Decidable Languages continued Theorem 4 9 Every contextfree
Decidable Languages (continued) • Theorem 4. 9: Every context-free language is decidable. 88 -89 ﻧﻴﻤﺴﺎﻝ ﺍﻝ ﺩﺍﻧﺸگﺎﻩ ﺻﻨﻌﺘی ﻧﻈﺮیﻪ ﺯﺑﺎﻥ ﻫﺎ ﻭ ﻣﺎﺷیﻦ ﻫﺎ
Turing-Unrecognizable Languages • DEFINITION A language is co. Turing-recognizable if it is the complement of a Turing-recognizable language. 88 -89 ﻧﻴﻤﺴﺎﻝ ﺍﻝ ﺩﺍﻧﺸگﺎﻩ ﺻﻨﻌﺘی ﻧﻈﺮیﻪ ﺯﺑﺎﻥ ﻫﺎ ﻭ ﻣﺎﺷیﻦ ﻫﺎ
• THEOREM 4. 22 A language is decidable iff it is Turingrecognizable and co-Turing-recognizable. • PROOF We have two directions to prove. First, if A is decidable, then both A and its complement AC are Turing recognizable. For the other direction, let M 1 be the recognizer for A an M 2 be the recognizer for AC. The following Turing Machin M is a decider for A. M = “On input w: 1. Run both M 1 and M 2 on input w in parallel. 2. If M 1 accepts, accept; if M 2 accepts, reject. ” 88 -89 ﻧﻴﻤﺴﺎﻝ ﺍﻝ ﺩﺍﻧﺸگﺎﻩ ﺻﻨﻌﺘی ﻧﻈﺮیﻪ ﺯﺑﺎﻥ ﻫﺎ ﻭ ﻣﺎﺷیﻦ ﻫﺎ
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