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+--------+-------------------------+-------------------------+--------+--------+
|00000000| 46 72 6f 6d 20 63 61 74 | 65 33 2e 6f 73 62 75 6e |From cat|e3.osbun|
|00000010| 6f 72 74 68 40 78 65 72 | 6f 78 2e 63 6f 6d 20 46 |orth@xer|ox.com F|
|00000020| 72 69 20 41 75 67 20 33 | 31 20 31 39 3a 33 33 3a |ri Aug 3|1 19:33:|
|00000030| 35 33 20 31 39 39 30 0d | 0a 46 72 6f 6d 3a 20 63 |53 1990.|.From: c|
|00000040| 61 74 65 33 2e 6f 73 62 | 75 6e 6f 72 74 68 40 78 |ate3.osb|unorth@x|
|00000050| 65 72 6f 78 2e 63 6f 6d | 20 28 48 65 6e 72 79 20 |erox.com| (Henry |
|00000060| 43 61 74 65 20 49 49 49 | 29 0d 0a 53 75 62 6a 65 |Cate III|)..Subje|
|00000070| 63 74 3a 20 48 6f 77 20 | 74 6f 20 70 72 6f 76 65 |ct: How |to prove|
|00000080| 20 73 6f 6d 65 74 68 69 | 6e 67 0d 0a 0d 0a 0d 0a | somethi|ng......|
|00000090| 0d 0a 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |..------|--------|
|000000a0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000000b0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|000000c0| 2d 2d 2d 2d 2d 2d 0d 0a | 0d 0a 53 75 72 76 65 79 |------..|..Survey|
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|000000f0| 76 65 79 20 77 61 73 20 | 77 72 69 74 74 65 6e 20 |vey was |written |
|00000100| 62 79 20 44 61 6e 61 20 | 41 6e 67 6c 75 69 6e 2e |by Dana |Angluin.|
|00000110| 20 20 4e 6f 74 20 72 65 | 61 6c 6c 79 20 73 75 72 |  Not re|ally sur|
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|00000490| 20 48 6f 77 20 63 6f 75 | 6c 64 20 74 68 72 65 65 | How cou|ld three|
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|000004c0| 65 20 77 72 6f 6e 67 3f | 0d 0a 0d 0a 50 72 6f 6f |e wrong?|....Proo|
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|00000520| 6c 79 20 4e 50 2d 63 6f | 6d 70 6c 65 74 65 2e 27 |ly NP-co|mplete.'|
|00000530| 0d 0a 0d 0a 50 72 6f 6f | 66 20 62 79 20 70 65 72 |....Proo|f by per|
|00000540| 73 6f 6e 61 6c 20 63 6f | 6d 6d 75 6e 69 63 61 74 |sonal co|mmunicat|
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|000005d0| 74 68 65 20 77 72 6f 6e | 67 20 70 72 6f 62 6c 65 |the wron|g proble|
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|000005f0| 61 74 20 69 6e 66 69 6e | 69 74 65 2d 64 69 6d 65 |at infin|ite-dime|
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|00000610| 63 79 63 6c 65 20 73 74 | 72 69 70 70 69 6e 67 20 |cycle st|ripping |
|00000620| 69 73 20 64 65 63 69 64 | 61 62 6c 65 2c 0d 0a 20 |is decid|able,.. |
|00000630| 20 77 65 20 72 65 64 75 | 63 65 20 69 74 20 74 6f | we redu|ce it to|
|00000640| 20 74 68 65 20 68 61 6c | 74 69 6e 67 20 70 72 6f | the hal|ting pro|
|00000650| 62 6c 65 6d 2e 27 0d 0a | 0d 0a 50 72 6f 6f 66 20 |blem.'..|..Proof |
|00000660| 62 79 20 72 65 66 65 72 | 65 6e 63 65 20 74 6f 20 |by refer|ence to |
|00000670| 69 6e 61 63 63 65 73 73 | 69 62 6c 65 20 6c 69 74 |inaccess|ible lit|
|00000680| 65 72 61 74 75 72 65 3a | 0d 0a 20 20 54 68 65 20 |erature:|..  The |
|00000690| 61 75 74 68 6f 72 20 63 | 69 74 65 73 20 61 20 73 |author c|ites a s|
|000006a0| 69 6d 70 6c 65 20 63 6f | 72 6f 6c 6c 61 72 79 20 |imple co|rollary |
|000006b0| 6f 66 20 61 20 74 68 65 | 6f 72 65 6d 20 74 6f 20 |of a the|orem to |
|000006c0| 62 65 20 66 6f 75 6e 64 | 20 69 6e 20 61 20 70 72 |be found| in a pr|
|000006d0| 69 76 61 74 65 6c 79 0d | 0a 20 20 63 69 72 63 75 |ivately.|.  circu|
|000006e0| 6c 61 74 65 64 20 6d 65 | 6d 6f 69 72 20 6f 66 20 |lated me|moir of |
|000006f0| 74 68 65 20 53 6c 6f 76 | 65 6e 69 61 6e 20 50 68 |the Slov|enian Ph|
|00000700| 69 6c 6f 6c 6f 67 69 63 | 61 6c 20 53 6f 63 69 65 |ilologic|al Socie|
|00000710| 74 79 2c 20 31 38 38 33 | 2e 0d 0a 0d 0a 50 72 6f |ty, 1883|.....Pro|
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|00000730| 3a 0d 0a 20 20 41 20 6c | 61 72 67 65 20 62 6f 64 |:..  A l|arge bod|
|00000740| 79 20 6f 66 20 75 73 65 | 66 75 6c 20 63 6f 6e 73 |y of use|ful cons|
|00000750| 65 71 75 65 6e 63 65 73 | 20 61 6c 6c 20 66 6f 6c |equences| all fol|
|00000760| 6c 6f 77 20 66 72 6f 6d | 20 74 68 65 20 70 72 6f |low from| the pro|
|00000770| 70 6f 73 69 74 69 6f 6e | 20 69 6e 0d 0a 20 20 71 |position| in..  q|
|00000780| 75 65 73 74 69 6f 6e 2e | 0d 0a 0d 0a 50 72 6f 6f |uestion.|....Proo|
|00000790| 66 20 62 79 20 61 63 63 | 75 6d 75 6c 61 74 65 64 |f by acc|umulated|
|000007a0| 20 65 76 69 64 65 6e 63 | 65 3a 0d 0a 20 20 4c 6f | evidenc|e:..  Lo|
|000007b0| 6e 67 20 61 6e 64 20 64 | 69 6c 69 67 65 6e 74 20 |ng and d|iligent |
|000007c0| 73 65 61 72 63 68 20 68 | 61 73 20 6e 6f 74 20 72 |search h|as not r|
|000007d0| 65 76 65 61 6c 65 64 20 | 61 20 63 6f 75 6e 74 65 |evealed |a counte|
|000007e0| 72 65 78 61 6d 70 6c 65 | 2e 0d 0a 0d 0a 50 72 6f |rexample|.....Pro|
|000007f0| 6f 66 20 62 79 20 63 6f | 73 6d 6f 6c 6f 67 79 3a |of by co|smology:|
|00000800| 0d 0a 20 20 54 68 65 20 | 6e 65 67 61 74 69 6f 6e |..  The |negation|
|00000810| 20 6f 66 20 74 68 65 20 | 70 72 6f 70 6f 73 69 74 | of the |proposit|
|00000820| 69 6f 6e 20 69 73 20 75 | 6e 69 6d 61 67 69 6e 61 |ion is u|nimagina|
|00000830| 62 6c 65 20 6f 72 20 6d | 65 61 6e 69 6e 67 6c 65 |ble or m|eaningle|
|00000840| 73 73 2e 20 20 50 6f 70 | 75 6c 61 72 0d 0a 20 20 |ss.  Pop|ular..  |
|00000850| 66 6f 72 20 70 72 6f 6f | 66 73 20 6f 66 20 74 68 |for proo|fs of th|
|00000860| 65 20 65 78 69 73 74 65 | 6e 63 65 20 6f 66 20 47 |e existe|nce of G|
|00000870| 6f 64 2e 0d 0a 0d 0a 50 | 72 6f 6f 66 20 62 79 20 |od.....P|roof by |
|00000880| 6d 75 74 75 61 6c 20 72 | 65 66 65 72 65 6e 63 65 |mutual r|eference|
|00000890| 3a 0d 0a 20 20 49 6e 20 | 72 65 66 65 72 65 6e 63 |:..  In |referenc|
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|000008b0| 73 20 73 61 69 64 20 74 | 6f 20 66 6f 6c 6c 6f 77 |s said t|o follow|
|000008c0| 20 66 72 6f 6d 20 54 68 | 65 6f 72 65 6d 20 33 20 | from Th|eorem 3 |
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|000008e0| 0a 20 20 77 68 69 63 68 | 20 69 73 20 73 68 6f 77 |.  which| is show|
|000008f0| 6e 20 74 6f 20 66 6f 6c | 6c 6f 77 20 66 72 6f 6d |n to fol|low from|
|00000900| 20 43 6f 72 6f 6c 6c 61 | 72 79 20 36 2e 32 20 69 | Corolla|ry 6.2 i|
|00000910| 6e 20 72 65 66 65 72 65 | 6e 63 65 20 43 2c 20 77 |n refere|nce C, w|
|00000920| 68 69 63 68 20 69 73 20 | 61 6e 0d 0a 20 20 65 61 |hich is |an..  ea|
|00000930| 73 79 20 63 6f 6e 73 65 | 71 75 65 6e 63 65 20 6f |sy conse|quence o|
|00000940| 66 20 54 68 65 6f 72 65 | 6d 20 35 20 69 6e 20 72 |f Theore|m 5 in r|
|00000950| 65 66 65 72 65 6e 63 65 | 20 41 2e 0d 0a 0d 0a 50 |eference| A.....P|
|00000960| 72 6f 6f 66 20 62 79 20 | 6d 65 74 61 70 72 6f 6f |roof by |metaproo|
|00000970| 66 3a 0d 0a 20 20 41 20 | 6d 65 74 68 6f 64 20 69 |f:..  A |method i|
|00000980| 73 20 67 69 76 65 6e 20 | 74 6f 20 63 6f 6e 73 74 |s given |to const|
|00000990| 72 75 63 74 20 74 68 65 | 20 64 65 73 69 72 65 64 |ruct the| desired|
|000009a0| 20 70 72 6f 6f 66 2e 20 | 20 54 68 65 20 63 6f 72 | proof. | The cor|
|000009b0| 72 65 63 74 6e 65 73 73 | 20 6f 66 20 74 68 65 0d |rectness| of the.|
|000009c0| 0a 20 20 6d 65 74 68 6f | 64 20 69 73 20 70 72 6f |.  metho|d is pro|
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|000009e0| 65 73 65 20 74 65 63 68 | 6e 69 71 75 65 73 2e 0d |ese tech|niques..|
|000009f0| 0a 0d 0a 50 72 6f 6f 66 | 20 62 79 20 70 69 63 74 |...Proof| by pict|
|00000a00| 75 72 65 3a 0d 0a 20 20 | 41 20 6d 6f 72 65 20 63 |ure:..  |A more c|
|00000a10| 6f 6e 76 69 6e 63 69 6e | 67 20 66 6f 72 6d 20 6f |onvincin|g form o|
|00000a20| 66 20 70 72 6f 6f 66 20 | 62 79 20 65 78 61 6d 70 |f proof |by examp|
|00000a30| 6c 65 2e 20 20 43 6f 6d | 62 69 6e 65 73 20 77 65 |le.  Com|bines we|
|00000a40| 6c 6c 20 77 69 74 68 20 | 70 72 6f 6f 66 20 62 79 |ll with |proof by|
|00000a50| 0d 0a 20 20 6f 6d 69 73 | 73 69 6f 6e 2e 0d 0a 0d |..  omis|sion....|
|00000a60| 0a 50 72 6f 6f 66 20 62 | 79 20 76 65 68 65 6d 65 |.Proof b|y veheme|
|00000a70| 6e 74 20 61 73 73 65 72 | 74 69 6f 6e 3a 0d 0a 20 |nt asser|tion:.. |
|00000a80| 20 49 74 20 69 73 20 75 | 73 65 66 75 6c 20 74 6f | It is u|seful to|
|00000a90| 20 68 61 76 65 20 73 6f | 6d 65 20 6b 69 6e 64 20 | have so|me kind |
|00000aa0| 6f 66 20 61 75 74 68 6f | 72 69 74 79 20 72 65 6c |of autho|rity rel|
|00000ab0| 61 74 69 6f 6e 20 74 6f | 20 74 68 65 20 61 75 64 |ation to| the aud|
|00000ac0| 69 65 6e 63 65 2e 0d 0a | 0d 0a 50 72 6f 6f 66 20 |ience...|..Proof |
|00000ad0| 62 79 20 67 68 6f 73 74 | 20 72 65 66 65 72 65 6e |by ghost| referen|
|00000ae0| 63 65 3a 0d 0a 20 20 4e | 6f 74 68 69 6e 67 20 65 |ce:..  N|othing e|
|00000af0| 76 65 6e 20 72 65 6d 6f | 74 65 6c 79 20 72 65 73 |ven remo|tely res|
|00000b00| 65 6d 62 6c 69 6e 67 20 | 74 68 65 20 63 69 74 65 |embling |the cite|
|00000b10| 64 20 74 68 65 6f 72 65 | 6d 20 61 70 70 65 61 72 |d theore|m appear|
|00000b20| 73 20 69 6e 20 74 68 65 | 20 72 65 66 65 72 65 6e |s in the| referen|
|00000b30| 63 65 0d 0a 20 20 67 69 | 76 65 6e 2e 0d 0a 0d 0a |ce..  gi|ven.....|
|00000b40| 50 72 6f 6f 66 20 62 79 | 20 66 6f 72 77 61 72 64 |Proof by| forward|
|00000b50| 20 72 65 66 65 72 65 6e | 63 65 3a 0d 0a 20 20 52 | referen|ce:..  R|
|00000b60| 65 66 65 72 65 6e 63 65 | 20 69 73 20 75 73 75 61 |eference| is usua|
|00000b70| 6c 6c 79 20 74 6f 20 61 | 20 66 6f 72 74 68 63 6f |lly to a| forthco|
|00000b80| 6d 69 6e 67 20 70 61 70 | 65 72 20 6f 66 20 74 68 |ming pap|er of th|
|00000b90| 65 20 61 75 74 68 6f 72 | 2c 20 77 68 69 63 68 20 |e author|, which |
|00000ba0| 69 73 20 6f 66 74 65 6e | 20 0d 0a 20 20 6e 6f 74 |is often| ..  not|
|00000bb0| 20 61 73 20 66 6f 72 74 | 68 63 6f 6d 69 6e 67 20 | as fort|hcoming |
|00000bc0| 61 73 20 61 74 20 66 69 | 72 73 74 2e 0d 0a 0d 0a |as at fi|rst.....|
|00000bd0| 50 72 6f 6f 66 20 62 79 | 20 73 65 6d 61 6e 74 69 |Proof by| semanti|
|00000be0| 63 20 73 68 69 66 74 3a | 0d 0a 20 20 53 6f 6d 65 |c shift:|..  Some|
|00000bf0| 20 73 74 61 6e 64 61 72 | 64 20 62 75 74 20 69 6e | standar|d but in|
|00000c00| 63 6f 6e 76 65 6e 69 65 | 6e 74 20 64 65 66 69 6e |convenie|nt defin|
|00000c10| 69 74 69 6f 6e 73 20 61 | 72 65 20 63 68 61 6e 67 |itions a|re chang|
|00000c20| 65 64 20 66 6f 72 20 74 | 68 65 20 73 74 61 74 65 |ed for t|he state|
|00000c30| 6d 65 6e 74 0d 0a 20 20 | 6f 66 20 74 68 65 20 72 |ment..  |of the r|
|00000c40| 65 73 75 6c 74 2e 0d 0a | 0d 0a 50 72 6f 6f 66 20 |esult...|..Proof |
|00000c50| 62 79 20 61 70 70 65 61 | 6c 20 74 6f 20 69 6e 74 |by appea|l to int|
|00000c60| 75 69 74 69 6f 6e 3a 0d | 0a 20 20 43 6c 6f 75 64 |uition:.|.  Cloud|
|00000c70| 2d 73 68 61 70 65 64 20 | 64 72 61 77 69 6e 67 73 |-shaped |drawings|
|00000c80| 20 66 72 65 71 75 65 6e | 74 6c 79 20 68 65 6c 70 | frequen|tly help|
|00000c90| 20 68 65 72 65 2e 0d 0a | 0d 0a 2d 2d 2d 2d 2d 2d | here...|..------|
|00000ca0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000cb0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 2d 2d |--------|--------|
|00000cc0| 2d 2d 2d 2d 2d 2d 2d 2d | 2d 2d 2d 2d 2d 2d 0d 0a |--------|------..|
|00000cd0| 0d 0a 0d 0a 0d 0a 0d 0a | 48 65 6e 72 79 20 43 61 |........|Henry Ca|
|00000ce0| 74 65 20 49 49 49 0d 0a | 2d 2d 2d 2d 2d 2d 2d 2d |te III..|--------|
|00000cf0| 2d 2d 2d 2d 2d 2d 0d 0a | 20 20 28 75 63 62 76 61 |------..|  (ucbva|
|00000d00| 78 21 78 65 72 6f 78 2e | 63 6f 6d 21 63 61 74 65 |x!xerox.|com!cate|
|00000d10| 33 2e 6f 73 62 75 6e 6f | 72 74 68 29 20 20 4f 52 |3.osbuno|rth)  OR|
|00000d20| 20 20 28 63 61 74 65 33 | 2e 6f 73 62 75 6e 6f 72 |  (cate3|.osbunor|
|00000d30| 74 68 40 58 65 72 6f 78 | 2e 43 6f 6d 29 0d 0a 45 |th@Xerox|.Com)..E|
|00000d40| 76 65 72 79 6f 6e 65 20 | 63 6f 6d 70 6c 61 69 6e |veryone |complain|
|00000d50| 73 20 6f 66 20 68 69 73 | 20 6d 65 6d 6f 72 79 2c |s of his| memory,|
|00000d60| 20 6e 6f 20 6f 6e 65 20 | 6f 66 20 68 69 73 20 6a | no one |of his j|
|00000d70| 75 64 67 6d 65 6e 74 2e | 0d 0a 0d 0a 1a          |udgment.|.....   |
+--------+-------------------------+-------------------------+--------+--------+