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LTb
6586 351 M
0 63 V
0 4555 R
0 -63 V
0 -4695 R
( ) Cshow
LTa
6969 351 M
0 4618 V
LTb
6969 351 M
0 63 V
0 4555 R
0 -63 V
0 -4695 R
(200) Cshow
840 351 M
6129 0 V
0 4618 V
-6129 0 V
840 351 L
140 2660 M
currentpoint gsave translate 90 rotate 0 0 M
(Upper bound on collision probablity, B\(N\)) Cshow
grestore
3904 71 M
(Number of buckets, N) Cshow
LT0
840 4875 M
3 -6 V
3 -5 V
3 -5 V
3 -6 V
3 -5 V
3 -5 V
3 -5 V
4 -5 V
3 -6 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -6 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
4 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
4 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -4 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -5 V
3 -4 V
3 -5 V
3 -5 V
3 -5 V
4 -5 V
3 -4 V
3 -5 V
3 -5 V
3 -5 V
3 -4 V
3 -5 V
3 -5 V
3 -5 V
3 -4 V
3 -5 V
3 -5 V
3 -4 V
3 -5 V
3 -5 V
4 -4 V
3 -5 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -5 V
4 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
4 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
4 -5 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -4 V
4 -5 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
4 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -5 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
4 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
4 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
4 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
4 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
4 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
4 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
4 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
4 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
4 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
4 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
4 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
4 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
4 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
4 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
4 -3 V
3 -3 V
3 -4 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
4 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
currentpoint stroke M
3 -3 V
3 -3 V
4 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
4 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
4 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
4 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
4 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
4 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
4 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
4 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
4 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
4 -3 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -3 V
3 -2 V
3 -3 V
4 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
4 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
4 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
4 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
4 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
4 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
4 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
4 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
4 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
4 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
currentpoint stroke M
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -3 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
4 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
4 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
4 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
4 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
4 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
4 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
