Transformational methods and their application to complexity problems

SummaryThe following results are proved by the use of transformabilities.1.NTAPE (log n)=TAPE (log n)⇔There exists a j such that every language accepted by a nondeterministic one-way one-counter automaton is contained in Dj. (Dj is the family of all languages accepted by deterministic j-head two-way finite automata.)2.NTAPE (n) =TAPE (n)⇔ There exists a j such that every language L ∉ {1}* accepted by a nondeterministic 5-head two-way finite automaton is contained in Dj.3. $$\mathop U\limits_d$$ TIME (nd=TAPE (log n)⇔ There exists a j such that every language accepted by a deterministic 1-head two-way pushdown automaton is contained in Dj.4.f $$\mathop U\limits_d$$ TIME (dn)=TAPE (n)⇔There exists a j such that every language L ⊂{1}* accepted by a deterministic 1-head two-way pushdown automaton is contained in Dj.5.Dj ≨ Dj+1 for all j ε εN.