In this chapter we shall study another computational model: the alternating Turing machine. This model combines the power of nondeterminism with parallelism by alternating the existential and universal states. Alternation connects time and space complexity rather well, in the sense that alternating polynomial time equals deterministic polynomial space, and alternating linear space equals deterministic exponential time. Analogous relationships hold for other time and space bounds. In the next chapter, we shall see how alternation links with the Parallel Computation Thesis presented in the previous chapters.
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