span programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

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Page 1: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Page 2: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Programs,and-or trees,and effective

resistance

stacey jefferyshelby kimmel

Page 3: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Page 4: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Part I: Span Programs

Part II: and-or trees

• Span Programs• Span Program for or• Span Program for st-connectivity

• and-or trees• average choice complexity• and-or trees and st-connectivity• winning a game tree

Page 5: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Part I:Span Programs

Page 6: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Quantum Query Complexity

Page 7: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Programs

Page 8: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Programs

Page 9: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Programs

REJECT

ED

ACCEPTED

Page 10: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Programs and Quantum Algorithms

Page 11: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Example: OR

Page 12: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 13: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 14: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 15: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 16: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 17: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 18: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 19: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 20: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for ST-Connectivity

Page 21: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Part II: and-or Trees

Page 22: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

AND-OR Trees

Page 23: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

AND-OR Trees

Page 24: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

AND-OR Trees

Page 25: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Two-Player Game

Page 26: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Two-Player Game

Page 27: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Two-Player Game

Page 28: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Two-Player Game

Page 29: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Two-Player Game

Page 30: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Two-Player Game

Page 31: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Fault Complexity

Page 32: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Fault Complexity

Page 33: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Fault Complexity

Page 34: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Average Choice Complexity

Page 35: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Criticality

Page 36: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Average Choice Complexity

Page 37: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Formulas and Connectivity

Page 38: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Formulas and Connectivity

Page 39: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Formulas and Connectivity

Page 40: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

And-or Trees and st-connectivity

Page 41: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for AND-OR Trees

Page 42: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for AND-OR Trees

Page 43: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for AND-OR Trees

Page 44: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for AND-OR Trees

Page 45: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Program for AND-OR Trees

Page 46: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Winning a Game

Page 47: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

future directions

Page 48: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

Span Programs for st-Connectivity

Page 49: Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel

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