Separating tape bounded auxiliary pushdown automata classes

Previous results in the literature which describe separation theorems for time bounded complexity classes serve also to separate classes defined by tape bounded auxiliary pushdown automata. Results described here refine these basic relationships between classes defined by tape bounded AuxPDA. It is shown that, for auxiliary PDA fully constructable functions S0 and S1 satisfying S1 (n+1) ε o,(S0 (n)), S0 tape bounded AuxPDA are more powerful than S1 tape bounded AuxPDA. Further results refine the resulting separation by the number of worktape symbols and the number of worktape heads. Results are also described for separating classes defined by tape bounded AuxPDA with one pushdown store symbol, i.e. auxiliary counter automata (AuxCA). Refinements of the known equivalence of nondeterministic L(n)-tape bounded AuxPDA and deterministic L(n)-tape bounded AuxPDA are also described. One corollary is that every two-way nondeterministic PDA can be simulated by a two-way deterministic PDA with four input tape heads and that every context-free language can be recognized by a deterministic two-way PDA with three heads. Another corollary of these results shows that there are languages over a single letter alphabet which are recognized by (k+1)-head two-way PDA but cannot be recognized by any k-head two-way PDA. It is shown also that AuxPDA and AuxCA can fully construct very slow growing functions so that even small amounts of worktape space (e.g. that bounded by log*n) increase their computational power.

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