Autumn Joint Lecture of Kansai Branches

Lecture notes- Applied Stability Theory (Math 414) Autumn 2003.

Sometimes the derivation is denoted by a→ a′. A ring equipped with a derivation is called a differential ring. The notions, differential subring, differential ring extension and homomorphism between differential rings, are clear. If (R, ∂) is a differential ring then the set of constants is by definition {r ∈ R : ∂(r) = 0}, and is easily seen to be a (differential) subring. ∂ means the k-fold i...

Introduction to spefication and verification Lecture Notes , autumn 2011

Coding Theory Autumn 2017 Lecture 6 : October 16 , 2017

Mathematical Toolkit Autumn 2015 Lecture 12 : November 11 , 2015

φ ≡ C1 ∧ · · · ∧ Cm , where each Ci is a clause of the form Ci = (li1 ∨ li2 ∨ li3) and each lij is in turn xij or its negation xij . We assume that each clause contains three distinct variables. In the problem Max 3-SAT, the goal is not necessarily to satisfy all the clauses, but rather find an assignment to the variables which satisfies as many clauses as possible. We show that for any formula...

CSE 533 : The PCP Theorem and Hardness of Approximation ( Autumn 2005 ) Lecture 1 : Introduction

The PCP Theorem is concerned with the notion of “proofs” for mathematical statements. We begin with a somewhat informal definition: Definition 1.1. A traditional proof system works as follows: • A statement is given. (e.g., “this graph G = · · · is 3-colorable” or “this CNF formula F = (x1 ∨ x2 ∨ x10) ∧ · · · is satisfiable”). • A prover writes down a proof, in some agreed-upon format. • A veri...