Analysis of random processes via And-Or tree evaluation

We introduce a new set of probabilistic analysis tools based on the analysis of And-Or trees with random inputs. These tools provide a unifying, intuitive, and powerful framework for carrying out the analysis of several previously studied random processes, including random loss-resilient codes, solving random k-SAT formulae using the pure literal rule, the greedy algorithm for matchings in random graphs. In addition, these tools allow generalizations of these problems not previously analyzed to be analyzed in a straightforward manner. We illustrate our methodology on the three problems listed above. International Computer Science Institute, Berkeley, CA. Parts of this research were done while still at the Digital Equipment Corporation Systems Research Center, Palo Alto, CA. Research partially supported by NSF operating grant NCR-9416101. y Digital Equipment Corporation, Systems Research Center, Palo Alto, CA. z International Computer Science Institute Berkeley, and Institut fur ...