4 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
4 -2 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
4 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
4 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
4 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
4 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
4 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
4 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
4 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
4 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
currentpoint stroke M
3 -1 V
3 -2 V
3 -1 V
3 -2 V
4 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
4 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
4 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
4 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
4 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
4 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
4 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -1 V
3 -2 V
3 -1 V
4 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
3 -1 V
3 -1 V
3 -2 V
3 -1 V
3 -2 V
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%%EndDocument
 @endspecial 325 1092 a
 currentpoint currentpoint translate 1 .5 div 1 .5 div scale neg exch
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1988 y Fs(\001)8 b(\001)g(\001)e Fu(y)1364 1995 y Fr(N)1398
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2045 y Fv(\)\).)19 b(Th)o(us)c Ff(State)q Fv(\()p Fu(h)1758
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y Fr(t)1887 2045 y Fv(\))14 b(is)0 2101 y(the)j(state)f(of)h
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2165 y Fr(t)936 2158 y Fv(\)\).)29 b(Th)o(us)18 b Ff(State)1233
2165 y Fr(\033)1256 2158 y Fv(\()p Fu(h)1300 2165 y Fp(1)1327
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y Fv(\))18 b(captures)g(the)g(state)g(of)g Fu(M)0 2214
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952 2824 y(13)p eop
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14 13 bop 0 79 a Fv(con)o(tin)o(uation)18 b(with)f(probabilit)o(y)i(at)
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1271 y Fr(h)p Fq(2B)253 1241 y Fv([)o Fu(h)p Fv(\()p
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Fv(\))13 b(=)g(0)o(])100 1466 y(=)121 b(Pr)177 1496 y
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Fr(;h)516 1536 y Fj(6)534 1531 y Fq(g\\f)p Fr(h)614 1536
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1466 y Fu(h)1121 1473 y Fp(1)1140 1466 y Fu(h)1166 1473
y Fp(2)1186 1466 y Fu(h)1212 1473 y Fp(3)1232 1466 y
Fu(h)1258 1473 y Fp(4)1278 1466 y Fu(h)1304 1473 y Fp(5)1324
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1629 y Fs(\024)103 b Fv(max)177 1659 y Fr(h)197 1664
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1659 y Fq(2)p Fr(D)332 1664 y Fi(t)p Fk(\000)p Fj(6)560
1629 y Fv(Pr)503 1658 y Fi(h)521 1665 y Fj(1)538 1658
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1793 y(=)96 b(Pr)177 1823 y Fr(h)197 1828 y Fj(1)215
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Fy(E)r Fx(,)e Fy(\033)i Fx(ac)n(c)n(or)n(dingly)100 1968
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Fr(;)p Fp(1)p Fq(g)208 1059 y Fi(n)230 1074 y Fq(\000f)p
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1399 y Fv(Man)o(y)c(thanks)g(to)g(the)h(t)o(w)o(o)e(anon)o(ymous)h
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1701 y Fv([1])22 b(N.)g(Alon,)j(O.)d(Goldreic)o(h,)j(J.)e(H)-6
b(\027)-28 b(astad)22 b(and)h(R.)f(P)o(eralta,)i(Simple)g
(constructions)f(of)f(almost)g Fu(k)q Fv(-wise)105 1757
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1814 y(IEEE)j(Computer)g(So)q(ciet)o(y)l(,)h(1990,)d(pp.)j(544{553.)34
1907 y([2])22 b(R.)15 b(Arnold)h(and)f(D.)g(Copp)q(ersmith,)g(An)h
(alternativ)o(e)f(to)g(p)q(erfect)g(hashing,)h(IBM)f(R)o(C)h(10332)d
(\(1984\).)34 2001 y([3])22 b(M.)f(Bellare,)k(R.)d(Canetti)g(and)g(H.)g
