The satisfiability problem is N P -complete.
Cook-Levin
Theorem
A prize of 1, 000, 000 dollars is offered by the Clay Mathematics Institute for its solution.
4.5
Logic and Computer Science Logical
Revolution
NOTE: The following material is from Moshe Var
Discrete Mathematics1
http:/iscasmc.ios.ac.cn/DM2016
Lijun Zhang
April 13, 2016
1 Materials
about the axiomatization are provided by Dr. Wanwei Liu.
Contents
1. The Foundations: Logic and Proofs
2. Basic Structures: Sets, Functions, Sequences, Sums, and
M
Discrete Mathematics1
http:/iscasmc.ios.ac.cn/DM2016
Lijun Zhang
March 30, 2016
1 Materials
about the axiomatization are provided by Dr. Wanwei Liu.
Contents
1. The Foundations: Logic and Proofs
2. Basic Structures: Sets, Functions, Sequences, Sums, and
M
Discrete Mathematics1
http:/iscasmc.ios.ac.cn/DM2016
Lijun Zhang
April 5, 2016
1 Materials
about the axiomatization are provided by Dr. Wanwei Liu.
Contents
1. The Foundations: Logic and Proofs
2. Basic Structures: Sets, Functions, Sequences, Sums, and
Ma
Discrete Mathematics1
http:/iscasmc.ios.ac.cn/DM2016
Lijun Zhang
March 16, 2016
1 Materials
about the axiomatization are provided by Dr. Wanwei Liu.
Contents
1. The Foundations: Logic and Proofs
2. Basic Structures: Sets, Functions, Sequences, Sums, and
M
Exercise sheet 3 on Discrete Mathematics
Lijun Zhang
Andrea Turrini
http:/iscasmc.ios.ac.cn/DM2016
To be submitted on April 12, 2016.
Exercise 3.1. Prove Lemma 3.4.3: a Hintikka set is consistent, and moreover, for
each formula , either 6 , or
6 .
Exerci
Discrete Mathematics1
http:/iscasmc.ios.ac.cn/DM2016
Lijun Zhang
March 16, 2016
1 Materials
about the axiomatization are provided by Dr. Wanwei Liu.
Contents
1. The Foundations: Logic and Proofs
2. Basic Structures: Sets, Functions, Sequences, Sums, and
M
Hintikka set
April 23, 2016
A Hintikka set is a set of FOL formulas fulfilling the following properties:
1. For each formula , either
/ or
/ .
2. implies that either or .
3. implies that .
4. ( ) implies that and .
5. x implies that (x/t) for each term
Exercise sheet 2 on Discrete Mathematics
Lijun Zhang
Andrea Turrini
http:/iscasmc.ios.ac.cn/DM2016
To be submitted on March 29, 2016.
Let A be a finite alphabet, such as the English alphabet, and consider the following
simple programming language WHILE wh
Exercise sheet 1 on Discrete Mathematics
Lijun Zhang
Andrea Turrini
http:/iscasmc.ios.ac.cn/DM2016
To be submitted on March 15, 2016.
We first define the following normal forms.
Conjunctive Normal Form (CNF):
Every formula is a conjunction of clauses C1
Concurrent Objects
Companion slides for
The Art of Multiprocessor Programming
Modified by ZHANG Yu & Huimin Lin
What Learned Last Week
Multicore Programming
Maximizing concurrent part
Mutual exclusion
Bakery and Peterson algorithms
Do not rely on lower
Introduction
Companion slides for
The Art of Multiprocessor Programming
by Maurice Herlihy & Nir Shavit
Modified by ZHANG Yu & Huimin Lin
Moore s Law
Transistor
count still
rising
Clock
speed
flattening
sharply
Art of Multiprocessor Programming
2
The Unip
Linked Lists: Locking, LockFree, and Beyond
Companion slides for
The Art of Multiprocessor
Programming
by Maurice Herlihy & Nir Shavit
Last Lecture: Spin-Locks
.
CS
spin critical
lock section
Resets lock
upon exit
Art of Multiprocessor Programming
2
Toda
Spin Locks and
Contention
Companion slides for
The Art of Multiprocessor
Programming
by Maurice Herlihy & Nir Shavit
Focus so far: Correctness
and Progress
Models
Accurate (we never lied to you)
But idealized (so we forgot to mention a few
things)
Pro
Monitors and Blocking Synchroniza
Peng WU
Modified by Yi Lv
Based on the slides by Avishai (Shai) Gretz for
Advanced Topics in Concurrent Programming, 236803
Instructor: Prof. Erez Petrank
Computer Science Department, Technion, Spring 2012
Table of Conten