Skip to main content
SpringerLink
Log in
Book cover

Handbook of Formal Languages pp 1–68Cite as

Tree Languages

  • Chapter

Abstract

The theory of tree automata and tree languages emerged in the middle of the 1960s quite naturally from the view of finite automata as unary algebras advocated by J. R. Büchi and J. B. Wright. From this perspective the generalization from strings to trees means simply that any finite algebra of finite type can be regarded as an automaton which as inputs accepts terms over the ranked alphabet formed by the operation symbols of the algebra, and these terms again can be seen as (formal representations of) labeled trees with a left-to-right ordering of the branches. Strings over a finite alphabet can then be regarded as terms over a unary ranked alphabet, and hence finite automata become special tree automata and string languages unary tree languages. The theory of tree automata and tree languages can thus be seen as an outgrowth of Büchi’s and Wright’s program which had as its goal a general theory that would encompass automata, universal algebra, equational logic, and formal languages. Some interesting vistas of this program and its development are opened by Büchi’s posthumous book [Büc89] in which many of the ideas are traced back to people like Thue, Skolem, Post, and even Leibniz.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adámek, J., Trnková, V.: Varietors and machines in a category. Algebra Universalis 13, (1981), 89–132

    Article  MathSciNet  MATH  Google Scholar 

  2. Aho, A., Ullman, J. D.: Translations on a context-free grammar. In formation Control 19 (1971), 439–475

    Article  MathSciNet  Google Scholar 

  3. Aigrain, P., Nivat, M.: Suffix, prefix and maximal tree codes. In: [TrAL92], 21–39

    Google Scholar 

  4. Alagić, S.: Natural state transformations. J. Comput. Systems Sci. 10 (1975), 266–307

    Article  MATH  Google Scholar 

  5. Almeida, J.: On pseudovarieties, varieties of languages, filters of congruences, pseudo-identities and related topics. Algebra Universalis 27 (1991), 333–350

    Article  MathSciNet  Google Scholar 

  6. Arbib, M. A., Give’on, Y.: Algebra automata I: parallel programming as a prolegomena to the categorical approach. Information Control 12 (1968), 331–345

    Article  MathSciNet  Google Scholar 

  7. Arbib, M. A., Manes, E. G.: Tree transformations and the semantics of loop-free programs. Acta Cybern. 4 (1978), 11–17

    MathSciNet  MATH  Google Scholar 

  8. Arnold, A.: Le théorè me transversale rationelle dans les langages d’arbres. Math. Systems Theory 13 (1980), 272–282

    Google Scholar 

  9. Arnold, A., Dauchet, M.: Transductions de forêts reconnaissables monadiques. Forêts corégulières. RAIRO Informat. Thćor. 10 (1976), No. 3, 5–28

    MathSciNet  Google Scholar 

  10. Arnold, A., Dauchet, M.: Bi-transductions de forêts. Automata, Lan-guages, and Programming (Proc. Conf. 1976), University Press, Edinburgh 1976, 74–86

    Google Scholar 

  11. Arnold, A., Dauchet, M.: Forêts algébriques et homomorphismes in verses. Information Control 37 (1978), 182–196

    Article  MathSciNet  MATH  Google Scholar 

  12. Arnold, A., Dauchet, M.: Theorie des magmoides. I. RAIRO Inform. Théor. 12 (1978) 235–257; II. ibid. 13 (1979), 135–154

    Google Scholar 

  13. Arnold, A., Dauchet, M.: Morphismes et bimorphismes d’arbres. Theoret. Comput. Sci. 20 (1982), 33–93

    Article  MathSciNet  MATH  Google Scholar 

  14. Avenhaus, J.: Reduktionssysteme. Springer-Verlag, Berlin 1995

    Book  MATH  Google Scholar 

  15. Baker, B. S.: Tree transducers and tree languages. Information Control 37 (1978), 241–266

    Article  MATH  Google Scholar 

  16. Baker, B. S.: Generalized syntax directed translation, tree transducers, and linear space. SIAM J. Comput. 7 (1978), 876–891