(Kra)o(w)o(czyk,)h(Keying)g(hash)g(functions)f(for)g(message)g(authen)o
(tica-)105 2058 y(tion,)14 b Fb(Adv)m(ances)i(in)f(Cryptology)f({)g(CR)
l(YPTO)h('96)p Fv(,)e(Lecture)i(Notes)f(in)h(Computer)f(Science,)i(v)o
(ol.)e(1109,)105 2114 y(Springer-V)l(erlag,)i(1996,)e(pp.)h(1{15.)34
2208 y([4])22 b(M.)16 b(Bellare,)j(O.)e(Goldreic)o(h)i(and)e(S.)g
(Goldw)o(asser,)g(Incremen)o(tal)i(cryptograph)o(y:)d(the)h(case)g(of)g
(hashing)105 2264 y(and)i(signing,)h Fb(Adv)m(ances)g(in)g(Cryptology)e
({)h(CR)l(YPTO)g('94)p Fv(,)f(Lecture)i(Notes)e(in)i(Computer)e
(Science,)105 2321 y(v)o(ol.)d(839,)f(Springer-V)l(erlag,)i(1994,)e
(pp.)h(216{233.)34 2415 y([5])22 b(M.)d(Bellare,)k(J.)d(Kilian)i(and)e
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(c)o(k)f(c)o(haining,)h Fb(Adv)m(ances)f(in)105 2471
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2527 y(1994,)13 b(pp.)j(341{358.)952 2824 y(18)p eop
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19 18 bop 34 79 a Fv([6])22 b(J.)12 b(Bierbrauer,)i(T.)d(Johansson,)i
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(functions)i(via)105 136 y(geometric)j(co)q(des)g(and)g(concatenation,)
g Fb(Adv)m(ances)h(in)g(Cryptology)e({)g(CR)l(YPTO)i('93)p
Fv(,)e(Lecture)h(Notes)105 192 y(in)f(Computer)f(Science,)h(v)o(ol.)f
(773,)f(Springer-V)l(erlag,)i(1994,)e(pp.)h(331{342.)34
286 y([7])22 b(A.)e(Bosselaers,)h(R.)f(Go)o(v)m(aerts)f(and)h(J.)h(V)l
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Fb(Adv)m(ances)g(in)105 342 y(Cryptology)c({)g(CR)l(YPTO)h(96)p
Fv(,)f(Lecture)i(Notes)e(in)h(Computer)f(Science,)j(v)o(ol.)d(1109,)g
(Springer-V)l(erlag,)105 399 y(1996,)c(pp.)j(298{312.)34
493 y([8])22 b(J.)15 b(Bondy)h(and)f(U.)g(Murt)o(y,)f
Fb(Graph)h(theory)f(with)i(Applications,)h Fv(North)d(Holland,)i(1976.)
34 587 y([9])22 b(G.)e(Brassard,)i(On)g(computationally)h(secure)f
(authen)o(tication)g(tags)e(requiring)j(short)d(secret)i(shared)105
643 y(k)o(eys,)14 b Fb(Adv)m(ances)j(in)f(Cryptology)e({)h(CR)l(YPTO)h
('82)p Fv(,)e(Springer-V)l(erlag,)i(1983,)e(pp.)h(79{86.)11
737 y([10])22 b(L.)13 b(Carter)f(and)h(M.)f(W)l(egman,)h(Univ)o(ersal)h
(hash)f(functions,)h Fb(J.)f(of)g(Computer)f(and)h(System)g(Sciences)k
Fv(18,)105 793 y(1979,)c(pp.)j(143{154.)11 887 y([11])22
b(Y.)g(Desmedt,)h(Unconditionally)i(secure)e(authen)o(tication)g(sc)o
(hemes)f(and)h(practical)g(and)f(theoretical)105 944
y(consequences,)17 b Fb(Adv)m(ances)h(in)f(Cryptology)f({)g(CR)l(YPTO)h
('85)p Fv(,)e(Lecture)i(Notes)f(in)h(Computer)f(Science,)105
1000 y(v)o(ol.)f(218,)f(Springer-V)l(erlag,)i(1985,)e(pp.)h(42{45.)11
1094 y([12])22 b(P)l(.)d(Gemmell)i(and)f(M.)f(Naor,)h(Co)q(des)g(for)f
(in)o(teractiv)o(e)h(authen)o(tication,)h Fb(Adv)m(ances)g(in)f
(Cryptology)f({)105 1150 y(CR)l(YPTO)d('93)p Fv(,)f(Lecture)i(Notes)f
(in)g(Computer)g(Science,)i(v)o(ol.)d(773,)g(Springer-V)l(erlag,)i
(1994,)e(pp.)h(355{)105 1207 y(367.)11 1301 y([13])22
b(O.)c(Goldreic)o(h,)i(S.)e(Goldw)o(asser)g(and)g(S.)g(Micali,)j(Ho)o
(w)c(to)h(construct)g(random)g(functions,)h Fb(Journal)g(of)105
1357 y(the)c(A)o(CM)p Fv(,)f(V)l(ol.)i(33,)e(No.)g(4,)h(1986,)f(pp.)h
(210{217.)11 1451 y([14])22 b(S.)c(Goldw)o(asser,)g(S.)g(Micali)i(and)e
(R.)g(Riv)o(est,)h(A)g(digital)g(signature)g(sc)o(heme)f(secure)h
(against)f(adaptiv)o(e)105 1507 y(c)o(hosen-message)12
b(attac)o(ks,)f Fb(SIAM)h(Journal)h(of)f(Computing,)g
Fv(v)o(ol.)g(17,)g(no.)f(2)h(\(April)h(1988\),)e(pp.)h(281{308.)11
1601 y([15])22 b(S.)c(Halevi)i(and)f(H.)g(Kra)o(w)o(czyk,)g(MMH:)f
(Message)g(authen)o(tication)h(in)h(soft)o(w)o(are)d(in)j(the)e
(Gbit/second)105 1658 y(rates,)c Fb(Pro)q(ceedings)i(of)f(the)g(4th)g
(W)l(orkshop)g(on)g(F)l(ast)f(Soft)o(w)o(are)g(Encryption)p
Fv(,)i(Springer-V)l(erlag,)g(1997.)11 1751 y([16])22
b(T.)27 b(Johansson,)j(Buc)o(k)o(et)d(hashing)h(with)g(small)g(k)o(ey)g
(size,)j Fb(Adv)m(ances)d(in)g(Cryptology)f({)g(EUR)o(O-)105
