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SIAM Journal on Computing
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Journal of the ACM (JACM)
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Communications of the ACM
Probabilistic, nondeterministic, and alternating decision trees (Preliminary Version)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
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STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
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STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
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FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
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SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
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MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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This work generalizes decision trees in order to study lower bounds on the running times of algorithms that allow probabilistic, nondeterministic, or alternating control. It is shown that decision trees that are allowed internal randomization (at the expense of introducing a small probability of error) run no faster asymptotically than ordinary decision trees for a collection of natural problems. Two geometric techniques from the literature for proving lower bounds on the time required by ordinary decision trees are shown to be special cases of one unified technique that, in fact, applies to nondeterministic decision trees as well. Finally, it is shown that any lower bound on alternating decision tree time also applies to alternating Turing machine time.