Tally languages accepted by alternating multitape finite automata

  • Dainis Geidmanis
  • Jānis Kaņeps
  • Kalvis Apsītis
  • Daina Taimirņa
  • Elena Calude
Session 12: Automata, Languages and Complexity
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1276)


We consider k-tape 1-way alternating finite automata (k-tape lafa). We say that an alternating automaton accepts a language L\(\subseteq\)*)k with f(n)-bounded maximal (respectively, minimal) leaf-size if arbitrary (respectively, at least one) accepting tree for any (w1, w2,..., wk) ∈ L has no more than
$$f\mathop {(\max }\limits_{1 \leqslant i \leqslant k} \left| {w_i } \right|)$$
leaves. The main results of the paper are the following. If k-tape lafa accepts language L over one-letter alphabet with o(log n)-bounded maximal leaf-size or o(log log n)-bounded minimal leaf-size then the language L is semilinear. Moreover, if a language L is accepted with o(log log(n))-bounded minimal (respectively, o(log(n))-bounded maximal) leaf-size then it is accepted by constant-bounded minimal (respectively, maximal) leaf-size by the same automaton. To show that this bound is optimal we prove that 4-tape lafa can accept a non-semilinear languages over one-letter alphabet with O(log log n)-bounded minimal leaf-size. For maximal leaf-size our bound is optimal due to King's results.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Dainis Geidmanis
    • 1
  • Jānis Kaņeps
    • 1
  • Kalvis Apsītis
    • 2
  • Daina Taimirņa
    • 3
  • Elena Calude
    • 4
  1. 1.Institute of Mathematics and Computer Science, University of LatviaRigaLatvia
  2. 2.Department of Computer ScienceUniversity of MarylandUSA
  3. 3.Department of MathematicsCornell UniversityIthacaUSA
  4. 4.Computer Science DepartmentUniversity of AucklandAucklandNew Zealand

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