    Google Scholar 

  17. Baker, B.: Composition of top-down and bottom-up tree transductions. Information Control 41 (1979), 186–213

    Article  MATH  Google Scholar 

  18. Bartha, M.: An algebraic definition of attributed tree transformations, Acta Cybern. 5 (1982), 409–421

    MathSciNet  MATH  Google Scholar 

  19. Berger, J., Pair, C.: Inference for regular bilanguages. J. Comput. Systems Sci. 16 (1978), 100–122

    Article  MathSciNet  MATH  Google Scholar 

  20. Berstel, J., Reutenauer, J.: Recognizable formal power series on trees. Theoret. Comput. Sci. 18 (1982), 115–148

    Article  MathSciNet  MATH  Google Scholar 

  21. Bogaert, B., Tison, S.: Equality and disequality constraints on direct subterms in tree automata. Theoret. Aspects Comput. Sci. (Proc. Symp., 9th STACS 92), Lect. Notes Comput. Sci. 577, Springer-Verlag, Berlin 1992, 161–171

    Google Scholar 

  22. Bozapalidis, S.: Sur une classe de transformations d’arbres. Inform. Théor. Appl. 22 (1988), 43–47

    MathSciNet  MATH  Google Scholar 

  23. Bozapalidis, S.: Effective construction of the syntactic algebra of a recognizable series on trees. Acta Inform. 28 (1991), 351–363

    Article  MathSciNet  MATH  Google Scholar 

  24. Bozapalidis, S.:Alphabetic tree relations. Theoret. Comput. Sci. 99 (1992), 177–211

    Article  MathSciNet  MATH  Google Scholar 

  25. Bozapalidis, S., Alexandrakis, A.: Reprćsentations matricelles des sćries d’arbre reconnaissables. Inform. Thèor. Applicat. 23 (1989), 449–459

    MathSciNet  MATH  Google Scholar 

  26. Bozapalidis, S., Louscou-Bozapalidou, O.: The rank of formal tree power series. Theoret. Comput. Sci. 27 (1983), 211–215

    Article  MathSciNet  MATH  Google Scholar 

  27. Brainerd, W. S.: Tree generating regular systems. Information Control 14 (1969), 217–231

    Article  MathSciNet  MATH  Google Scholar 

  28. Brayer, J. M., Fu, K.-S.: A note on the k-tail method of tree grammar inference. IEEE Trans. Systems Man Cybernetics SMC-7 (1977), 293–300

    MathSciNet  Google Scholar 

  29. Buda, A.: Generalized1.5 sequential machines. Inform. Process. Lett. 8 (1979), 38–40

    Article  MathSciNet  MATH  Google Scholar 

  30. Burris, S., Sankappanavar, H. P.: A course in universal algebra. Springer-Verlag, New York 1981

    Book  MATH  Google Scholar 

  31. Büchi, J. R.: Finite automata and their algebras (ed. D. Siefkes). Springer-Verlag, New York 1989

    Google Scholar 

  32. Caron, A.-L., Coquidé, J.-L., Dauchet, M.: Encompassment properties and automata with constraints. Rewriting Techniques and Applications (Proc. 5th Intern. Conf. 1993), Lect. Notes Comput. Sci. 690, Springer-Verlag, Berlin 1993, 328–342

    Google Scholar 

  33. Caron, A.-C., Comon, H., Coquidé, J.-L., Dauchet, M., Jacquemard, F.: Pumping, cleaning and symbolic constraint solving. Automata, Languages and Programming (Proc. 21st Coll., ICALP’94), Lect. Notes Comput. Sci. 820, Springer-Verlag, Berlin 1994, 436–449

    Google Scholar 

  34. Coquidé, J.-L., Dauchet, M., Gilleron, R., Vágvölgyi, S.: Bottom-up tree pushdown automata: classification and connection with rewrite systems. Theoret. Comput. Sci. 127 (1994), 69–98

    Article  MathSciNet  MATH  Google Scholar 

  35. Courcelle, B., Franchi-Zannettacci, P.: Attribute grammars and program schemes. I. Theoret. Comput. Sci. 17 (1982), 163–191; II. ibid 235–257

    Google Scholar 

  36. Courcelle, B.: A representation of trees by languages. I. Theoret. Comput. Sci. 6 (1978), 255–279; II. ibid 7 (1978), 25–55

    Google Scholar 

  37. Courcelle, B.: Equivalence and transformation of regular systems. Theoret. Comput. Sci. 42 (1986), 1–122

    Article  MathSciNet  MATH  Google Scholar 

  38. Courcelle, B.: On recognizable sets and tree automata. Resolution of Equations in Algebraic Structures (eds. H. Aït-Kaci and M. Nivat), Academic Press, Boston 1989, 93–126

    Google Scholar 

  39. Courcelle, B.: Recursive applicative program schemes. Handbook of Theoretical Computer Science. Vol. B. Formal Models and Semantics (ed. J. van Leeuwen), Elsevier, Amsterdam 1990, 460–492

