regular languages

Question

A Language is said to be regular iff
(a) There exists a Right Linear Regular Grammar for L
(b) There exists a Left Linear Regular Grammar for L
(c) There exists a nfa with single final state
(d) There exists a dfa with single final state
(e) There exists a nfa without ԑ - move
Which are true?
(i) All are true   (b) a, b, c are true
(c) a, b, c, e are true   (d) a, b, d are true

Comments

All seems to be correct.

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DFA with single final state has the same powers as DFA with more than one final state.

@bikram

Answer 1

(c) is correct option!

Statement (d) is not true, DFA with single final state has less power than NFA with one state, it's because in DFA there are no epsilon transitions defined for DFA.
for example, Language L=a*b* is a regular language but you can not draw DFA for it with single final state.

Hence statement (d) is false!

Comments

Sir as we know just need a finite automata for regular language it can be an nfa with multiple states and ԑ - move so why option (C) and option (e) are correct,can you explain with an example?

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1. for ALL the regular languages you can build an NFA with single Final state because with epsilon transitions you can connect multiple final states into one final state.

2. As any NFA with epsilon transitions can be converted into an equivalent NFA without epsilon transitions.

Statements c and e are individually correct because these both statements are independent to each other , bot need not to be true at the same time.