Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel.

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Transcript of Span Programs, and-or trees, and effective resistance stacey jeffery shelby kimmel.

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Span Programs,and-or trees,and effective

resistance

stacey jefferyshelby kimmel

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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

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Part I:Span Programs

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Quantum Query Complexity

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Span Programs

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Span Programs

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Span Programs

REJECT

ED

ACCEPTED

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Span Programs and Quantum Algorithms

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Example: OR

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Span Program for ST-Connectivity

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Part II: and-or Trees

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AND-OR Trees

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AND-OR Trees

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AND-OR Trees

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Two-Player Game

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Two-Player Game

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Two-Player Game

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Two-Player Game

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Two-Player Game

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Two-Player Game

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Fault Complexity

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Fault Complexity

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Fault Complexity

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Average Choice Complexity

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Criticality

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Average Choice Complexity

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Formulas and Connectivity

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Formulas and Connectivity

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Formulas and Connectivity

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And-or Trees and st-connectivity

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Span Program for AND-OR Trees

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Span Program for AND-OR Trees

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Span Program for AND-OR Trees

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Span Program for AND-OR Trees

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Span Program for AND-OR Trees

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Winning a Game

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future directions

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Span Programs for st-Connectivity

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