all possible of all-out problem

All Possible of All-Out All Possible of All-Out ProblemProblem

IntroductionIntroduction

IntroductionIntroduction

IntroductionIntroduction

IntroductionIntroduction

IntroductionIntroduction

IntroductionIntroduction

PurposePurpose

BoundaryBoundary

MethodMethod

MethodMethod

XorXor

P Q P xor Q

1 1 0

1 0 1

0 1 1

0 0 0

Invariant & parityInvariant & parity

Invariant & parityInvariant & parity

Invariant & parityInvariant & parity

Invariant & parityInvariant & parity

ResultsResults

a11 a12 a13 a14 a15

a21 a22 a23 a24 a25

a31 a32 a33 a34 a35

a41 a42 a43 a44 a45

a51 a52 a53 a54 a55

b11 b12 b13 b14 b15

b21 b22 b23 b24 b25

b31 b32 b33 b34 b35

b41 b42 b43 b44 b45

b51 b52 b53 b54 b55

a11xorb11 a12xorb12 a13xorb13 a14xorb14 a15xorb15

a21xorb11 a22xorb11 a23 xorb11 a24xorb11 a25xorb11

a31xorb11 a32xorb11 a33xorb11 a34xorb11 a35xorb11

a41xorb11 a42xorb11 a43xorb11 a44xorb11 a45xorb11

a51xorb11 a52xorb11 a53xorb11 a54xorb11 a55 xorb11

xor

=

ResultsResults

o o o o o

o o x o o

o o o o o

o o o o o

o o o o o

0 0 1 0 0

0 1 1 1 0

0 0 1 0 0

0 0 0 0 0

0 0 0 0 0

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ResultsResults

ConclusionConclusion