1808 y(CR)l(YPT)15 b('97,)f Fv(Lecture)i(Notes)f(in)h(Computer)f
(Science,)h(Springer-V)l(erlag,)h(1997.)11 1902 y([17])22
b(T.)c(Johansson,)h(G.)e(Kabatianskii)j(and)f(B.)f(Smeets,)h(On)g(the)g
(relation)g(b)q(et)o(w)o(een)g(A-co)q(des)g(and)f(co)q(des)105
1958 y(correcting)13 b(indep)q(enden)o(t)j(errors.)c
Fb(Adv)m(ances)i(in)g(Cryptology)e({)h(EUR)o(OCR)l(YPT)h('93,)f
Fv(Lecture)g(Notes)g(in)105 2014 y(Computer)i(Science,)h(v)o(ol.)f
(765,)f(Springer-V)l(erlag,)i(1994,)e(pp.)h(1{11.)11
2108 y([18])22 b(H.)38 b(Kra)o(w)o(czyk,)k(LFSR-based)e(hashing)f(and)f
(authen)o(tication,)44 b Fb(Adv)m(ances)39 b(in)g(Cryptology)e({)105
2165 y(CR)l(YPTO)16 b('94,)f Fv(Lecture)i(Notes)f(in)g(Computer)g
(Science,)i(v)o(ol.)d(839,)g(Springer-V)l(erlag,)i(1994,)e(pp.)h(129{)
105 2221 y(139.)11 2315 y([19])22 b(M.)14 b(Lub)o(y)i(and)f(C.)g(Rac)o
(k)o(o\013,)e(Ho)o(w)i(to)f(construct)h(pseudorandom)g(p)q(erm)o
(utations)g(from)g(pseudorandom)105 2371 y(functions,")g
Fb(SIAM)h(J.)f(Comput,)f Fv(v)o(ol.)h(17,)f(no.)h(2)g(\(April)h
(1988\).)11 2465 y([20])22 b(X.)10 b(Lai,)i(R.)f(Ruepp)q(el)j(and)d(J.)
f(W)l(o)q(ollv)o(en,)j(A)e(fast)f(cryptographic)h(c)o(hec)o(ksum)g
(algorithm)g(based)g(on)g(stream)105 2522 y(ciphers,)k
Fb(Adv)m(ances)g(in)f(Cryptology)l(,)g(Pro)q(ceedings)h(of)e(A)o(USCR)l
(YPT)h(92,)g Fv(Lecture)g(Notes)g(in)g(Computer)105 2578
y(Science,)j(v)o(ol.)d(718,)g(Springer-V)l(erlag,)j(1992,)c(pp.)j
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cleartomark
{ restore } if
/DJB findfont
dup length dict begin
  {1 index /FID ne {def} {pop pop} ifelse} forall
  /Encoding showcaseisoencoding def
  currentdict
end
/DJB-SHOWISO exch definefont pop
/Haeberli where { pop save true } { false } ifelse
% %!PS-AdobeFont-2.0: Haeberli 001.001

% To load to VM, remove the '' character from the 'exitserver' line.

% serverdict begin 0 exitserver % for VM installation

11 dict begin
/FontInfo 10 dict dup begin
version (001.000) readonly def
/Notice (Adobe Type 1 format font) readonly def
/Copyright (This is a spot for a copywrite notice) readonly def
/FullName (SGI Haeberli) readonly def
/FamilyName (SGI Haeberli) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
/UnderlinePosition -110 def
/UnderlineThickness 49 def
end readonly def
/FontName /Haeberli def
/Encoding StandardEncoding def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/UniqueID 53457 def
/FontBBox{-129 -396 747 707}readonly def
currentdict end
currentfile eexec
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 @endspecial 436 917 a
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 436 917 a 0 1015 a Fv(Figure)15
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Fv(0)p Fu(;)8 b Fv(1)p Fu(;)g Fv(2)p Fu(;)g Fv(3)p Fu(;)f
Fv(4)o Fu(;)h Fv(6)o Ff(.)18 b(Divide)d(the)h(numb)q(er)g(lab)q(eling)g
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(robabilit)o(y)f Fu(P)640 1135 y Fr(ij)671 1128 y Ff(.)0
1270 y Fv(The)i(\014rst)g(argumen)o(t)f(to)h(MA)o(C)f(and)h(MA)o(CV)g
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b(W)l(e)17 b(demand)h(that)0 1326 y(for)d(an)o(y)f Fu(x)f
Fs(2)g Fv(Messages)o(,)i Fu(k)f Fs(2)f Fv(Keys,)i(and)g(cn)o(t)e
Fs(2)g(f)p Fv(1)p Fu(;)8 b(:)g(:)g(:)t(;)g Fv(MAX)o Fs(g)p
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Fu(x;)g Fv(cn)o(t)o(\)\))k(=)h(1)g(.)71 1383 y(Let)g
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(authen)o(tication)i(sc)o(heme)f Fs(M)f Fv(is)i(an)e(algorithm)h
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1672 y Fr(k)257 1665 y Fv(\()p Fs(\001)p Fv(\).)18 b(Adv)o(ersary)12
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Fv(\),)f(if)g Fu(E)j Fv(outputs)d(a)g(string)g(\()p Fu(x)829
1705 y Fq(\003)848 1721 y Fu(;)8 b(\033)897 1705 y Fq(\003)916
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b(\033)1362 1705 y Fq(\003)1381 1721 y Fv(\))17 b(=)h(1)g(y)o(et)g
Fu(E)i Fv(made)f(no)f(oracle)0 1778 y(query)f(of)g Fu(x)208