    Google Scholar 

  40. Dauchet, M., Mongy, J.: Transformations de noyaux reconnaissables capacité générative des bimorphismes de forêts. Fundam. Comput. Theory ‘79 (Proc. Conf. FCT’79), Akademie-Verlag, Berlin 1979, 9297

    Google Scholar 

  41. Davey, B. A., Priestley, H. A.: Introduction to lattices and order. Cambridge University Press, Cambridge 1990

    MATH  Google Scholar 

  42. Dauchet, M., Tison, S.: Decidability of confluence for ground term rewriting systems. Fundam. Comput. Theory (Proc. Conf. FCT’85), Lect. Notes Comput. Sci. 199, Springer-Verlag, Berlin 1985, 80–89

    Google Scholar 

  43. Dauchet, M., Tison, S.: Structural complexity classes of tree languages. In: [TrAL92], 327–353

    Google Scholar 

  44. Dershowitz, N, Jouannaud, J.-P.: Rewrite systems. Handbook of Theoretical Computer Science. Vol. B. Formal Models and Semantics (ed. J. van Leeuwen), Elsevier, Amsterdam 1990, 243–320

    Google Scholar 

  45. Dauchet, M., Heuillard, T., Lescanne, P., Tison, S.: Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems. Information Control 88 (1990), 187–201

    MathSciNet  MATH  Google Scholar 

  46. Doner, J. E.: Tree acceptors and some of their applications. J. Comput. Syst. Sci. 4 (1970), 406–451

    Article  MathSciNet  MATH  Google Scholar 

  47. Eilenberg, S., Wright, J. B.: Automata in general algebras. Information Control 11 (1967), 452–470

    Article  MathSciNet  MATH  Google Scholar 

  48. Engelfriet, J.: Tree automata and tree grammars. Lecture notes, DAIMI FN-10, Inst. Mathem., Aarhus University, Aarhus 1975

    Google Scholar 

  49. Engelfriet, J.: Bottom-up and top-down tree transformations. A com- parison. Math. Systems Theory 9 (1975), 198–231

    Article  MathSciNet  MATH  Google Scholar 

  50. Engelfriet, J.: Top-down tree transducers with regular look-ahead. Math. Systems Theory 10 (1976/1977), 289–303

    Google Scholar 

  51. Engelfriet, J.: A hierarchy of tree transducers. Les Arbres en Algèbreet en Programmation (Proc. 3rd Coll., Lille 1979), University of Lille, Lille 1978, 103–106

    Google Scholar 

  52. Engelfriet, J.: Some open questions and recent results on tree transducers and tree languages. Formal Language Theory (ed. R. V. Book), Academic Press, New York 1980, 241–286

    Google Scholar 

  53. Engelfriet, J.: Three hierarchies of transducers. Math. Systems Theory 15 (1982), 95–125

    Article  MathSciNet  MATH  Google Scholar 

  54. Engelfriet, J., Schmidt, E. M.: IO and OI. I. J. Comput. Systems Sci. 15 (1977), 328–353; II. ibid 16 (1978), 67–99

    Google Scholar 

  55. Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comput. Systems Sci. 31 (1985), 71–145

    Article  MathSciNet  MATH  Google Scholar 

  56. Engelfriet, J., Vogler, H.: Pushdown machines for macro tree transducers. Theoret. Comput. Sci. 42 (1986), 251–369

    Article  MathSciNet  MATH  Google Scholar 

  57. Engelfriet, J., Vogler, H.: Look-ahead on pushdowns. Information Control 73 (1987), 245–279

    MathSciNet  MATH  Google Scholar 

  58. Engelfriet, J., Vogler, H.: High level tree transducers and iterated pushdown tree transducers. Acta Inform. 26 (1988), 131–192

    Article  MathSciNet  MATH  Google Scholar 

  59. Engelfriet, J., Vogler, H.: Modular tree transducers. Theoret. Comput. Sci. 78 (1991), 267–303

    Article  MathSciNet  MATH  Google Scholar 

  60. Ésik, Z.: Decidability results concerning tree transducers. I. Acta Cybern. 5 (1980), 1–20; II. ibid 6 (1983), 303–314

    Google Scholar 

  61. Ésik, Z., Gćcseg, F.: Type independent varieties and metric equivalence of tree automata. Fundam. Inform. IX (1986), 205–216

    Google Scholar 

  62. Ésik, Z., Gćcseg, F.: On a representation of tree automata. Theoret. Comput. Sci. 53 (1987), 243–255

    Article  MathSciNet  MATH  Google Scholar 

  63. Fischer, M. J.: Grammars with macro-like productions. 9th Ann. IEEE Symp. on Switching and Automata Theory (Proc. Symp. 1968), 131–142

