REGULAR language (Automata theory)

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REGULAR language (Automata theory)



Is it true that the language accepted by any NFA is different from the regular language? I just started TOC, and someone asked me this question, I'm not sure what it exactly means and how to justify it, i tried googling it, but no results.. can someone help me with this?





Every NFA has an equivalent DFA, and both accept regular languages.
– Xufox
Aug 6 at 14:09





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– Ali Soltani
Aug 12 at 4:10





My reputation is under 15 as i just started, so my upvote won't be public, regardless, i did upvote ur answer
– Dhiraj Sharma
Aug 12 at 4:35




2 Answers
2



A language L is called regular if and only if there exists some deterministic finite accepter (DFA) M such that


L= L(M)



Let L be the language accepted by a non-deterministic finite accepter (NFA) MN= (QN, Σ,δN,q0
,FN). Then
there exists a deterministic finite accepter MD= (QD, Σ,δD,q0,FD) such that


L= L(MD)



So we can design at least one DFA for one NFA and as a result, language of both of them is regular.


DFA


NFA



You can see more information about it in An introduction to formal languages and automata Peter Linz, section 2.3.



An language accepted by a FA (whatever NFA or DFA) is Regular Language!



What's more, regular sets, DFA, NFA, pattern, regular expression are equivalent.






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