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(probabilit)o(y)h(is)f(tak)o(en)0 1834 y(o)o(v)o(er)g
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Fu(k)h Fv(for)e(the)g(MA)o(C)g(oracle.)28 b(Running)20
b(times)d(are)h(measured)g(in)g(a)0 1891 y(standard)g(RAM)g(mo)q(del)i
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(step.)30 b(By)18 b(con)o(v)o(en)o(tion,)0 1947 y(the)d(running)i(time)
e(of)g Fu(E)i Fv(also)e(includes)j(the)d(size)h(of)f
Fu(E)s Fv('s)f(description.)0 2029 y Fw(PRF)26 b(security.)42
b Fv(W)l(e)22 b(follo)o(w)h([13)o(,)f(5].)42 b(A)23 b(\014nite)h
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2085 y Fu(F)28 b Fv(:)21 b Fs(f)p Fv(0)p Fu(;)8 b Fv(1)p
Fs(g)202 2064 y Fr(\024)238 2085 y Fs(\002)14 b(f)p Fv(0)p
Fu(;)8 b Fv(1)p Fs(g)398 2064 y Fr(l)432 2085 y Fs(!)22
b(f)p Fv(0)p Fu(;)8 b Fv(1)p Fs(g)610 2064 y Fr(b)627
2085 y Fv(.)36 b(W)l(e)20 b(write)h Fu(F)910 2092 y Fr(a)931
2085 y Fv(\()p Fu(x)p Fv(\))f(in)h(place)g(of)f Fu(F)6
b Fv(\()p Fu(a;)i(x)p Fv(\).)35 b(Let)20 b Fu(R)1560
2092 y Fr(l;b)1618 2085 y Fv(b)q(e)h(the)g(set)f(of)g(all)0
2147 y(functions)e(mapping)g Fs(f)p Fv(0)p Fu(;)8 b Fv(1)p
Fs(g)498 2126 y Fr(l)528 2147 y Fv(to)17 b Fs(f)p Fv(0)p
Fu(;)8 b Fv(1)p Fs(g)697 2126 y Fr(b)714 2147 y Fv(.)26
b(A)17 b Ft(distinguisher)22 b Fv(is)c(an)f(algorithm)g
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Fu(t;)8 b(q)r Fv(\)-secure)16 b(if)g(for)e(ev)o(ery)i(distinguisher)h
Fu(D)f Fv(whic)o(h)h(runs)e(in)h(time)g Fu(t)g Fv(and)g(mak)o(es)0
2268 y Fu(q)i Fv(or)d(few)o(er)h(queries)h(to)e(its)h(oracle,)70
b(Pr)634 2300 y Fr(k)q Fq( f)p Fp(0)p Fr(;)p Fp(1)p Fq(g)768
2285 y Fi(\024)796 2221 y Fm(h)816 2268 y Fu(D)855 2249
y Fr(F)877 2255 y Fi(k)896 2249 y Fp(\()p Fq(\001)p Fp(\))948
2268 y Fv(=)13 b(1)1019 2221 y Fm(i)1049 2268 y Fs(\000)44
b Fv(Pr)1095 2297 y Fr(\032)p Fq( )p Fr(R)1175 2303 y
Fi(l;b)1218 2221 y Fm(h)1237 2268 y Fu(D)1276 2249 y
Fr(\032)p Fp(\()p Fq(\001)p Fp(\))1346 2268 y Fv(=)13
b(1)1417 2221 y Fm(i)1450 2268 y Fs(\024)i Fu(\017)p
Fv(\()p Fu(t;)8 b(q)r Fv(\))i(.)22 b(Running)c(times)0
2348 y(are)d(measured)g(in)g(a)g(standard)f(RAM)h(mo)q(del)h(of)f
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(step.)0 2405 y(By)g(con)o(v)o(en)o(tion,)g(the)h(running)g(time)f(of)g
Fu(E)i Fv(also)f(includes)h(the)e(size)i(of)d Fu(E)s
Fv('s)g(description.)952 2824 y(21)p eop
%%Page: 22 22
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162 234 2 95 v 533 234 V 448 w(1)p 668 234 V 940 234
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Fv(1)p 1561 329 V 263 w(1)p 1846 329 V 1928 329 V 163
330 1766 2 v 42 388 a Fu(t)g Fv(=)g(3)p 162 423 2 95
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423 2 95 v 1561 423 V 1846 423 V 1876 388 a Fv(1)p 1928
423 V 163 425 1766 2 v 42 482 a Fu(t)g Fv(=)g(4)p 162
518 2 95 v 297 464 a Fp(324)p Fr(N)383 453 y Fj(4)p 297
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95 v 668 518 V 695 464 a Fp(60)p 695 471 36 2 v 696 498
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1846 518 2 95 v 1928 518 V 163 519 1766 2 v 42 577 a
Fu(t)g Fv(=)g(5)p 162 612 2 95 v 533 612 V 668 612 V
940 612 V 966 559 a Fp(4320)p Fr(N)1070 547 y Fj(8)1086
559 y Fp(+25680)p Fr(N)1235 547 y Fj(7)p 966 566 284
2 v 1083 594 a Fq(N)1117 584 y Fj(4)p 1275 612 2 95 v
1561 612 V 1846 612 V 1928 612 V 163 614 1766 2 v 42
671 a Fu(t)g Fv(=)g(6)p 162 707 2 95 v 188 653 a Fp(25920)p
Fr(N)310 642 y Fj(8)325 653 y Fp(+154080)p Fr(N)492 642
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533 707 2 95 v 668 707 V 940 707 V 1275 707 V 1561 707
V 1846 707 V 1928 707 V 163 708 1766 2 v 0 832 a Fv(Figure)18
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832 y Fv(\()p Fu(t)p Fv(\))p Ff(.)29 b(The)18 b(only)h(value)f(needed)i
(is)f Fu(f)1588 839 y Fp(0)1608 832 y Fv(\(6\))p Ff(;)f(w)o(e)g(need)i