    Google Scholar 

  64. Fu, K.-S.: Syntactic pattern recognition and applications. Prentice-Hall, Englewood Cliffs, N. J. 1982

    Google Scholar 

  65. Fu, F.-S., Brayer, J. M.: Tree systems for syntactic pattern recognition. IEEE Trans. Computers C-22 (1973), 1087–1099

    Google Scholar 

  66. Fukuda, H., Kamata, K.: Inference of tree automata from sample set of trees. Intern. J. Comput. Inform. Sci. 13 (1984), 177–196

    Article  MathSciNet  MATH  Google Scholar 

  67. Fülöp, Z.: On attributed tree transducers. Acta Cybern. 5 (1981), 261–279

    MATH  Google Scholar 

  68. Fülöp, Z.: A complete description for a monoid of deterministic bottom-up tree transformation classes. Theoret. Comput. Sci. 88 (1991), 253–268

    Article  MathSciNet  MATH  Google Scholar 

  69. Fülöp, Z.: Undecidable properties of deterministic top-down tree transducers, Theoret. Comput. Sci. 134 (1994), 311–328

    Article  MathSciNet  MATH  Google Scholar 

  70. Fülöp, Z., Herrmann, F., Vágvölgyi, S., Vogler, H.: Tree transducers with external functions. Theoret. Comput. Sci. 108 (1993), 185–236

    Article  MathSciNet  MATH  Google Scholar 

  71. Fülöp, Z., Vágvölgyi, S.: Results on compositions of deterministic root- to-frontier tree transformations. Acta Cybern. 8 (1987), 49–61

    MATH  Google Scholar 

  72. Fülöp, Z., Vágvölgyi, S.:On ranges of compositions of deterministic root-to-frontier tree transformations. Acta Cybern. 8 (1987), 259–266

    MATH  Google Scholar 

  73. Fülöp, Z., Vágvölgyi, S.: Iterated deterministic top-down look-ahead. Fundam. Comput. Theory (Proc. FCT’89), Lect. Notes Comput. Sci. 380, Springer-Verlag, Berlin 1989, 175–184

    Google Scholar 

  74. Fülöp, Z., Vágvölgyi, S.: Congruential tree languages are the same as recognizable tree languages. Bull. EATCS 39 (1989), 175–185

    MATH  Google Scholar 

  75. Fülöp, Z., Vágvölgyi, S.: Variants of top-down tree transducers with look-ahead. Math. Systems Theory 21 (1989), 125–145

    Article  MathSciNet  Google Scholar 

  76. Fülöp, Z., Vágvölgyi, S.: Top-down tree transducers with deterministic top-down look-ahead. Inform. Process. Lett. 33 (1989/90), 3–5

    Article  MathSciNet  MATH  Google Scholar 

  77. Fülöp, Z., Vágvölgyi, S.: A characterization of irreducible sets modulo left-linear term rewriting systems by tree automata. Fundam. Inform. XIII (1990), 211–226

    Google Scholar 

  78. Fülöp, Z., Vágvölgyi, S.: A complete classification of deterministic root-to-frontier tree transformation classes. Theor. Comput. Sci. 81 (1991), 1–15

    Article  MATH  Google Scholar 

  79. Fiilöp, Z., Vágvölgyi, S.: Decidability of the inclusion in monoids generated by tree transformation classes. In: [TrAL92], 381–408

    Google Scholar 

  80. Fiilöp, Z., Vágvölgyi, S.: Attributed tree transducers cannot induce all deterministic bottom-up tree transformations. Information Computation 116 (1995), 231–240

    Article  Google Scholar 

  81. Gallier, J. H., Book, R. V.: Reductions in tree replacement systems. Theor. Comput. Sci. 37 (1985), 123–150

    Article  MathSciNet  MATH  Google Scholar 

  82. Gécseg, F.: Metric equivalence of tree automata. Acta Sci. Math. 48 (1985), 163–171

    MATH  Google Scholar 

  83. Gécseg, F.: Homomorphic representations by products of tree au-tomata. Results and Trends in Theoretical Computer Science (Proc. Coll. 1994), Lect. Notes Comput. Sci. 812, Springer-Verlag, Berlin 1994,131–139

    Google Scholar 

  84. Gécseg, F., Imreh, B.: On finite isomorphically complete systems of tree automata. Acta Sci. Math. 57 (1993), 497–502

