The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 ·...

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The Story Next To the Story Behind the Results The Story Next To the Story Behind the Results “Pip” Buff Georgia Unitech Oxford University, 4 November 2015

Transcript of The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 ·...

Page 1: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

The Story Next To the Story Behind the Results

“Pip”Buff Georgia Unitech

Oxford University, 4 November 2015

Page 2: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

My Association With Richard Lipton

1986 – Logic and P=?NP.

1994–1997 – Keys and Codes and Graph Separators

2008 – 60th Birthday Workshop

2009–present – Working Up on the GLL Blog.

Shared values of sharing values...and Ideas.

Page 3: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

My Association With Richard Lipton

1986 – Logic and P=?NP.

1994–1997 – Keys and Codes and Graph Separators

2008 – 60th Birthday Workshop

2009–present – Working Up on the GLL Blog.

Shared values of sharing values...and Ideas.

Page 4: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

My Association With Richard Lipton

1986 – Logic and P=?NP.

1994–1997 – Keys and Codes and Graph Separators

2008 – 60th Birthday Workshop

2009–present – Working Up on the GLL Blog.

Shared values of sharing values...and Ideas.

Page 5: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

My Association With Richard Lipton

1986 – Logic and P=?NP.

1994–1997 – Keys and Codes and Graph Separators

2008 – 60th Birthday Workshop

2009–present – Working Up on the GLL Blog.

Shared values of sharing values...and Ideas.

Page 6: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

My Association With Richard Lipton

1986 – Logic and P=?NP.

1994–1997 – Keys and Codes and Graph Separators

2008 – 60th Birthday Workshop

2009–present – Working Up on the GLL Blog.

Shared values of sharing values...

and Ideas.

Page 7: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

My Association With Richard Lipton

1986 – Logic and P=?NP.

1994–1997 – Keys and Codes and Graph Separators

2008 – 60th Birthday Workshop

2009–present – Working Up on the GLL Blog.

Shared values of sharing values...and Ideas.

Page 8: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 9: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 10: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 11: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 12: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 13: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .

1 below P , or2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 14: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or

2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 15: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or

3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 16: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or3 in edges in any branch, or

4 in edges in any branch that is a play of the program.

Page 17: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Fault Tolerance in Alternating Game Setting

Given a chess engine E that may make up to K errors, can we useit to play perfectly?

Perfect � plays any move that wins in a won position, or doesn’tlose in a drawn position. Lost position—no restriction.

Program can play against itself and return a value v = E�(P) fromany position P .

Can usefully abstract as “optimal” and “sub-optimal” values;optimal 1:0.

Starting node P is winning (gives optimal value) for player tomove.

Limit is K errors. . .1 below P , or2 at nodes in any branch, or3 in edges in any branch, or4 in edges in any branch that is a play of the program.

Page 18: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Smullyan-Style Liar Puzzle

Proof that we can play perfectly given E makes at most 1 errorbelow P .

Convert into induction on K . . .F (E ; Q ; j ) = E 0 such that if E makes at most j � 1 errors belowQ , then E 0 plays perfectly below Q .Can we modify the proof to work for criteria 2–4?

Page 19: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Smullyan-Style Liar Puzzle

Proof that we can play perfectly given E makes at most 1 errorbelow P .Convert into induction on K . . .

F (E ; Q ; j ) = E 0 such that if E makes at most j � 1 errors belowQ , then E 0 plays perfectly below Q .Can we modify the proof to work for criteria 2–4?

Page 20: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Smullyan-Style Liar Puzzle

Proof that we can play perfectly given E makes at most 1 errorbelow P .Convert into induction on K . . .F (E ; Q ; j ) = E 0 such that if E makes at most j � 1 errors belowQ , then E 0 plays perfectly below Q .

Can we modify the proof to work for criteria 2–4?

Page 21: The Story Next To the Story Behind the Resultsregan/Talks/OxfordChessLiarGame.pdf · 2015-11-04 · The Story Next To the Story Behind the Results FaultToleranceinAlternatingGameSetting

The Story Next To the Story Behind the Results

Smullyan-Style Liar Puzzle

Proof that we can play perfectly given E makes at most 1 errorbelow P .Convert into induction on K . . .F (E ; Q ; j ) = E 0 such that if E makes at most j � 1 errors belowQ , then E 0 plays perfectly below Q .Can we modify the proof to work for criteria 2–4?