On The Space Complexity Of Turn Bounded Pushdown Automata

A pushdown automaton is said to make a turn at a given instant if it changes at that instant from stack increasing to stack decreasing. Let \hbox{NPDA-TURN}(\,f(n)) and \hbox{DPDA-TURN}(\,f(n)) denote the classes of languages accepted by nondeterministic and deterministic pushdown automata respectively that make at most f v ( n ) turns for any input of length n . In this paper the following inclusions that express the space complexity of turn bounded pushdown automata are given: \hbox{DPDA-TURN}(\,f(n)) \subseteq {\bf DSPACE}(\log f(n)\log n) , and \hbox{NPDA-TURN}(\,f(n)) \subseteq {\bf NSPACE} (\log f(n)\log n) . In particular, it follows that finite-turn pushdown automata are logarithmic space bounded: \hbox{DPDA-TURN}(O(1))\subseteq {\bf DL} and \hbox{NPDA-TURN}(O(1))\subseteq {\bf NL} , from which two corollaries follow: one is that the class of metalinear context-free languages is complete for NL , and the other is that a more tight inclusion \hbox{NPDA-TURN}(\,f(n)) \subseteq {\bf DSPACE}(\log^2 f(n)\log n) cannot be derived unless {\bf DL}={\bf NL} , though \hbox{NPDA-TURN} (\,f(n)) \subseteq {\bf DSPACE}(\log^2 f(n)\log^2n) holds.

Keywords:

• Pushdown Automaton
• Turn (head Reversal)
• Space Complexity