    MATH  Google Scholar 

  85. Gécseg, F., Steinby, M.: Tree automata. Akadémiai Kiadó, Budapest 1984

    MATH  Google Scholar 

  86. Gonzalez, R. C., Edwards, J. J., Thomason, M. G.: An algorithm for the inference of tree grammars. Intern. J. Comput. Information Sci. 5 (1976), 145–164

    Article  MATH  Google Scholar 

  87. Gilleron, R.: Decision problems for term rewriting systems and recognizable tree languages. Theoret. Aspects Comput. Sci. (Proc. STACS’91), Lect. Notes Comput. Sci. 480, Springer-Verlag, Berlin 1991, 148–159

    Google Scholar 

  88. Gonzalez, R. C., Thomason, M. G.: Syntactic pattern recognition: an introduction. Addison-Wesley, Reading, MA 1978

    Google Scholar 

  89. Guessarian, I.: Pushdown tree automata. Math. Systems Theory 16 (1983), 237–263

    Article  MathSciNet  MATH  Google Scholar 

  90. Guessarian, I.: Trees and algebraic semantics. In: [TrAL92], 291–310

    Google Scholar 

  91. Heuter, U.: Definite tree languages. Bull. EATCS 35 (1988), 137–144

    MATH  Google Scholar 

  92. Heuter, U.: Zur Klassifizierung regulärer Baumsprachen. Disseration, RWTH, Technical University of Aachen, Faculty of Science, 1989

    Google Scholar 

  93. Heuter, U.: Generalized definite tree languages. Mathem. Found. Comput. Sci. (Proc. Symp. MFCS’89), Lect. Notes in Comput. Sci. 379, Springer-Verlag, Berlin 1989, 270–280

    Google Scholar 

  94. Heuter, U.: First-order properies of trees, star-free, and periodicity. Inform. Thćor. Applic. 25 (1991), 125–145

    MathSciNet  MATH  Google Scholar 

  95. Horvath, Gy.: Functor state machines. Acta Cybernet. 6 (1981), 147–172

    Google Scholar 

  96. Huet, G., Oppen, D. C.: Equations and rewrite rules: a survey. Formal Language Theory: Perspectives and Open Problems (ed. R. Book), Academic Press, New York 1980, 349–405

    Google Scholar 

  97. Imreh, B.: On a special composition of tree automata. Acta Cybern. 10 (1992), 237–242

    MathSciNet  MATH  Google Scholar 

  98. Imreh, B.: On isomorphic representation of nondeterministic tree au-tomata. Acta Cybern. 12 (1995), 11–22

    MathSciNet  MATH  Google Scholar 

  99. Joshi, A. K., Levy, L. S., Takahashi, M.: Tree adjunct grammars. J. Comput. Systems Sci. 10 (1975), 136–163

    Article  MathSciNet  MATH  Google Scholar 

  100. Joshi, A. K., Schabes, Y.: Tree-adjoining grammars and lexicalized grammars. In: [TrAL92], 409–431

    Google Scholar 

  101. Jurvanen, E.: The Boolean closure of DR-recognizable tree languages. Acta Cybern. 10 (1992), 255–272

    MathSciNet  MATH  Google Scholar 

  102. Jurvanen, E.: On recognizing trees deterministically from root to fron-tier. Doctoral Thesis, University of Turku, Turku 1995

    Google Scholar 

  103. Jurvanen, E., Potthoff, A., Thomas, W.: Tree languages recognizable by regular frontier check. Developments in Language Theory (eds. G. Rozenberg and A. Salomaa, Proc. Conf. Turku, Finland 1993). World Scientific, Singapore 1994, 3–17

    Google Scholar 

  104. Kamimura, T.: Tree automata and attribute grammars. Information Control 57 (1983), 1–20

    Article  MathSciNet  MATH  Google Scholar 

  105. Kamata, K.: Inference methods for tree automata from sample set of trees. Systems, Man and Cybernetics (Proc. 1988 IEEE Intern. Conf.), 490–493

    Google Scholar 

  106. Knuutila, T.: On the inductive inference of regular string and tree languages. Dissertation, University of Turku, Dept. of Computer Science, Turku 1994

    Google Scholar 

  107. Knuutila, T., Steinby, M.: The inference of tree languages from finite samples: an algebraic approach. Theoret. Comput. Sci. 129 (1994), 337–367

    Article  MathSciNet  MATH  Google Scholar 

  108. Kozen, D.: Complexity of finitely presented algebras. 9th Ann. ACM Symp. on Theory of Computing (Proc. Symp., 1977), 164–177

