On recursive and non-recursive trade-offs between finite-turn pushdown automata

  • Authors:

  • Andreas Malcher

  • Affiliations:

  • Institut für Informatik, Johann Wolfgang Goethe-Universität, Frankfurt am Main, Germany

  • Venue:
  • Journal of Automata, Languages and Combinatorics
  • Year:
  • 2007

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Abstract

It is shown that between one-turn pushdown automata (1-turn PDAs) and deterministic finite automata (DFAs) there will be savings concerning the size of description not bounded by any recursive function, so-called non-recursive trade-offs. Considering the number of turns of the stack height as a consumable resource of PDAs, the existence of non-recursive trade-offs between PDAs performing k+1 turns and k turns for k≥1 is proven. Furthermore, non-recursive trade-offs are shown between arbitrary PDAs and PDAs which perform only a finite number of turns. In the second part, k-turn deterministic PDAs (k-turn DPDAs) are considered. The trade-offs between nondeterministic and deterministic k-turn PDAs are still non-recursive whereas it is an open question whether the trade-offs between DPDAs performing k+1 turns and k turns for k≥1 is recursive. If the trade-offs are recursive, then a doubly exponential function serves as a lower bound.