Find cfgs that for these regular languages over the alphabet...

Name: find cfgs that for these regular languages over the alphabet ab draw a finite automata first and use this to create the cfg a the language of all words that contain the substring aba b the l 39323
Uploaded: 2023-12-09T05:48:22-08:00
Duration: 2 min 2 s
Channel: Akash M
Description: find cfgs that for these regular languages over the alphabet ab draw a finite automata first and use this to create the cfg a the language of all words that contain the substring aba b the l 39323

Find CFGs that for these regular languages over the alphabet Σ={a,b}. Draw a Finite Automata first and use this to create the CFG. (a) The language of all words that contain the substring aba. (b) The language of all words that have an odd number letters and contains the string bb. (c) The language of all words that begin with the substring ba and contains an odd number of letters

(a) The set of words that contain an 'a' followed somewhere later (not necessarily in the next position) by a 'b', followed still later by an 'a'. For example, 'bbaabbabbb' satisfies this property, but 'bbbbaaaab' does not. (b) The set of words in which the number of 'a's and the number of 'b's are congruent modulo 3. (You can do this with 9 states by keeping separate mod 3 counts of both the numbers of 'a's and the number of 'b's. But a more efficient implementation is to keep track of the value mod 3 of the difference between the number of 'a's and the number of 'b's.) (c) The set of words over the alphabet {0,1,2,3,4,5,6,7,8,9} that are decimal representations of numbers divisible by 3. For instance, the word '126' is accepted by this DFA, but '124' is not. (HINT: You can use the fact that the value represented is congruent mod 3 to the sum of its digits.)

Akash M.

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