    Google Scholar 

  109. Kucherov, G.: On relationship between term rewriting systems and regular tree languages. Rewriting Techniques and Applications (Proc. 4th Intern. Conf.), Lect. Notes Comput. Sci. 488, Springer-Verlag, Berlin 1991, 299–311

    Google Scholar 

  110. Kühnemann, A., Vogler, H.: A pumping lemma for output languages of attributed tree transducers. Acta Cybern. 11 (1994), 261–305

    Google Scholar 

  111. Levy, L. S.: Structural aspects of local adjunct grammars. Information Control 23 (1973), 260–287

    Article  MATH  Google Scholar 

  112. Levine, B.: Derivatives of tree sets with applications to grammatical inference. IEEE Trans. Pattern Anal. Machine Intelligence PAMI-3 (1981), 285–293

    Google Scholar 

  113. Levy, L. S., Joshi, A. K.: Skeletal structural descriptions. Information Control 39 (1978), 192–211

    Article  MathSciNet  MATH  Google Scholar 

  114. Magidor, M., Moran, G.: Finite automata over finite trees. Technical Report 30, Hebrew University, Jerusalem 1969

    Google Scholar 

  115. Mezei, J., Wright, J. B.: Algebraic automata and context-free sets. Information Control 11 (1967), 3–29

    Article  MathSciNet  MATH  Google Scholar 

  116. Miclet, L.: Structural methods in pattern recognition. North-Oxford, London 1986

    Google Scholar 

  117. Moriya, E.: On two-way tree automata. Inform. Process. Lett. 50 (1994), 117–121

    Article  MathSciNet  MATH  Google Scholar 

  118. Neumüller, I.: The invertability of tree transducers. Acta Cybern. 8 (1987), 63–78

    MATH  Google Scholar 

  119. Nivat, M.: On the interpretation of recursive polyadic program schemes. Symp. Mathematica 15 (1975), 255–281

    MathSciNet  Google Scholar 

  120. Nivat, M.: Binary tree codes. In: [TrAL92], 1–20

    Google Scholar 

  121. Nivat, M., Podelski, A.: Definite tree automata (cont’d). Bull. EATCS 38 (1989), 186–190

    MATH  Google Scholar 

  122. Nivat, M., Podelski, A.: Another variation on the common subexpression problem. Discr. Math. 114 (1993), 379–401

    Article  MathSciNet  MATH  Google Scholar 

  123. Oyamaguchi, M.: The Church¡ªRosser property for ground term-rewriting systems is decidable. Theoret. Comput. Sci. 49 (1987), 43–79

    Article  MathSciNet  MATH  Google Scholar 

  124. Pair, C.: Inference for regular bilanguages. Formal Languages and Programming (Proc. Semin. 1975), North-Holland, Amsterdam 1976, 1530

    Google Scholar 

  125. Pair, C., Quere, A.: Définition et etude des bilangages réguliers. Information Control 13 (1968), 565–593

    Article  MathSciNet  MATH  Google Scholar 

  126. Péladeau, P., Podelski, A.: On reverse and general definite tree languages. Automata, Languages and Programming (Proc. 19th ICALP), Lect. Notes in Comput. Sci. 623, Springer-Verlag, Berlin 1992, 150–161

    Google Scholar 

  127. Podelski, A.: A monoid approach to tree automata. In: [TrAL92], 41–56

    Google Scholar 

  128. Potthoff, A.: Modulo counting quantifiers over finite trees. Theoret. Comput. Sci. 126 (1994), 97–112

    Article  MathSciNet  MATH  Google Scholar 

  129. Potthoff, A.: Logische Klassifizierung regulärer Baumsprachen. Bericht Nr. 9410, Inst. Informatik u. Prakt. Math., Chr.-Albrechts University, Kiel, Kiel 1994

    Google Scholar 

  130. Potthoff, A., Thomas, W.: Regular tree languages without unary symbols are star-free. Fundam. Comput. Theory (Proc. Conf. FCT’93), Lect. Notes in Comput. Sci. 710, Springer-Verlag, Berlin 1993,396–405

    Google Scholar 

  131. Raoult, J.-C.: A survey of tree transductions. In: [TrAL92], 311–325

    Google Scholar 

  132. Rosen, B. K.: Tree-manipulating systems and Church-Rosser theorems. J. ACM 20 (1973), 160–187

    Article  MATH  Google Scholar 

  133. Rosenthal, K. I.: Quantaloid nuclei, the syntactic congruence and tree automata. J. Pure Appl. Algebra 77 (1992), 189–205