(that)0 889 y Fv(2)p Fu(f)45 896 y Fp(0)65 889 y Fv(\(6\))11
b Fs(\024)i Fu(B)r Fv(\()p Fu(N)5 b Fv(\))p Ff(.)0 1029
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(pro)o(v)o(e)g(Lemma)g(12,)h(giving)g(a)f(suitable)i(upp)q(er)f(b)q
(ound)g(on)f Fu(f)1298 1137 y Fp(0)1318 1130 y Fv(\(6\).)37
b(W)l(e)21 b(do)h(this)f(b)o(y)g(direct)h(cal-)0 1187
y(culation,)k(pa)o(ying)e(atten)o(tion)f(to)g(the)h(states)e(0)p
Fu(;)8 b Fv(1)p Fu(;)g Fv(2)p Fu(;)g Fv(3)p Fu(;)f Fv(4)p
Fu(;)g Fv(6)20 b(and)k(\\ev)o(erything)g(else.")45 b(T)l(o)24
b(that)f(end,)i(let)0 1243 y Fu(R)d Fv(=)g Fs(f)p Fv(5)p
Fu(;)8 b Fv(7)p Fu(;)g Fv(8)p Fu(;)g(:)f(:)g(:)t(;)h(N)d
Fs(g)20 b Fv(\(i.e.,)h(\\ev)o(erything)g(else"\))g(and)g(de\014ne)h
Fu(f)1179 1250 y Fr(R)1208 1243 y Fv(\()p Fu(t)p Fv(\))g(=)1339
1211 y Fm(P)1383 1255 y Fr(r)q Fq(2)p Fr(R)1460 1243
y Fu(f)1482 1250 y Fr(r)1501 1243 y Fv(\()p Fu(t)p Fv(\).)37
b(Let)21 b(us)g(write)g Fu(P)1905 1250 y Fr(Rj)0 1300
y Fv(for)68 1267 y Fm(P)112 1311 y Fr(r)q Fq(2)p Fr(R)189
1300 y Fu(P)218 1307 y Fr(r)q(j)253 1300 y Fv(.)f(Keep)15
b(in)g(mind)g(that)e Fu(R)h Fv(is)g Ft(not)k Fv(a)c(state)f(of)h(an)o
(y)f(Mark)o(o)o(v)g(c)o(hain)i(w)o(e)e(ha)o(v)o(e)h(de\014ned;)h(this)g
(is)f(just)0 1356 y(a)h(con)o(v)o(enien)o(t)h(shorthand.)71
1412 y(W)l(e)g(will)i(establish)f(the)f(b)q(ounds)h(indicated)h(in)f
(Figure)f(4,)g(where)g(ro)o(w)f Fu(t)p Fv(,)h(column)h
Fu(i)f Fv(is)h(the)f(upp)q(er)h(b)q(ound)0 1469 y(w)o(e)i(sho)o(w)f
(for)g Fu(f)282 1476 y Fr(i)296 1469 y Fv(\()p Fu(t)p
Fv(\).)31 b(T)l(o)18 b(see)h(ho)o(w)g(these)g(b)q(ounds)g(are)g
(computed,)g(refer)g(to)f(Figure)h(3,)g(whic)o(h)h(depicts)g(the)0
1525 y(relev)m(an)o(t)c(transition)f(probabilities)j(of)d
Fu(M)5 b Fv(.)71 1582 y(W)l(e)17 b(start)f(with)i(the)f(trivial)h(b)q
(ounds:)25 b Fu(f)787 1589 y Fp(1)807 1582 y Fv(\(1\))15
b Fs(\024)i Fv(1,)g Fu(f)1008 1589 y Fp(3)1028 1582 y
Fv(\(1\))e Fs(\024)h Fv(1,)h Fu(f)1228 1589 y Fr(R)1257
1582 y Fv(\(1\))f Fs(\024)g Fv(1,)h Fu(f)1458 1589 y
Fp(4)1478 1582 y Fv(\(2\))e Fs(\024)i Fv(1,)g(and)g Fu(f)1769
1589 y Fp(2)1789 1582 y Fv(\(6\))e Fs(\024)i Fv(1.)0
1638 y(These)g(are)g(ob)o(vious,)g(since)h(eac)o(h)f
Fu(f)629 1645 y Fr(i)643 1638 y Fv(\()p Fu(t)p Fv(\))g(represen)o(ts)g
(a)g(probabilit)o(y)l(.)26 b(No)o(w)16 b(refer)h(to)f(Figure)h(3)g(and)
g(calculate.)0 1695 y(Some)j(of)f(the)h(m)o(undane)g(arithmetic)g(is)g
(omitted.)34 b(In)20 b(cases)g(suc)o(h)g(as)f(the)h(calculation)h(of)e
Fu(f)1682 1702 y Fp(6)1702 1695 y Fv(\(4\),)h(the)g(sec-)0
1751 y(ond)e(inequalit)o(y)i(is)f(easily)g(seen)g(to)e(hold)i(for)f
(su\016cien)o(tly)h(large)g Fu(N)5 b Fv(;)18 b(the)h(crosso)o(v)o(er)e
(p)q(oin)o(t)h(w)o(as)g(determined)0 1808 y(n)o(umerically)l(.)303
1949 y Fy(f)323 1955 y Fe(0)342 1949 y FC(\(2\))41 b(=)h
Fy(f)530 1955 y Fe(3)549 1949 y FC(\(1\))9 b Fd(\001)g
Fy(P)659 1955 y Fe(30)436 2031 y Fd(\024)42 b FC(1)9
b Fd(\001)575 2003 y FC(6)p 566 2021 41 2 v 566 2059
a Fd(N)436 2131 y FC(=)525 2102 y(6)p 515 2121 V 515
2159 a Fd(N)303 2255 y Fy(f)323 2261 y Fe(2)342 2255
y FC(\(2\))41 b(=)h Fy(f)530 2261 y Fe(1)549 2255 y FC(\(1\))9
b Fd(\001)g Fy(P)659 2261 y Fe(12)703 2255 y FC(+)g Fy(f)764
2261 y Fe(3)783 2255 y FC(\(1\))h Fd(\001)e Fy(P)893
2261 y Fe(32)937 2255 y FC(+)i Fy(f)999 2261 y Fc(R)1026
2255 y FC(\(1\))p Fy(P)1106 2261 y Fc(R)p Fe(2)436 2341
y Fd(\024)42 b FC(1)9 b Fd(\001)566 2313 y FC(3\()p Fy(N)p
Fd(\000)r FC(1\)\()p Fy(N)p Fd(\000)r FC(2\))p 566 2332
263 2 v 677 2370 a Fd(N)842 2341 y FC(+)h(1)f Fd(\001)940
2313 y FC(18\()p Fy(N)p Fd(\000)r FC(3\))p 940 2332 163
2 v 1001 2370 a Fd(N)1116 2341 y FC(+)h(1)f Fd(\001)1213
2313 y FC(60)p 1213 2332 42 2 v 1214 2370 a Fd(N)436
2448 y(\024)515 2420 y FC(3)p Fy(N)574 2405 y Fe(2)601
2420 y FC(+)h(10)p Fy(N)p 515 2439 208 2 v 598 2477 a
Fd(N)741 2448 y FC(\()p Fy(N)17 b Fd(\025)11 b FC(12\))303
2573 y Fy(f)323 2579 y Fe(1)342 2573 y FC(\(3\))41 b(=)h
