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ø˙‡„Â≠ȇ ÌÈ„„ÂÓ Íȇ<br />
ÌÈÙ˙˙˘ÓÏ ÌÈÚ„ȉ ¨ÌÈapple¢ ÌÈÚ·ˆ ∏≠· Ìȯ„Π∏ ‰·Â ‰ÒÙ˜ ˘È ∫‰Ê‰ ˜Á˘Ó· ÌȘÁ˘Ó È˙ÈÓ‡ Ô˘‰ ÂappleÈÈÁ‡Â Ô¯„<br />
ƱØ∏ ‡È‰ ˘ÁappleÏ ˙¯·˙Ò‰‰ ƯÁ·˘ ¯Â„Ή Ú·ˆ ˙‡ ˙ÂÏ‚Ï Íȯˆ Ô¯„ ¨„Á‡ ¯Â„Πȇ¯˜‡· ¯Á· È˙ÈÓ‡ Æ˘‡¯Ó<br />
¯Â„Ή È·‚Ï ˙‡„‰≠ȇ ˙„ÈÓ ∫˘„Á ‚˘ÂÓ Á˙ÈÙ ÔÂapple˘ ÆÏÎÏ ÚÂ„È Ô·ÂÓÎ ‰È‰ ˙¯·˙Ò‰‰ ‚˘ÂÓ ¨ÔÂapple˘ Ï˘ Â˙Ù˜˙·<br />
¨¢˙Âȯ‡appleÈ·¢ ˙Âχ˘ ≥ χ˘Ï ÂÈÏÚ˘ ÔÂÂÈÎÓ øÚÂ„Ó Æ≥ ‡È‰ ¨˘ÁappleÓ‰ ¨Ô¯„ Ï˘ ˙‡„‰≠ȇ ˙„ÈÓ ¨‰Ê ‰¯˜Ó· ƯÁ·apple‰<br />
ƯÁ·apple ÈÓ ˙‡„· ˙Ú„Ï È„Î ¨¢‡Ï¢ ‡ ¢Ô΢ ˜¯ ‡È‰ Ô‰ÈÏÚ ‰·Â˘˙‰˘ ˙Âχ˘ ¯ÓÂÏÎ<br />
‡ˆÓapple ¯Á·apple˘ ¯Â„Ή ̇‰¢ ∫Ï‡Â˘Â ¨ß·≠ ߇ ˙¢ ˙ˆ·˜ È˙˘Ï ¨ÏÎ ÈappleÈÚÏ ¨Ìȯ„Ή ˙‡ ˜ÏÁÓ ˘ÁappleÓ‰ ¨Ï˘ÓÏ<br />
¯‡˘apple˘ Ìȯ„Ή ¥ ˙‡ ˜ÏÁÓ ‡Â‰ ¨‰Ó„ ÔÙ‡· ÆÌȯ„Π¥≠Ï ÂÏ˘ ˙‡„‰≠ȇ ˙‡ ˙ÓˆÓˆÓ ‰·Â˘˙‰ Æ¢ø߇ ‰ˆÂ·˜·<br />
≠ȇ ˙‡ ̈ӈ˙ ¢øß‚ ‰ˆÂ·˜· ‡ˆÓapple ¯Á·apple˘ ¯Â„Ή ̇‰¢ ‰Ï‡˘Ï ‰·Â˘˙‰Â ¨ß„≠ ߂ Ìȯ„Π≤ Ï˘ ˙ˆ·˜ È˙˘Ï<br />
ƉappleÂÎapple ‰·Â˘˙ ˙‡„· ÂÏ Ô˙È˙ ¯‡˘apple˘ ÌÈ¯Â„Î‰Ó „Á‡ ÏÚ ‰Ó„ ˙È˘ÈÏ˘ ‰Ï‡˘ ÆÌȯ„Π≤≠Ï ÂÏ˘ ˙‡„‰<br />
