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I am fairly new to automata, regular expressions and regular grammar. I am struggling to understand how to define the regular expression (abc)* into one or several regular grammar expressions. Following production rules are applied

  1. N={S,A,B}
  2. Σ={a, b c}
  3. S being the start symbol

So far i have found these two.

S → aA

A → bB

B → cS

S → ε

and

S → Ac

A → Bb

B → Sa

S → ε

Are both of the grammars over correct or do i have the wrong idea? I just dont understand why the two grammars over are correct while the bottom two are not.

S → aA

A → bB

B → cS

B → c

and

S → Ac

A → Bb

B → Sa

B → a

$\endgroup$
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    $\begingroup$ Looks fine to me. What doubts did you have that this wasn't right? By the way, two things: (1) Welcome to the site! (2) These "check my results" posts are discouraged here; we'll be happy to clear up things you don't quite understand, but in those cases you should help us help you by pointing out where you don't get what's going on. $\endgroup$
    – Rick Decker
    Mar 25, 2020 at 18:05
  • $\begingroup$ Thank you for the welcome! I understand, i didn't know quite how to formulate myself. I will articulate the question better next time. Well the reason why i was wondering if wasn't right was because of the test i ran in JFLAP. First i generated random strings using my regular expression (abc)* then i tested those for match using the regular grammar expressions. Two of them had full match while the two i listed here didn't. I got confused to as why that would happen if they were the same in the first place. I hope that made sense. $\endgroup$
    – Dusan Biga
    Mar 25, 2020 at 18:18
  • $\begingroup$ I don't understand what "full match" means but it scarcely matters--your answer is correct. It might be nice to edit your original post to include your clarifying comment. Who knows? Maybe there's a JFLAP expert here who'll say "Yeah, that's a known bug, they say they're working on a fix." $\endgroup$
    – Rick Decker
    Mar 25, 2020 at 23:23
  • $\begingroup$ Would you care to explain why the two solutions on top are correct while the two a the bottom are not? $\endgroup$
    – Dusan Biga
    Mar 26, 2020 at 1:24
  • $\begingroup$ Is the empty string in the language with the first two grammars? Is it in the languages generated by the third and fourth? $\endgroup$
    – Rick Decker
    Mar 26, 2020 at 18:00

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