Fy(f)530 2579 y Fe(2)549 2573 y FC(\(2\))9 b Fd(\001)g
Fy(P)659 2579 y Fe(21)703 2573 y FC(+)g Fy(f)764 2579
y Fe(4)783 2573 y FC(\(2\))h Fd(\001)e Fy(P)893 2579
y Fe(41)952 2824 y Fv(22)p eop
%%Page: 23 23
23 22 bop 436 95 a Fd(\024)515 67 y FC(3)p Fy(N)574 52
y Fe(2)601 67 y FC(+)10 b(10)p Fy(N)p 515 86 208 2 v
598 124 a Fd(N)736 95 y(\001)762 67 y FC(6\()p Fy(N)p
Fd(\000)r FC(2\))p 762 86 142 2 v 813 124 a Fd(N)918
95 y FC(+)g(1)f Fd(\001)1015 67 y FC(24)p 1015 86 42
2 v 1016 124 a Fd(N)436 202 y FC(=)515 174 y(\(3)p Fy(N)590
159 y Fe(2)617 174 y FC(+)h(10)p Fy(N)5 b FC(\)\(6)p
Fy(N)14 b Fd(\000)9 b FC(12\))g(+)g(24)p Fy(N)c FC(\()p
Fy(N)p Fd(\000)r FC(1\)\()p Fy(N)p Fd(\000)r FC(2\))p
515 193 795 2 v 883 231 a Fd(N)923 219 y Fe(2)436 309
y Fd(\024)515 281 y FC(42)p Fy(N)595 266 y Fe(3)p 515
300 99 2 v 534 338 a Fd(N)574 326 y Fe(2)303 434 y Fy(f)323
440 y Fe(3)342 434 y FC(\(3\))41 b(=)h Fy(f)530 440 y
Fe(0)549 434 y FC(\(2\))9 b Fd(\001)g Fy(P)659 440 y
Fe(03)703 434 y FC(+)g Fy(f)764 440 y Fe(2)783 434 y
FC(\(2\))h Fd(\001)e Fy(P)893 440 y Fe(23)937 434 y FC(+)i
Fy(f)999 440 y Fe(4)1018 434 y FC(\(2\))f Fd(\001)g Fy(P)1128
440 y Fe(43)1172 434 y FC(+)g Fy(f)1233 440 y Fe(6)1252
434 y FC(\(2\))h Fd(\001)e Fy(P)1362 440 y Fe(63)436
523 y Fd(\024)525 495 y FC(6)p 515 513 41 2 v 515 551
a Fd(N)569 523 y(\001)h FC(1)g(+)666 495 y(3)p Fy(N)725
480 y Fe(2)753 495 y FC(+)g(10)p Fy(N)p 666 513 208 2
v 750 551 a Fd(N)888 523 y(\001)914 495 y FC(6\()p Fy(N)p
Fd(\000)r FC(2\)\()p Fy(N)p Fd(\000)r FC(3\))p 914 513
263 2 v 1025 551 a Fd(N)1191 523 y FC(+)g(1)g Fd(\001)1288
495 y FC(36\()p Fy(N)p Fd(\000)r FC(4\))p 1288 513 163
2 v 1349 551 a Fd(N)1464 523 y FC(+)h(1)f Fd(\001)1562
495 y FC(120)p 1562 513 63 2 v 1573 551 a Fd(N)436 630
y(\024)515 602 y FC(54)p Fy(N)595 587 y Fe(4)p 515 620
99 2 v 534 658 a Fd(N)574 646 y Fe(2)303 754 y Fy(f)323
760 y Fe(0)342 754 y FC(\(4\))41 b(=)h Fy(f)530 760 y
Fe(3)549 754 y FC(\(3\))9 b Fd(\001)g Fy(P)659 760 y
Fe(30)436 843 y Fd(\024)515 815 y FC(54)p Fy(N)595 800
y Fe(4)p 515 834 V 534 872 a Fd(N)574 860 y Fe(3)627
843 y Fd(\001)663 815 y FC(6)p 653 834 41 2 v 653 872
a Fd(N)436 950 y(\024)515 922 y FC(324)p Fy(N)616 907
y Fe(4)p 515 940 119 2 v 545 979 a Fd(N)585 967 y Fe(3)303
1075 y Fy(f)323 1081 y Fe(2)342 1075 y FC(\(4\))41 b(=)h
Fy(f)530 1081 y Fe(1)549 1075 y FC(\(3\))9 b Fd(\001)g
Fy(P)659 1081 y Fe(12)703 1075 y FC(+)g Fy(f)764 1081
y Fe(3)783 1075 y FC(\(3\))h Fd(\001)e Fy(P)893 1081
y Fe(32)937 1075 y FC(+)i Fy(f)999 1081 y Fc(R)1026 1075
y FC(\(3\))p Fy(P)1106 1081 y Fc(R)p Fe(2)436 1163 y
Fd(\024)515 1135 y FC(42)p Fy(N)595 1120 y Fe(3)p 515
1154 99 2 v 534 1192 a Fd(N)574 1180 y Fe(2)627 1163
y Fd(\001)653 1135 y FC(3\()p Fy(N)p Fd(\000)r FC(1\)\()p
Fy(N)p Fd(\000)r FC(2\))p 653 1154 263 2 v 764 1192 a
Fd(N)930 1163 y FC(+)976 1135 y(54)p Fy(N)1056 1120 y
Fe(4)p 976 1154 99 2 v 996 1192 a Fd(N)1036 1180 y Fe(2)1088
1163 y Fd(\001)1114 1135 y FC(18\()p Fy(N)p Fd(\000)r
FC(3\))p 1114 1154 163 2 v 1175 1192 a Fd(N)1291 1163
y FC(+)f(1)g Fd(\001)1388 1135 y FC(60)p 1388 1154 42
2 v 1389 1192 a Fd(N)436 1270 y(\024)515 1242 y FC(60)p
515 1261 V 516 1299 a Fd(N)571 1270 y FC(+)617 1242 y(1098)p
Fy(N)739 1227 y Fe(5)p 617 1261 140 2 v 657 1299 a Fd(N)697
1287 y Fe(3)775 1270 y FC(\()p Fy(N)17 b Fd(\025)12 b
FC(3\))303 1395 y Fy(f)323 1401 y Fe(4)342 1395 y FC(\(4\))41
b(=)h Fy(f)530 1401 y Fe(1)549 1395 y FC(\(3\))9 b Fd(\001)g
Fy(P)659 1401 y Fe(14)703 1395 y FC(+)g Fy(f)764 1401
y Fe(3)783 1395 y FC(\(3\))h Fd(\001)e Fy(P)893 1401
y Fe(34)937 1395 y FC(+)i Fy(f)999 1401 y Fc(R)1026 1395
y FC(\(3\))g Fd(\001)e Fy(P)1136 1401 y Fc(R)p Fe(4)436
1484 y Fd(\024)515 1456 y FC(42)p Fy(N)595 1441 y Fe(3)p
515 1474 99 2 v 534 1512 a Fd(N)574 1500 y Fe(2)627 1484
y Fd(\001)h FC(1)g(+)724 1456 y(54)p Fy(N)804 1441 y
Fe(4)p 724 1474 V 744 1512 a Fd(N)784 1500 y Fe(2)837
1484 y Fd(\001)862 1456 y FC(9\()p Fy(N)p Fd(\000)r FC(3\)\()p