‰È‰˙ ˙‡„‰≠ȇ ˙„ÈÓ ¨®±ØN© ΩP ‡È‰ ÔÂÎapple ˘ÂÁÈappleÏ ˙¯·˙Ò‰‰ ÆÌȯ„ΠN Ï˘ ÈÏÏÎ ‰¯˜ÓÏ ‰Ï‡ ÌÈÏÏÎ ·ÈÁ¯‰Ï Ϙ<br />
ÆÌÈËÈ· LOG ≤ ®±ØP©<br />
˙„È„ÓÏ ‰„ÈÁÈÎ ¨±π¥∏ ˙apple˘· ¨Â‰˘ÏÎ È‚ÂÏÂappleÎË Â‡ ÈÚ„Ó ¯Ó‡Ó· bit ‰ÏÓ· ˘Ó˙˘‰˘ Ô¢‡¯‰ ¨¯ÂӇΠ¨‰È‰ ÔÂapple˘<br />
Æ˙‡„Â≠ȇ<br />
ȇ¯˜‡· ‰Èȷ˜ ‡ ¯Â„Î ¯Á· È˙ÈÓ‡ ¨ÌÚÙ‰ ÆÌÈapple¢ ÌÈÚ·ˆ· ˙Âȷ˜ ±∂ ÌÚ ‰ÒÙ˜ „ÂÚ ˜Á˘ÓÏ ÂÈ˘ÎÚ ÛÈÒÂapple<br />
ÆÚ·ˆÂ ‰¯Âˆ ¨¯Á·apple ‰Ó ˜ÂÈ„· ˘ÁappleÏ Íȯˆ Ô¯„ Æ®‰Â¢ ˙¯·˙Ò‰· ¨¯ÓÂÏΩ<br />
¢ø¯Â„Î ¯Á·apple ̇‰¢ ∫‡È‰ ˙ȯ˘Ù‡ ‰apple¢‡¯ ‰Ï‡˘ ¨‰Ê ‰¯˜Ó·<br />
‰Êȇ ˙‡„· ˙Ú„Ï È„Î ¢˙Âȯ‡appleÈ·¢ ˙Âχ˘ ≥ „ÂÚ Ï‡˘Ï ÍȯˆÂ ¨Ì„˜‰ ·ˆÓÏ ÌÈÚÈ‚Ó˘ ȯ‰ ¨¢Ô΢ ‡È‰ ‰·Â˘˙‰ ̇<br />
ÆÌÈËÈ· ¥ Ï˘ ˙‡„Â≠ȇ ˙„ÈÓ ¯ÓÂÏÎ ¨¢˙Âȯ‡appleÈ·¢ ˙Âχ˘ ¥ ÏΉ≠ÍÒ· ƯÁ·apple ¯Â„Î<br />
¢˙Âȯ‡appleÈ·¢ ˙Âχ˘ ¥ „ÂÚ Ï‡˘Ï Íȯˆ ¨∏ ̘ӷ ÌÈÚ·ˆ ±∂≠Ï ‰·Á¯‰· Ï·‡ ¨‰Ó„ ÔÙ‡· ȯ‰ ¨¢‡Ï¢ ‡È‰ ‰·Â˘˙‰ ̇<br />
ÆÌÈËÈ· μ Ï˘ ˙‡„Â≠ȇ ˙„ÈÓ ¯ÓÂÏÎ ¨˙Âȯ‡appleÈ· ˙Âχ˘ μ ÏΉ≠ÍÒ· Ɖ¯Á·apple ‰Èȷ˜ ÂÊȇ ˙‡„· ˙Ú„Ï È„Î<br />
̇ ∫‰apple¢‡¯‰ ‰Ï‡˘Ï ‰·Â˘˙· ‰ÈÂÏ˙ ‡È‰ — ˙ÈÚÓ˘Ó≠„Á ‰appleappleȇ ˙‡„‰≠ȇ ˙„ÈÓ ·Á¯ÂÓ‰ ˜Á˘Ó·˘ Ô‡ÎÓ<br />
