Degrees of nondeterminism for pushdown automata
Savitch and Vermeir in  introduced two measures for nondeterminism of pushdown automata and showed interestingly that the second measure yields an infinite hierarchy of language families between the deterministic context-free and general context-free languages. However, the proof given in  for this hierarchy theorem was incorrect. In this paper, we show that all the languages used in  to separate different families of the hierarchy actually belong to the first level above the DCFLs. We give a new proof for the hierarchy theorem. We also introduce a new and intuitive measure for nondeterminism and show that it is equivalent to Savitch and Vermeir's second measure.
KeywordsNondeterminism pushdown automata context-free languages pumping lemmas
Unable to display preview. Download preview PDF.
- J. Goldstine, C.M.R. Kintala, and D. Wotschke, “On measuring nondeterminism in regular languages”, manuscript.Google Scholar
- M.A. Harrison, Introduction to Formal Language Theory, Addison-Wesley, Reading, MA, 1978.Google Scholar
- C.M.R. Kintala and P.C. Fischer, “Computations with a restricted number of nondeterministic steps”, Proceedings of the 9th ACM Symposium on the Theory of Computing, (1977) 178–185.Google Scholar
- C.M.R. Kintala and D. Wotschke, “Amounts of nondeterminism in finite automata”, Acta Informatica 13 (1980) 199–204.Google Scholar
- M. Li and P. Vitanyi, “A new approach to formal language theory by Kolmogorov complexity”, Proceedings of the 16th ICALP, Lecture Notes in Computer Science 372 (1989) 506–520.Google Scholar
- A. Salomaa, Formal Languages, Academic Press, New York, 1973.Google Scholar
- D. Vermeir and W.J. Savitch, “On the amount of nondeterminism in pushdown automata”, Fundamenta Informaticae 4 (1981) 401–418.Google Scholar
- S. Yu, “A pumping lemma for deterministic context-free languages”, Information Processing Letters 31 (1989) 47–51.Google Scholar