Question 2 (10%) Write a grammar for each of the following languages. Note that N represents the set of natural numbers N = { 0 , 1 , 2 , 3 , . . . } .
(a) { bb, bbbb, bbbbbb, . . . } = { ( bb ) ^n +1 | n ∈ N }
(b) { a, ba, bba, bbba, . . . } = { b ^n a | n ∈ N }
Question 2 (10%) Write a grammar for each of the following languages. Note that N represents...
[Easy] Theoretical Computer Science
Find a grammar for the following languages: (a) Set of binary numerals that represent odd natural numbers (b) Set of binary numerals that represent even natural numbers
Question 3 Give a context-free grammar for each of the following languages over = {a,b,c}. 1. {a^jen: n >0}. 2. {animck : k=n+m} 3. Strings of a's and b's that contain twice as many a's as b's (for example, aba).
Part C Only
Let Σ = {a,b}. For each of the following languages, find a grammar that generates it. (a) Li {a"6" : n > 0,m< n}. (b) L2 = {ang 2n: n > 2). (c) L3 {an+35" : n > 2}.
1. Write DFA, NFA (small), regular expression and right linear grammar for strings over {a,b} a. End in either aa or bb b. ( an | bna) n >= 0 c. {w : w such that w contains the substring “bb” or w contains an odd number of a’s (or both). d. {w : w does not contain exactly two a’s} e. { w : w starts with substring abb and contains substring bba}
Write a regular expression to describe each of the following languages: {w Î {a, b}* : every a in w is immediately preceded and followed by b}. {w Î {a, b}* : w has bba as a substring}.
In each of the following, find a Chomsky Normal Form (CNF) grammar equivalent to the given context-free grammar (CFG). 1. SaA Sab A+ ab | BA ASD BaS b 2. SAIC A → AaB AaC | B | a B Bb Cb (→ cclc 3. S → SabA; AAA bc | Bc; B → Aab | BS a
Question 5 10 pts Select all the statements below which are true: The grammar below is CS. SaSa bb O Any CS language is RE. The language L = {a”b"c" : n > 1}is CF. The language L = {wwR : w€ {a, b}" } is DCF, CF, CS, REC, and RE. There are languages which are not accepted by TMs. Any REC language is accepted by some Decider (a TM that halts for every input).
Define a context-free grammar that generates exactly each of the following languages. For consistency, please use S for the start variable in all three grammars 1. A- E 10,1) the middle symbol in is 0 and is odd)
1. Write regular expressions to capture the following regular languages: (a) The set of binary strings which have a 1 in every even position. (Note: odd positions may be either 0 or 1.) (b) The set of binary strings that do not contain 011 as a substring. (c) Comments in Pascal. These are delimited by (* and *) or by { and }, and can contain anything in between; they are NOT allowed to nest, however. 2. Write a DFA...
3) Construct a regular expression defining each of the following languages over the alphabet {a, b}. (a) L = {aab, ba, bb, baab}; (b) The language of all strings containing exactly two b's. (c) The language of all strings containing at least one a and at least one b. (d) The language of all strings that do not end with ba. (e) The language of all strings that do not containing the substring bb. (f) The language of all strings...