Berlin (1995)

    Book  MATH  Google Scholar 

  20. Elgot, C.C.: Decision problems of finite automata design and related arithmetics. Transactions of the American Mathematical Society 98(1), 21–51 (1961)

    Article  MathSciNet  Google Scholar 

  21. Engelfriet, J., Hoogeboom, H.J.: MSO definable string transductions and two-way finite-state transducers. ACM Trans. Comput. Logic 2, 216–254 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  22. Engelfriet, J., Maneth, S.: Macro tree transducers, attribute grammars, and MSO definable tree translations. Inf. Comput. 154(1), 34–91 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  23. Engelfriet, J., Maneth, S.: Macro tree translations of linear size increase are MSO definable. SIAM J. Comput. 32(4), 950–1006 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  24. Engelfriet, J., Maneth, S.: The equivalence problem for deterministic MSO tree transducers is decidable. Inf. Process. Lett. 100(5), 206–212 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. Filiot, E., Gauwin, O., Reynier, P.A., Servais, F.: From two-way to one-way finite state transducers. In: LICS, pp. 468–477 (2013)

    Google Scholar 

  26. Filiot, E., Krishna, S.N., Trivedi, A.: First-order definable string transformations. To appear in FSTTCS (2014)

    Google Scholar 

  27. Fülöp, Z., Vogler, H.: Syntax-Directed Semantics - Formal Models Based on Tree Transducers. Monographs in Theoretical Computer Science. An EATCS Series. Springer (1998)

    Google Scholar 

  28. Griffiths, T.V.: The unsolvability of the equivalence problem for -free nondeterministic generalized machines. Journal of the ACM (1968)

    Google Scholar 

  29. Howard, W.: The formulae-as-types notion of construction. In: To H.B.Curry: Essays on Combinatory Logic, Lambda-Calculus and Formalism. Academic Press (1980)

    Google Scholar 

  30. Immerman, N.: Languages that capture complexity classes. SIAM Journal on Computing 16(4), 760–778 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  31. Berstel, J.: Transductions and Context-Free Languages. Teubner, Stuttgart (1979)

    Google Scholar 

  32. Lautemann, C., McKenzie, P., Schwentick, T., Vollmer, H.: The descriptive complexity approach to LOGCFL. Journal of Computer and System Sciences 62 (2001)

    Google Scholar 

  33. Maneth, S.: Equivalence problems for tree transducers: A brief survey. In: AFL, pp. 74–93 (2014)

    Google Scholar 

  34. McKenzie, P., Schwentick, T., Therienand, D., Vollmer, H.: The many faces of a translation. Journal of Computer and System Sciences 72 (2006)

    Google Scholar 

  35. McNaughton, R.: Testing and generating infinite sequences by a finite automaton. Information and Control 9, 521–530 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  36. Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Amer.Math.Soc. 141, 1–35 (1969)

    MATH  MathSciNet  Google Scholar 

  37. Sakarovich, J.: Elements of Automata Theory. Cambridge University Press, Cambridge (2009)

    Book  Google Scholar 

  38. Schützenberger, M.P.: On finite monoids having only trivial subgroups. Information and Control 8(2), 190–194 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  39. Shepherdson, J.C.: The reduction of two-way automata to one-way automata. In: Moore, E.F. (ed.) Sequential Machines: Selected Papers. Addison-Wesley (1964)

    Google Scholar 

  40. Straubing, H.: Finite Automata, Formal Logic, and Circuit Complexity. Birkhäuser, Boston, Basel and Berlin (1994)

    Book  MATH  Google Scholar 

  41. Thomas, W.: Languages, automata and logic. In: Salomaa, A., Rozenberg, G. (eds.) Handbook of Formal Languages. Beyond Words, vol. 3. Springer, Berlin (1997)

    Google Scholar 

  42. Trakhtenbrot, B.A.: Finite automata and logic of monadic predicates. Dokl. Akad. Nauk SSSR 140, 326–329 (1961) (in Russian)

    Google Scholar 

  43. Turing, A.M.: On computable numbers, with an application to the entscheidungsproblem. Procedings of the London Mathematical Society 42(2), 230–265 (1936)

    MathSciNet  Google Scholar 

  44. Vardi, M.Y., Wilke, T.: Automata: from logics to algorithms. In: Logic and Automata: History and Perspectives (in Honor of Wolfgang Thomas), pp. 629–736 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Université Libre de Bruxelles, Brussels, Belgium

    Emmanuel Filiot

Authors
  1. Emmanuel Filiot
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, 208016, Kanpur, India

    Mohua Banerjee

  2. Department of Computer Science and Engineering, Indian Institute of Technology Bombay, Powai, 400076, Mumbai, India

    Shankara Narayanan Krishna

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Filiot, E. (2015). Logic-Automata Connections for Transformations. In: Banerjee, M., Krishna, S.N. (eds) Logic and Its Applications. ICLA 2015. Lecture Notes in Computer Science, vol 8923. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45824-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-45824-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-45823-5

  • Online ISBN: 978-3-662-45824-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation