REGULAR language (Automata theory)

Question

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?

Answer 1

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.

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

Answer 2

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.