Moed_A_part_2_Solution

Moed_A_part_2_Solution - (236343 zeiaeyigd zxez r"yz...

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Unformatted text preview: (236343) zeiaeyigd zxez r"yz sxeg 2 wlg '` cren zepexzt 1 dl`y xear M 1 PSPACE zpekn dpap . L 2 xear PSPACE zpekn M 2 `dze L 2-l L 1-n divwecxd zivwpet f `dz .1 .denk dpere f ( x ) lr M 2 z` dvixn okn xg`le f ( x ) z` zaygn ziy`x x hlw lr M 1 :`ad ote`a L 1 zlret M 2 mbe , | x |-a inepilet oexkfa aeyigl zpzip f-y oeeikn .cinz caer mzixebl`d ,d`ln f ( x )-y oeeikn `id eay oexkfdn wlgk aygp f ly hltd ik) | x |-a inepilet gxkda | f ( x ) | mbe , | f ( x ) |-a inepilet oexkfa okle , | x |-a inepilet oexkfa zlret M 2-y o`kne , | x |-a mepilet mb `ed | f ( x ) |-a mepilet lk okle (zynzyn x ∈ L 1 ⇐⇒ f ( x ) ∈ L 2 ⇐⇒-y ciin dler M 2 zepekpe f zetwz it lr . | x |-a inepilet oexkfa zlret M 1 mb .yxcpk , L ( M 1 ) = L 1 ok lre , M 2 ( f ( x )) = acc ⇐⇒ M 1 ( x ) = acc `dze L 6 = ∅ , Σ * `dz . PSPACE zeivwecxl qgia dyw- PSPACE `id L 6 = ∅ , Σ * zil`ieeixh `l dty lk .2-y jk a,b milin yi ,zil`ieeixh dpi` L-y oeeikn .inepilet oexkfa zlretd M dpekn mr L ∈ PSPACE ,dlaiw M m`e , M z` uixp x hlw lr :`ad ote`a L ≤ PSPACE L divwecx xicbp . a ∈ L,b / ∈ L inepilet oexkfa aeyigl zpzip ,d`ln xexiaa `id xicbn df mzixebl`y divwpetd . b heltp zxg`e , a heltp-e x ∈ L ⇒ M ( x ) = acc ⇒ f ( x ) = a ⇒ f ( x ) ∈ L oky dtwze ,inepilet oexkfa zlret M ik dnly- PSPACE mb didz dyw- PSPACE dtyy ick . x / ∈ L ⇒ M ( x ) = rej ⇒ f ( x ) = b ⇒ f ( x ) / ∈...
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