A generalization of spira's theorem and circuits with small segregators or separators
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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Abstract: We give the first extension of the result due to Paul, Pippenger, Szemeredi and Trotter [24] that deterministic linear time is distinct from nondeterministic linear time. We show that NTIME(n{\sqrt log^*(n))}\neq DTIME(n{\sqrt log^*(n))}. We show that if the class of multi-pushdown graphs has (o(n); o(n=log(n))) segregators, then NTIME(nlog(n)) \neq DTIME(nlog(n)). We also show that at least one of the following facts holds - (1) P \neq L, (2) For all polynomially bounded constructible time bounds t, NTIME(t) \neq DTIME(t). We consider the problem of whether NTIME(t) is distinct from NSPACE(t) for constructible time bounds t. A pebble game on graphs is defined such that the existence of a "good" strategy for the pebble game on multi-pushdown graphs implies a "good" simulation of nondeterministic time bounded machines by nondeterministic space-bounded machines. It is shown that there exists a "good" strategy for the pebble game on multi-pushdown graphs iff the graphs have sublinear separators. Finally, we show that nondeterministic time bounded Turing machines can be simulated by \Sigma_4 machines with an asymptotically smaller time bound, under the assumption that the class of multi-pushdown graphs has sublinear separators.