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We prove the following four results on communication complexity:
1) For every k ≥ 2, the language L<subscrpt>k</subscrpt> of encodings of directed graphs of out degree one that contain a path of length k+1 from the first vertex to the last vertex and can be recognized by exchanging O(k log n) bits using a simple k-round protocol requires exchanging… (More)

It is known that k tapes are no better than two tapes for nondeterministic machines. We show here that two tapes are better than one. In fact, we show that two pushdown stores are better than one tape. Also, k tapes are no better than two for nondeterministic reversal-bounded machines. We show here that two tapes are better than one for such machines. In… (More)

We prove the following lower bounds for <underline>on line</underline> computation.
1) Simulating two tape <underline>nondeterministic</underline> machines by one tape machines requires Ω(n log log n) time.
2) Simulating k tape (deterministic) machines by machines with k pushdown stores requires Ω(n log<supscrpt>1/(k+1)</supscrpt>n) time.

The following lower bounds for on-line computation are proved: (1) Simulating two-tape nondeterministic machines by one-tape machines requires I2(n log n) time. (2) Simulating k-tape (deterministic) machines by machines with k-pushdown stores requires Q(n log 1/~k+ 1)n) time.