Methods via Automata and Bounded Treewidth

  • Rodney G. Downey
  • Michael R. Fellows
Part of the Texts in Computer Science book series (TCS)


This chapter explores the basics of finite-state automata theory, including the generalization of the main theorems of linear automata theory to tree automata, and how these tools lead to FPT algorithmic methods, meta-theorems, and important concrete applications.


Composition Operator Regular Language Finite Automaton Parse Tree Load Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 4.
    K. Abrahamson, M. Fellows, Cutset regularity beats well-quasi-ordering for bounded treewidth, Preprint (1989) Google Scholar
  2. 5.
    K. Abrahamson, M. Fellows, Finite automata, bounded treewidth, and well-quasiordering, in Proceedings of the AMS Summer Workshop on Graph Minors, Graph Structure Theory, ed. by N. Robertson, P. Seymour. Contemporary Mathematics, vol. 147 (Am. Math. Soc., Providence, 1993), pp. 539–564 Google Scholar
  3. 53.
    Y. Bar-Hillel, M. Perles, E. Shamir, On formal properties of simple phrase structure grammars. Z. Phon. Sprachwiss. Kommun.forsch. 14(2), 143–172 (1961) MathSciNetzbMATHGoogle Scholar
  4. 178.
    B. Courcelle, J. Engelfriet, Graph Structure and Monadic Second Order Logic: A Language-Theoretic Approach. Encyclopedia of Mathematics and Its Applications, vol. 138 (Cambridge University Press, Cambridge, 2012) CrossRefGoogle Scholar
  5. 228.
    J. Doner, Tree acceptors and some of their applications. J. Comput. Syst. Sci. 4, 406–451 (1970) MathSciNetCrossRefzbMATHGoogle Scholar
  6. 247.
    R. Downey, M. Fellows, Parameterized Complexity. Monographs in Computer Science (Springer, Berlin, 1999) CrossRefGoogle Scholar
  7. 345.
    F. Giécseg, M. Steinby, Tree Automata (Akad. Kiadó, Budapest, 1984) Google Scholar
  8. 401.
    J. Hopcroft, J. Ullmann, Introduction to Automata Theory, Languages and Computation (Addison-Wesley, Reading, 1979) zbMATHGoogle Scholar
  9. 403.
    D. Huffmann, The synthesis of sequential switching circuits. J. Franklin Inst. 257(3–4), 161–190, 275–303 (1954) Google Scholar
  10. 448.
    S. Kleene, Representation of events in nerve nets and finite automata, in Automata Studies, ed. by C. Shannon, J. McCarthy. Annals of Mathematical Studies (Princeton University Press, Princeton, 1956), pp. 3–42 Google Scholar
  11. 463.
    D. Kozen, On the Myhill–Nerode theorem for trees. Bull. Eur. Assoc. Theor. Comput. Sci. 47, 170–173 (1992) zbMATHGoogle Scholar
  12. 464.
    D. Kozen, On regularity preserving functions. Bull. Eur. Assoc. Theor. Comput. Sci. 58, 131–138 (1996) zbMATHGoogle Scholar
  13. 484.
    E. Leiss, The complexity of restricted regular expressions and the synthesis problem for finite automata. J. Comput. Syst. Sci. 23(3), 348–354 (1981) MathSciNetCrossRefzbMATHGoogle Scholar
  14. 524.
    W. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biophys. 5, 115–133 (1943) MathSciNetCrossRefzbMATHGoogle Scholar
  15. 525.
    R. McNaughton, H. Yamada, Regular expressions and state graphs for automata. IEEE Trans. Electron. Comput. ED-9(1), 39–47 (1960) CrossRefGoogle Scholar
  16. 526.
    G. Mealy, A method for synthesising sequential circuits. Bell Syst. Tech. J. 34(5), 1045–1079 (1955) MathSciNetCrossRefGoogle Scholar
  17. 530.
    J. Mezei, J. Wright, Algebraic automata and context free sets. Inf. Control 11, 3–29 (1967) MathSciNetCrossRefzbMATHGoogle Scholar
  18. 537.
    E. Moore, Gedanken experiments on sequential machines, in Automata Studies, ed. by C. Shannon, J. McCarthy. Annals of Mathematics Studies, vol. 34 (Princeton University Press, Princeton, 1956), pp. 129–153 Google Scholar
  19. 539.
    J. Myhill, Finite automata and representation of events, WADD TR-57-624, Wright-Patterson AFB, Ohio, 1957, pp. 112–137 Google Scholar
  20. 545.
    A. Nerode, Linear automaton transformations. Proc. Am. Math. Soc. 9, 541–544 (1958) MathSciNetCrossRefzbMATHGoogle Scholar
  21. 569.
    M. Rabin, D. Scott, Finite automata and their decision problems. IBM J. Res. Dev. 3, 114–125 (1959) MathSciNetCrossRefGoogle Scholar
  22. 640.
    J. Thatcher, J. Wright, Generalized finite automata. Not. Am. Math. Soc. 12, 820 (1965) Google Scholar
  23. 644.
    K. Thompson, Regular expression search algorithm. Commun. ACM 11(6), 419–422 (1968) CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rodney G. Downey
    • 1
  • Michael R. Fellows
    • 2
  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria UniversityWellingtonNew Zealand
  2. 2.School of Engineering and Information TechnologyCharles Darwin UniversityDarwinAustralia

Personalised recommendations