Fy(N)p Fd(\000)r FC(4\))p 862 1474 263 2 v 973 1512 a
Fd(N)1139 1484 y FC(+)h(1)f Fd(\001)1236 1456 y FC(60\()p
Fy(N)p Fd(\000)r FC(5\))h(+)f(210)p 1236 1474 276 2 v
1354 1512 a Fd(N)436 1591 y(\024)515 1563 y FC(60)p 515
1581 42 2 v 516 1619 a Fd(N)571 1591 y FC(+)617 1563
y(438)p Fy(N)718 1548 y Fe(6)p 617 1581 119 2 v 647 1619
a Fd(N)687 1607 y Fe(3)303 1715 y Fy(f)323 1721 y Fe(6)342
1715 y FC(\(4\))41 b(=)h Fy(f)530 1721 y Fe(3)549 1715
y FC(\(3\))9 b Fd(\001)g Fy(P)659 1721 y Fe(36)703 1715
y FC(+)g Fy(f)764 1721 y Fc(R)792 1715 y FC(\(3\))g Fd(\001)g
Fy(P)902 1721 y Fc(R)p Fe(6)436 1804 y Fd(\024)515 1776
y FC(54)p Fy(N)595 1761 y Fe(4)p 515 1795 99 2 v 534
1833 a Fd(N)574 1821 y Fe(2)627 1804 y Fd(\001)g FC(1)g(+)g(1)g
Fd(\001)775 1776 y FC(15\()p Fy(N)p Fd(\000)r FC(5\)\()p
Fy(N)p Fd(\000)r FC(6\))i(+)e(126\()p Fy(N)p Fd(\000)r
FC(7\))g(+)h(504)p 775 1795 631 2 v 1070 1833 a Fd(N)436
1911 y FC(=)515 1883 y(15)p Fy(N)595 1868 y Fe(2)p 515
1902 99 2 v 544 1940 a Fd(N)627 1911 y FC(+)674 1883
y(15)p Fy(N)754 1868 y Fe(4)781 1883 y FC(+)f(189)p Fy(N)923
1868 y Fe(3)950 1883 y Fd(\000)h FC(294)p Fy(N)1093 1868
y Fe(2)1120 1883 y Fd(\000)f FC(144)p Fy(N)p 674 1902
588 2 v 938 1940 a Fd(N)978 1928 y Fe(2)436 2018 y Fd(\024)515
1990 y FC(15)p Fy(N)595 1975 y Fe(4)p 515 2008 99 2 v
534 2046 a Fd(N)574 2034 y Fe(2)627 2018 y FC(+)674 1990
y(25)p Fy(N)754 1975 y Fe(2)p 674 2008 V 702 2046 a Fd(N)790
2018 y FC(\()p Fy(N)17 b Fd(\025)12 b FC(18\))303 2143
y Fy(f)323 2149 y Fe(3)342 2143 y FC(\(5\))41 b(=)h Fy(f)530
2149 y Fe(0)549 2143 y FC(\(4\))9 b Fd(\001)g Fy(P)659
2149 y Fe(03)703 2143 y FC(+)g Fy(f)764 2149 y Fe(2)783
2143 y FC(\(4\))h Fd(\001)e Fy(P)893 2149 y Fe(23)937
2143 y FC(+)i Fy(f)999 2149 y Fe(4)1018 2143 y FC(\(4\))f
Fd(\001)g Fy(P)1128 2149 y Fe(43)1172 2143 y FC(+)g Fy(f)1233
2149 y Fe(6)1252 2143 y FC(\(4\))h Fd(\001)e Fy(P)1362
2149 y Fe(63)436 2231 y Fd(\024)515 2203 y FC(324)p Fy(N)616
2188 y Fe(4)p 515 2222 119 2 v 545 2260 a Fd(N)585 2248
y Fe(3)648 2231 y Fd(\001)h FC(1)g(+)740 2173 y Fm(\022)776
2203 y FC(60)p 776 2222 42 2 v 777 2260 a Fd(N)831 2231
y FC(+)878 2203 y(1098)p Fy(N)1000 2188 y Fe(5)p 878
2222 140 2 v 918 2260 a Fd(N)958 2248 y Fe(3)1022 2173
y Fm(\023)1062 2231 y Fd(\001)1088 2203 y FC(6\()p Fy(N)p
Fd(\000)r FC(2\)\()p Fy(N)p Fd(\000)r FC(3\))p 1088 2222
263 2 v 1199 2260 a Fd(N)1365 2231 y FC(+)634 2291 y
Fm(\022)670 2321 y FC(60)p Fy(N)p 670 2340 80 2 v 690
2378 a Fd(N)764 2349 y FC(+)810 2321 y(438)p Fy(N)911
2306 y Fe(6)p 810 2340 119 2 v 840 2378 a Fd(N)880 2366
y Fe(3)934 2291 y Fm(\023)974 2349 y Fd(\001)999 2321
y FC(36\()p Fy(N)p Fd(\000)r FC(4\))p 999 2340 163 2
v 1060 2378 a Fd(N)1176 2349 y FC(+)1217 2291 y Fm(\022)1253
2321 y FC(15)p Fy(N)1333 2306 y Fe(2)p 1253 2340 99 2
v 1282 2378 a Fd(N)1365 2349 y FC(+)1412 2321 y(25)p
Fy(N)1492 2306 y Fe(4)p 1412 2340 V 1431 2378 a Fd(N)1471
2366 y Fe(2)1515 2291 y Fm(\023)1554 2349 y Fd(\001)1580
2321 y FC(120)p 1580 2340 63 2 v 1591 2378 a Fd(N)436
2467 y(\024)515 2439 y FC(4320)p Fy(N)637 2424 y Fe(8)664
2439 y FC(+)g(25680)p Fy(N)848 2424 y Fe(7)p 515 2458
351 2 v 661 2496 a Fd(N)701 2484 y Fe(4)303 2601 y Fy(f)323
2607 y Fe(0)342 2601 y FC(\(6\))41 b(=)h Fy(\031)534
2607 y Fe(3)552 2601 y FC(\(5\))9 b Fd(\001)650 2573
y FC(6)p 640 2591 41 2 v 640 2629 a Fd(N)952 2824 y Fv(23)p
eop
%%Page: 24 24
24 23 bop 436 95 a Fd(\024)515 67 y FC(4320)p Fy(N)637
52 y Fe(8)664 67 y FC(+)9 b(25680)p Fy(N)848 52 y Fe(7)p
515 86 351 2 v 661 124 a Fd(N)701 112 y Fe(4)880 95 y
Fd(\001)915 67 y FC(6)p 905 86 41 2 v 905 124 a Fd(N)436
202 y FC(=)515 174 y(25920)p Fy(N)658 159 y Fe(8)684
174 y FC(+)h(154080)p Fy(N)890 159 y Fe(7)p 515 193 393
2 v 681 231 a Fd(N)721 219 y Fe(5)0 357 y Fv(This)16
b(completes)g(the)f(pro)q(of)g(of)g(the)g(lemma.)1130
b Fs(})952 2824 y Fv(24)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF