Handout 7 Jonathan Katz

Notes on Complexity Theory Last updated : October , 2005 Handout 8

Recall from last time that a random walk on a graph gave us an RL algorithm for the problem of undirected graph connectivity. In this class, we also saw an RP algorithm for solving 2-SAT (see [2, Chapter 7] for details). We now develop some of the theory behind Markov chains and random walks on (undirected) graphs, toward a proof of the following result that was used to analyze both of the abov...

Notes on Complexity Theory Last updated : October , 2005 Handout 5

(Note that the {αa1···an} are simply “selector bits” which determine whether a given term contributes to the sum.) To see this, consider the arithmetization of f over Z2: write f in conjunctive normal form and then map x̄ to (1− x); map C ∧ C ′ to CC ′ (where C,C ′ are expressions); and map C ∨C ′ to 1− (1−C)(1−C ′). Expanding everything out, we obtain a sum over all possible monomials. The abov...

Confirmation Theory as a Branch of Inductive Logic: Historical and Philosophical Reflections APA Eastern 2005 Inductive Logic Symposium Script

Slide #0 (Title). Before I get underway, I’d like to quickly thank a few people. First, Jonathan Vogel and John MacFarlane for working behind the scenes to make this thing happen. And, of course, David Christensen for chairing, and Patrick Maher and Jim Joyce for participating. I especially want to thank Patrick for his terrific feedback on my work this term, which has helped me to get much cle...

Security Models and Reasoning about Security

The primary goal of this class is to bring students to a level where they understand enough about cryptography to use it intelligently, while gaining some insight into how cryptographic operations work. However, it is not a cryptography class in the sense of learning the science of cryptography, and the Stallings book is similarly focused and does not discuss the science of cryptography. The pu...

Worst - Case Analysis Handout 7