Space and Time Efficient Simulations and Characterizations of Some Restricted Classes of PDAs

In this paper we present some space/time efficient Turing machine algorithms for recognizing some subclasses of DCFL's. In particular, we show that the finite minimal stacking and “simple” strict restricted (a subclass of strict restricted) deterministic pushdown automata (FMS-DPDA's SSR-DPDA's, respectively) can be simulated by offline Turing machines simultaneously in space S(n) and time n2/S(n) for any tape function S(n) satisfying log n ≤ S(n) ≤ n which is constructable in n2/S(n) time. Related techniques can be used to give interesting characterizations of 2-head 2-way finite automata, both deterministic and nondeterministic. In particular we show that a 2-head 2-way deterministic finite automataton is equivalent to a simple type of 2-way deterministic checking stack automaton. This is in contrast to a result which shows that 2-way nondeterministic checking stack automata are equivalent to nondeterministic linear bounded automata. We also show that a language L is accepted by a 2k-head two-way nondetermistic finite automaton if and only if it is accepted by a k-head two-way nondeterministic pushdown automaton which makes at most one reversal on its stack.