    Article  MathSciNet  MATH  Google Scholar 

  134. Rosenthal, K. I.: A categorical look at tree automata and context-free languages. Math. Struct. in Comp. Science 4 (1994), 287–293

    Article  MATH  Google Scholar 

  135. Rounds, W. C.: Context-free grammars on trees. 1st Ann. ACM Symp. Theory Comput. (Proc. Symp. 1969), 143–148

    Google Scholar 

  136. Rounds, W. C.: Tree-oriented proofs of some theorems on context-free and indexed languages. 2nd Ann. ACM Symp. Theory Comput. (Proc. Symp. 1970), 109–116

    Google Scholar 

  137. Rounds, W. C.: Mappings and grammars on trees. Math. Systems Theory 4 (1970), 257–287

    Article  MathSciNet  MATH  Google Scholar 

  138. Salomaa, K.: Syntactic monoids of forests (in Finnish). Master’s Thesis, University of Turku, Dept. of Mathematics, Turku 1983

    Google Scholar 

  139. Salomaa, K.: Alternating bottom-up tree automata. Trees in Algebra and Programming (Proc. 11th CAAP), Lect. Notes Comput. Sci. 214, Springer-Verlag, Berlin 1986, 158–171

    Google Scholar 

  140. Salomaa, K.: Yield-languages recognized by alternating tree recognizers. RAIRO Inform. Thćor. 22 (1988), 319–339

    MathSciNet  MATH  Google Scholar 

  141. Salomaa, K.: Alternating tree pushdown automata. Acta Univ. Turkuensis, Ser. A 192, Turku 1988

    Google Scholar 

  142. Salomaa, K.: Deterministic tree pushdown automata and tree rewriting systems. J. Comput. System Sci. 37 (1988), 367–394

    Article  MathSciNet  MATH  Google Scholar 

  143. Salomaa, K.: Representation of recursively enumerable languages using alternating finite tree recognizers. Fundam. Comput. Theory (Proc. FCT’89), Lect. Notes Comput. Sci. 380, Springer-Verlag, Berlin 1989, 372–383

    Google Scholar 

  144. Salomaa, K.: Alternation bounds for tree automata. Acta Cybern. 10 (1992), 173–197

    MathSciNet  MATH  Google Scholar 

  145. Salomaa, K.: Synchronized tree automata. Theoret. Comput. Sci. 127 (1994), 25–51

    Article  MathSciNet  MATH  Google Scholar 

  146. Schimpf, K. M., Gallier, J. H.: Tree pushdown automata. J. Comput. System Sci. 30 (1985), 25–40

    Article  MathSciNet  MATH  Google Scholar 

  147. Seidl, H.: Deciding equivalence of finite tree automata.. Theor. Aspects Comput. Sci. (Proc. STACS’88), Lect. Notes Comput. Sci. 349, Springer-Verlag, Berlin 1989, 480–492

    Google Scholar 

  148. Seidl, H.: On the finite degree of ambiguity of finite tree automata. Acta Inform. 26 (1989), 527–542

    Article  MathSciNet  MATH  Google Scholar 

  149. Seidl, H.: Single-valuedness of tree transducers is decidable in polynomial time. Theoret. Comput. Sci. 106 (1992), 135–181

    Article  MathSciNet  MATH  Google Scholar 

  150. Seidl, H.: Ambiguity and valuedness. In: [TrAL92], 355–380

    Google Scholar 

  151. Seidl, H.: Equivalence of finite-valued tree transducers is decidable. Math. Systems Theory 27 (1994), 285–346

    Article  MathSciNet  MATH  Google Scholar 

  152. Slutzki, G.: Alternating tree automata. Theoret. Comput. Sci. 41 (1985), 305–318

    Article  MathSciNet  MATH  Google Scholar 

  153. Slutzki, G., Vágvölgyi, S.: Deterministic top-down tree transducers with iterated look-ahead. Theoret. Comput. Sci. 143 (1995), 285–308

    Article  MathSciNet  MATH  Google Scholar 

  154. Steinby, M.: Syntactic algebras and varieties of recognizable sets. Les Arbres en Algèbre et en Programmation (Proc. 4th Coll., Lille 1979), University of Lille, Lille 1979, 226–240

    Google Scholar 

  155. Steinby, M.: On certain algebraically defined tree transformations. Al-gebra, Combinatorics and Logic in Computer Science (Proc. Conf. 1983), North-Holland, Amsterdam 1986, 745–764

    Google Scholar 

  156. Steinby, M.: Tree language problems in pattern recognition theory. Fundam. Comput. Theory (Proc. FCT’89), Lect. Notes Comput. Sci. 380, Springer-Verlag, Berlin 1989, 444–450

