lect_11 - £ 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:A ÐgÓ Ö iØhÑ ×ÓÒD FA × F eb ÖÙa ÖÝ Ò Øh i× ÐeØÙ ÖeÛ eÛ iÐÐd i×Ù ×××eÚ eÖa Ða ÐgÓ Ö iØhÑ × fÓ ÖÖegÙ Ða Ö ÐaÒgÙag e×Ô Öe×eÒ Øeda ×D FA × EÑ Ô Ø iÒ e ×× h eeÑ Ô Ø iÒ e××Ô ÖÓb ÐeÑ fÓ ÖD FA ×i×d e idab Ðe ;ieÛ eaÒÛ Ö iØeaÒa ÐgÓ Ö iØhÑ ØÓh ek Û h eØh eÖØh e ÐaÒgÙag eÓ faÒ iÒÔÙ ØD FA A i×ÒÓÒeÑ Ô ØÝAD FA aÒb eeÒÓd eda ×a ×ØÖ iÒg ×aÝbÝeÒÓd iÒg Øh eØÙÔ Ðe ( Q, Σ ,δ,q ,F ) h eØÙÔ ÐeaÒb eaÔÔ ÖÓÔ Ö ia Øe ÐÝeÒÓd eda × iØ i× Ò iØe Q aÒd Σ a ÖeÒ iØeaÒdh eÒe δ : Q × Σ → Q i×ÖeÔ Öe×eÒ Øab Ðea ×aÒ iØeØab ÐeeØ ÓÛÓÒ × id eÖØh eD FA a ×ag ÖaÔhÛ iØhÒÓd e×a ××Øa Øe×aÒd Ðab e Ðed edg e×a ×ØÖaÒ × iØ iÓÒ × Ó fØh eD FAh eÒ iØ i×ea ×Ý ØÓ ×eeØha Ø L ( A ) i×ÒÓÒeÑ Ô ØÝ iØh eÖe i×aÔa Øh fÖÓÑ Øh e iÒ iØ ia Ð ×Øa ØeØÓ ×ÓÑ eÒa Ð×Øa Øe iÒ Øh i×g ÖaÔhh i×Ô ÖÓb ÐeÑ i×× iÑ Ô ÐÝa Öeahab iÐiØÝÔ ÖÓb ÐeÑ s − t Öeahab iÐiØÝ aÒdaÒb e×Ó ÐÚ ed iÒ ÐiÒ ea ÖØ iÑ e iÒ Øh eÒÙÑ b eÖÓ fÒÓd e×aÒd edg e× ×aÝÙ × iÒg d eÔ ØhÖ×Ø×ea ÖheÒeØh eeÑ Ô Ø iÒ e××Ô ÖÓb ÐeÑ i×d e idab Ðe fÓ ÖD FA × A × iÑ iÐa Öa ÐgÓ Ö iØhÑÛ Ó Ök ×fÓ ÖFA ×a ×Û e ÐÐ Ò ÐÙ × iÓÒE ÕÙ iÚa ÐeÒee Ø ØÒÓÛ fÓ ÐÐÓÛ ×Øha Ø iÒ ÐÙ × iÓÒaÒd eÕÙ iÚa ÐeÒeÓ fÖegÙ Ða Ö ÐaÒgÙag e×ÖeÔ Öe×eÒ Øeda ×D FA ×i× d e idab ÐeÙ × iÒg ÐÓ ×Ù ÖeÔ ÖÓÔ eÖØ ie× G iÚ eÒD FA × A 1 aÒd A 2 ÓÚ eÖØh e×aÑ ea ÐÔhab eØÛ eaÒd e id e if L ( A 1 ) ⊆ L ( A 2 ) bÝ ÒÓ Ø iiÒgØha ØØh i× i×ØÖÙ e i L ( A 1 ) ∩ ¯ L ( A 2 ) = ∅ iÒeD FA ×a ÖeÓÒ ×ØÖÙ Ø iÚ e ÐÝ ÐÓ ×edÙÒd eÖ Ò ega Ø iÓÒaÒd iÒ ØeÖ×eØ iÓÒÛ eaÒÓÑ Ô ÐeÑ eÒ Ø A 2 aÒd iÒ ØeÖ×eØØh eÖe×Ù ÐØ iÒgaÙ ØÓÑ a ØÓÒ Û iØh A 1 aÒdh ek Øh eÖe×Ù ÐØ iÒgaÙ ØÓÑ a ØÓÒ fÓ ÖeÑ Ô Ø iÒ e××Û h ih i×d e idab Ðe G iÚ eÒD FA × A 1 aÒd A 2 ÓÚ eÖØh e×aÑ ea ÐÔhab eØÛ eaÒd e id e if L ( A 1 ) = L ( A 2 ) bÝ h ek iÒg if L ( A 1 ) ⊆ L ( A 2 ) aÒd L ( A 2 ) ⊆ L ( A 1 ) eÒeeÕÙ iÚa ÐeÒe i×a Ð×Ód e idab Ðe ÒÒ iØeÒ e ×× G iÚ eÒaD FA A aÒÛ ed e id e if L ( A ) i× iÒÒ iØe?ØØÙ ÖÒ ×ÓÙ ØØha ØÛ eaÒeØÙ ×Ö×Ø Ô ÖÓÚ eØh e fÓ ÐÐÓÛ iÒg h eÓ ÖeÑ e Ø A beaD FAÛ iØh n × Øa...
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