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Home7CFGs - CS 341 Automata Theory Elaine Rich Homework 7...

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CS 341 Automata Theory Elaine Rich Homework 7 Due Thursday, Oct. 19 1) Let Σ = { a , b }. For the languages that are defined by each of the following grammars, do each of the following: i . List five strings that are in L . ii . List five strings that are not in L (or as many as there are, whichever is greater). iii . Describe L concisely. You can use regular expressions, expressions using variables (e.g., a n b n , or set theoretic expressions (e.g., { x : …}) iv . Indicate whether or not L is regular. Prove your answer. a) S a S | S b | ε b) S a S a | b S b | a | b c) S a S | b S | ε d) S a S | a S b S | ε 2) Consider the following grammar G : S 0 S 1 | SS | 10 Show a parse tree produced by G for each of the following strings: a) 010110 b) 00101101 3) For each of the following languages L , construct a context-free grammar that generates it: a) L = { a n b m : m n , m - n is even} b) L = { x c n : x { a , b }*, # a ( x ) = n or # b ( x ) = n } c) L = { a i b j : 2 i = 3 j + 1} d) L = { b i # b i +1 R : b i is the binary representation of some integer i , i 0, without leading zeros} e) L = { x R # y : x , y {0, 1}* and x
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