Finite Automata to Regex via Arden's Theorem | Tips & Tricks

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theory of computation in hindi, gate, lecture, example, finite automata to regular expression by arden's theorem, Consider the non-deterministic finite automaton (NFA) shown in the figure.
State X is the starting state of the automaton. Let the language accepted by the NFA with Y as the only accepting state be L1. Similarly, let the language accepted by the NFA with Z as the only accepting state be L2. Which of the following statements about L1 and L2 is TRUE?
Which of the following statements is TRUE about the regular expression 01*0?
A) It represents a finite set of finite strings.
B)
It represents an infinite set of finite strings.
C) It represents a finite set of infinite strings.
D) It represents an infinite set of infinite strings
Let L be a regular language and M be a context-free language, both over the alphabet Σ. Let Lc and Mc denote the complements of L and M respectively. Which of the following statements about the language Lc∪ Mc is TRUE?
A) It is necessarily regular but not necessarily context-free.
B) It is necessarily context-free.
C) It is necessarily non-regular.
D)
None of the above
Which one of the following statements is FALSE?
A) There exist context-free languages such that all the context-free grammars generating them are ambiguous
B)
An unambiguous context-free grammar always has a unique parse tree for each string of the language generated by it
C)

Both deterministic and non-deterministic pushdown automata always accept the same set of languages
D) A finite set of string from some alphabet is always a regular language
Let L be a regular language. Consider the constructions on L below:

repeat (L) = {ww | w ∊ L)
prefix (L) = {u | ∃v : uv ∊ L}
suffix (L) = {v | ∃u uv ∊ L}
half (L) = {u | ∃v : | v | = | u | and uv ∊ L}

Which of the constructions could lead to a non-regular language?
Let L be a regular language. Consider the constructions on L below:

repeat (L) = {ww | w ∊ L}
prefix (L) = {u | ∃v : uv ∊ L}
suffix (L) = {v | ∃u : uv ∊ L}
half (L) = {u | ∃v : | v | = | u | and uv ∊ L}

Which of the constructions could lead to a non-regular language?