    Google Scholar 

  157. Steinby, M.: A formal theory of errors in tree representations of pat-terns. J. Inform. Process. Cybern. EIK 26 (1990) 1/2, 19–32

    Google Scholar 

  158. Steinby, M.: A theory of tree language varieties. In: [TrAL92], 57–81

    Google Scholar 

  159. Steinby, M.: General varieties of tree languages. Technical Report LITP 95/30, Institute Blaise Pascal, Universite Denis Piderot, Paris 1995

    Google Scholar 

  160. Takahashi, M.: Primitive transformations of regular sets and recognizable sets. Automata, Languages and Programming (Proc. Coll. 1972), North-Holland, Amsterdam 1973, 475–480

    Google Scholar 

  161. Takahashi, M.: Generalizations of regular sets and their application to a study of context-free languages. Information Control 27 (1975), 1–36

    Article  MATH  Google Scholar 

  162. Takahashi, M.: Rational relations on binary trees. Automata, Languages and Programming (Proc. 4th Coll. 1977), Lect. Notes Comput. Sci. 52, Springer-Verlag, Berlin 1977, 524–538

    Google Scholar 

  163. Thatcher, J. W.: Characterizing derivation trees of context-free grammars through a generalization of finite automata theory. J. Comput. Systems Sci. 1 (1967), 317–322

    Article  MathSciNet  MATH  Google Scholar 

  164. Thatcher, J. W.: Generalized2 sequential machines. J. Comput. System Sci. 4 (1970), 339–367

    Article  MathSciNet  MATH  Google Scholar 

  165. Thatcher, J. W.: Tree automata: an informal survey. Currents in the Theory of Computing (ed. A. V. Aho), Prentice-Hall, Englewood Cliffs, N.J. (1973), 143–172

    Google Scholar 

  166. Thatcher, J. W., Wright, J. B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Systems Theory 2 (1968), 57–81

    Article  MathSciNet  Google Scholar 

  167. Thomas, W.: Logical aspects in the study of tree languages. Trees in Algebra and Programming (Proc. 9th CAAP), Cambridge University Press, Cambridge 1984, 270–280

    Google Scholar 

  168. Thomas, W.: Automata on infinite objects. Handbook of Theoretical Computer Science. Vol. B. Formal Models and Semantics (ed. J. van Leeuwen), Elsevier, Amsterdam 1990, 133–191

    Google Scholar 

  169. Tree Automata and Languages (eds. M. Nivat, A. Podelski). North-Holland, Amsterdam 1992

    MATH  Google Scholar 

  170. Tsomokos, I.: K-treeautomata and their relation to weighted context-free grammars Intern. J. Computer Math. 26 (1989), 91–99

    MATH  Google Scholar 

  171. Vágvölgyi, S.:Top-down tree transducers with two-way tree walking look-ahead. Theoret. Comput. Sci. 93 (1992), 43–74

    Article  MathSciNet  MATH  Google Scholar 

  172. Vágvölgyi, S.: A fast algorithm for constructing a tree automaton recognizing a congruential tree language. Theoret. Comput. Sci. 115 (1993), 391–399

    Article  MathSciNet  MATH  Google Scholar 

  173. Vágvölgyi, S., Fülöp, Z.: An infinite hierarchy of tree transformations in the class NDR.. Acta Cybern. 8 (1987), 153–168

    MATH  Google Scholar 

  174. Virágh, J.: Deterministic ascending tree automata. I. Acta Cybern. 5 (1980), 33–45; II.ibid 6 (1983), 291–301

    Google Scholar 

  175. Wechler, W.: Universal algebra for computer scientists. Springer-Verlag, Berlin 1992

    MATH  Google Scholar 

  176. Wilke, Th.: Algebras for classifying tree languages. Automata, Languages and Programming (Proc. 20th ICALP), Lect. Notes Comput. Sci. 668, Springer-Verlag, Berlin 1993, 347–358

    Google Scholar 

  177. Zachar, Z.: The solvability of the equivalence problem for deterministic frontier-to-root tree transducers. Acta Cybern. 4 (1979), 167–177

    MathSciNet  MATH  Google Scholar 

Download references

Authors
  1. Ferenc Gécseg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Magnus Steinby
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Leiden University, P.O. Box 9512, NL-2300 RA, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Turku Centre for Computer Science Data City, FIN-20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gécseg, F., Steinby, M. (1997). Tree Languages. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59126-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-59126-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-63859-6

  • Online ISBN: 978-3-642-59126-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation