lect_10 - £ C7:h eÓ ÖÝÓ fC ÓÑ ÔÙ Øa Ø iÓÒ £...

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Unformatted text preview: £ C7 :h eÓ ÖÝÓ fC ÓÑ ÔÙ Øa Ø iÓÒ £ adhÙ ×ÙdaÒa ÖØha ×a Öa ØhÝ eØÙ Öe:ÖÓÚ iÒgÒÓÒ ÖegÙ Ða Ö iØÝÙ × iÒgÝh iÐÐ e ÖÓd ehÑ aÒdÙÑ Ô iÒgeÑÑ a 8F eb ÖÙa ÖÝ Ò Øh i× ÐeØÙ ÖeÛ eÛ iÐÐ×eehÓÛ ØÓÔ ÖÓÚ eØha Øa ÐaÒgÙag e i× ÒÓ Ø ÖegÙ Ða Ö eÛ iÐÐ×eeØÛ ÓÑ eØhÓd ×fÓ Ö×hÓÛ iÒg Øha Øa ÐaÒgÙag e i×ÒÓ ØÖegÙ Ða Öh eÝh iÐÐeÖÓd e Øh eÓ ÖeÑ aÒd Øh eÔÙÑ Ô iÒg ÐeÑÑ a×hÓÛ Øha ØeÖØa iÒk eÝ×eed ÐaÒgÙag e×a ÖeÒÓ ØÖegÙ Ða Ö F ÖÓÑ Øh e×e×eed ÐaÒgÙag e×Û eaÒ ×hÓÛ Øha ØÑ aÒÝ × iÑ iÐa Ö ÐaÒgÙag e×a Öea Ð×ÓÒÓ ØÖegÙ Ða Ö Ù × iÒg ÐÓ ×Ù ÖeÔ ÖÓÔ eÖØ ie× ÖÓÚ iÒgÒÓÒ ÖegÙ Ða Ö iØÝÚ iaØh eÝh iÐÐeÖÓd eh eÓ ÖeÑ ea ÐÐØha ØØh eÝh iÐÐeÖÓd eØh eÓ ÖeÑ ×aÝ ×aÑ ÓÒgÓ Øh eÖØh iÒg ×Øha Ø if L i×a ÐaÒgÙag e Øha Øha ×aÒ iÒÒ iØeÒÙÑ b eÖÓ f×ÙÜ ÐaÒgÙag e×Øh eÒ L i×ÒÓ ØÖegÙ Ða ÖÒ ØÙ iØ iÚ e ÐÝÛ eÒ eeda ×Øa ØeÓ faD FA fÓ ÖeÚ eÖÝ ×ÙÜ ÐaÒgÙag eÓ f L aÒdh eÒeÒ eedaÒ iÒÒ iØeÒÙÑ b eÖÓ f×Øa Øe× Øha ØÒÓD FA aÒaÓÑÑ Óda Øe h i×g iÚ e×aÛ aÝÓ fÔ ÖÓÚ iÒga ÐaÒgÙag e i×ÒÓ ØÖegÙ Ða ÖeØ L ⊆ Σ ∗ h eÒ L i×ÒÓ ØÖegÙ Ða Ö ifØh eÖea ÖeaÒ iÒÒ iØeÒÙÑ b eÖÓ f×ÙÜ ÐaÒgÙag e××aÝ { largellbracket L/x 1 largerrbracket , largellbracket L/x 2 largerrbracket , . . . } Øha Øa Öea ÐÐ d i×Ø iÒ Ø fÖÓÑ eahÓ Øh eÖ ie largellbracket L/x i largerrbracket negationslash = largellbracket L/x j largerrbracket fÓ ÖaÒÝ i negationslash = j ÒÓ Øh eÖÛ Ó Öd ×iÒÓ Öd eÖØÓÔ ÖÓÚ e L i×ÒÓ ØÖegÙ Ða ÖÛ eÒ eed ØÓeÜh ib iØaÒ iÒÒ iØe×eØÓ f ×ØÖ iÒg × S = { x 1 , x 2 , . . . } ×Ùh Øha ØfÓ Öeah x, y ∈ S if x negationslash = y Øh eÒ largellbracket L/x largerrbracket negationslash = largellbracket L/y largerrbracket B Ù Ø Û h eÒ i× largellbracket L/x largerrbracket negationslash = largellbracket L/y largerrbracket hÓ Ðd ?C Ðea Ö ÐÝ Øh i×hÓ Ðd × ifaÒdÓÒ ÐÝ ifØh eÖeeÜ i×Ø×a z ∈ Σ ∗ Øha Ø i× iÒ ÓÒ e×ÙÜ ÐaÒgÙag ebÙ ØÒÓ Ø iÒ Øh eÓ Øh eÖie ∃ z ∈ Σ ∗ ×Ùh Øha Ø z ∈ largellbracket L/x largerrbracket and z negationslash∈ largellbracket L/y largerrbracket Ó Ö z negationslash∈ largellbracket L/x largerrbracket and z ∈ largellbracket L/y largerrbracket e×Øa Ø iÒgØh i×Û eÑ Ù ×Ø×hÓÛ Øha Ø ∃ z ∈ Σ ∗ ×Ùh Øha Ø ( xz ∈ L and yz negationslash∈ L ) Ó Ö ( xz negationslash∈ L and yz ∈ L ) h i×Ðead ×Ù ×ØÓ Øh e fÓ ÐÐÓÛ iÒgd eÒ iØ iÓÒÓ fÛ h eÒ ØÛ Ó ×ØÖ iÒg × x aÒd y a Öe d i× ØigÙ i×hab Ðe Û iØh Öe×Ô eØØÓ L :Øh eÝa Öed i×Ø iÒgÙ i×hab Ðe ifÛ eaÒÒda z ×Ùh Øha Ø xz aÒd yz haÚ ea d ieÖeÒ ØÑ eÑ b eÖ×h iÔ ×Øa ØÙ × iÒ L D eÒ iØ iÓÒ Û Ó ×ØÖ iÒg...
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This note was uploaded on 03/04/2010 for the course CS 373 taught by Professor Kuma during the Spring '10 term at University of Illinois at Urbana–Champaign.

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lect_10 - £ C7:h eÓ ÖÝÓ fC ÓÑ ÔÙ Øa Ø iÓÒ £...

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