Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Simulated annealing
2/8/05
M. A. Breuer
1
Introduction: Bipartitioning a graph
! A simple initial assignment
Cut=6
Nodes can have weights, e.g. associated with area or power; edges can have weights, e.g. associated with criticality or bus width.
2/8/05 M
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
fillin animation only answer
Some introductory mathematical concepts
M. A. Breuer Ming Hsieh Department of Electrical Engineering Viterbi School of Engineering University of Southern California EE581 Fall 2007
1/9'06; rev. 8/06, 9/07 Copyright (c) 2006 M
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Mathematical proof techniques
Fillin Answer Only Animation
EE581 Fall 2009 USC
January 23, 2006; rev. 8/29/06; 9/09
Melvin A. Breuer
1
Definitions
fillin
Theorem: A result stating the _ of two or more concepts. From the Greek Oeopeiv (theorein) meaning
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Combinatorics
Animation fillin workon answer only read only
Melvin A. Breuer
EE581, Fall 2009
Ming Hsieh Department of Electrical Engineering Viterbi School of Engineering University of Southern California
January 1, 2006; rev. 10/1/06, 9/09
Melvin A. B
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Fillin Answer Animation only
Boolean switching functions
Melvin A. Breuer University of Southern California Viterbi School of Engineering Ming Hsieh Department of Electrical Engineering
7/29/07
Melvin A. Breuer
1
Background material
Boolean
George Bool
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Graphs and Related Theory and Algorithms
with applications to VLSI layout Part 1 of 3
Melvin A. Breuer
EE 581 Fall 2006 University of Southern California
Fillin Answer Animation Only
2/2/2006,rev. 9/24/06
M. A. Breuer and others
1
What you should get fr
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Graphs and Related Theory and Algorithms
with applications to VLSI layout
Part 2 of 3
fillin answer animated only
Melvin A. Breuer
EE581 Fall 2006 University of Southern California
2/2/2006; rev. 9/24/06
M. A. Breuer and others
1
Graphs related to VLSI
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Graphs and Related Theory and Algorithms
with applications to VLSI layout Part 3 of 3
Fillin Answer Animation Only
2/2/2006; rev. 9/24/06
M. A. Breuer and others
1
Basic graph algorithms commonly used in VLSI CAD
Spanning Trees
Minimum Spanning Tree (
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Fillin Answer Only Animation
SOME COMMON ALGORITHMIC TECHNIQUES USED IN VLSI CAD
Part 1
Melvin A. Breuer
EE581 Fall 2009 Ming Hsieh Department of Electrical Engineering Vitebi School of Engineering University of Southern California
2/24/06; 10/4/06; 10/0
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
Genetic Algorithms
3/10/05
M.A. Breuer
1
Genetic Algorithms (GA)
! ! ! !
A class of probabilistic search algorithms Inspired by natural genetics and biological evolution Uses concept of survival of fittest GA originally developed by John Holland (1975)
3/
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581
fillin animation only
Heuristic techniques in design automation
EE581 Fall 2009
Melvin A. Breuer
Ming Hsieh Department of Electrical Engineering Viterbi School of Engineering University of Southern California
2/8/05, 11/09
M. A. Breuer
1
Definition of a
Mathematical Foundations for Computer Aided Design of VLSI Circuits
EE 581

Fall 2009
Binary Decision Diagrams
Melvin A. Breuer
EE581, Fall 2006 University of Southern California
N ovem ber 25, 2006
M e lv in A . B r e u e r
1
Motivation
Boolean functions (BFs or BSFs) are used in
Synthesis (e.g. EE681) Validation (e.g. EE681) Test Gener