Ch2-qs - Chapter 2 Languages 1 Let L be the language over...

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Unformatted text preview: Chapter 2. Languages 1. Let L be the language over the alphabet {(1, (9} defined by (1) Basis: )1 E L. 1 (ii) Recursion: If u E L and u = (ryz, then 9061be E L and mbyaz E L. l (iii) Closure. A string 11 E L only if u can be obtained by a finite number of applications of the recursive step. , {(130, 19a} Describe L (Example 2. 2 3 on page 46),1.e., What are the strings in L? l {algal-n 11' 01/ flangomgfl cmrlxlgivg {f 61% film 1351 M11 141 the Jame hvvmter 059 ‘ [03° kg) 01.1 and LI. 0L4 ) la 61 10a) 2. Give a recursive defintion of the set of strings over r{a, b} that contains twice as qfllol" many a’s as b’s. (Problem 8 on page 59). WM} £631: L lee Jal'xcflet ‘c‘l/ 1171711131 Over Z=fa1laj Wot Cowtw'h 45111;an "WM c1} / 011 la} L 1.1‘ 1/60W11v6% «calmed an , a ' 1 L #11 % fill/21$ 6136 t1 eL 1116K that 1,1 11 written ac X31700,- (Mere nae-1106.3. 38611. (11 quaauo 01) xegloqgaw 61119111111 XlOfla;tflt/O 111611011 Cfliflwewm MG L 07% 1:? U CCU» l9€ Obtaineykzgvm 0) 1111119 a§1111£2 “WMLGV 9g 1 €1Covl1o'm 12, 1 3. - or False. { )1 }, the language consisting of only the null string, is a language l , (MN be, over any alphabet. 7( 6 89“ all?“ 1 4. -or False. (l), the empty language, is a languageOver any alphabet. l 5. Give a regular expression that represents each of the follvvoing described sets: (a) The set of strings over { a, b } in which every a is either immediately preceded 1 1 ' or immediately followed by b, e.g., bddb, aim, and b. (Problem 28 on page 60) 1 ((thflotaU») (b) The set of strings over { CL, 1) } that do not contain the substring dad. (Problem 3 31 on page 60) (lo U Ola U aal‘of‘é ( A U a U 0101) ...
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