ÆÌÈËÈ· μ ‡È‰ ˙‡„‰≠ȇ ˙„ÈÓ ¨¢‡Ï¢ ‡È‰ ‰·Â˘˙‰ ̇ ªÌÈËÈ· ¥ ‡È‰ ˙‡„‰≠ȇ ˙„ÈÓ ¨¢Ô΢ ‡È‰ ‰·Â˘˙‰<br />
Æ˙ÚˆÂÓÓ ˙‡„Â≠ȇ ¯È„‚‰Ï ¯˘Ù‡ ¨®±Ø≤ ‰Ê ‰¯˜Ó·© ‰Èȷ˜ ‡ ¯Â„Î ˙¯ÈÁ·Ï ˙¯·˙Ò‰‰ ˙‡ ÌÈÚ„ÂÈ˘ ÔÂÂÈÎÓ<br />
Æ®±Ø≤ ¥ ´ ±Ø≤ μ© ÌÈËÈ· ¥Æμ ‡È‰ ˙ÚˆÂÓÓ‰ ˙‡„‰≠ȇ ¨ÂÊ ‰Ó‚„·<br />
Æ®Entropy© ‰ÈÙ¯Ëapple‡ Ì˘· ÔÂapple˘ ‰appleÈÎ ˙ÚˆÂÓÓ‰ ˙‡„‰≠ȇ ˙‡<br />
ÆÌȯ„Ή ˙ÒÙ˜ ˙‡ ¯Á· ‡Â‰ ÚˆÂÓÓ· Ìȯ˜Ó‰Ó ±Ø¥≠· ˜¯Â ¨˙ÂÈ·Â˜Ï ‰Ù„Ú‰ ˘È È˙ÈÓ‡Ï˘ Ú„ÂÈ Ô¯„˘ ÁÈappleapple<br />
Ɖ˙ÏÚ ˙‡„‰≠ȇ ˙Ó¯ — ®±Ø¥ ¥ ´ ≥Ø¥ μ© ÌÈËÈ· ¥Æ∑μ ‰È‰˙ ÔÂÎapple‰ ˘ÂÁÈapple‰ È·‚Ï ˙ÚˆÂÓÓ‰ ˙‡„‰≠ȇ ¨‰Ê ·ˆÓ·<br />
‰Ï„‚ ˙‡„Â≠ȇ ˘È ˙Âȷ˜‰ È·‚Ï ¨‰Èȷ˜ Ï˘ Ú·ˆ ˘ÁappleÏ Íȯˆ Ìȯ˜Ó ¯˙ÂÈ· ÂÈ˘ÎÚ˘ ÔÂÂÈÎÓ ¨˙‡ȈÓÏ Ìȇ˙Ó ‰Ê<br />
Æ®Ìȯ„η ∏ ≠Ó ± ˙ÓÂÚÏ ¨˙Âȯ˘Ù‡ ±∂ ÍÂ˙Ó ±© Ìȯ„η ¯˘‡Ó ¯˙ÂÈ<br />
˙‡„‰≠ȇ ˙„ÈÓ Èʇ ¨®i Ω ±¨≤¨≥…¨N© Pi ‡È‰ ˙¯˘Ù‡ ÏÎ ˙ÚÙÂ‰Ï ˙¯·˙Ò‰‰Â ¨˙Âȯ˘Ù‡ N ˘È˘Î ¨ÈÏÏÎ ÔÙ‡·<br />
·Ï ÂÓÈ˘© ÔÂapple˘ Ï˘ ˙ÓÒ¯ÂÙÓ‰ ¢˙È҇Ϙ‰ ˙Èapple·˙¢· ‡ H Ω ∑ Pi LOG ≤ ®±ØPi© ∫‡È‰ ®ÔÂÎapple ¢˘ÂÁÈapple¢Ï© ˙ÚˆÂÓÓ‰<br />
■ Æ H Ω — ∑ Pi LOG ≤ ®Pi© ∫®ÒÂappleÈÓ‰ ÔÓÈÒÏ<br />
041<br />
‡ÈÏÈÏ‚<br />
ÈappleÂÈ<br />
≤∞∞∏