In the context of regular languages, what is the purpose of the final state in a Finite Automaton?a.Define the alphabet of the automatonb.Specify the set of accepting statesc.Determine the initial stated.Represent the set of strings in the language

What is finite automata? How it can be used in string matching?

What is the primary purpose of a finite automaton in the context of theory of computation?

19. Consider the following modification of Definition 2.6. An nfa with multipleinitial states is defined by the quintupleM = (Q, Σ, δ, Q0, F ) ,58 Chapter 2 Finite Automatawhere Q0 ⊆ Q is a set of possible initial states. The language accepted bysuch an automaton is defined asL (M ) = {w : δ∗ (q0, w) contains qf , for any q0 ∈ Q0, qf ∈ F } .Show that for every nfa with multiple initial states there exists an nfa with asingle initial state that accepts the same language.20. Suppose that in Exercise 19 we made the restriction Q0 ∩ F = . Would thisaffect the conclusion?

Write regular expressions for the following languages.1. the set of all alphabetic strings;2. the set of all lower case alphabetic strings ending in a b;3. the set of all strings from the alphabet a, b such that each a is immedi-ately preceded by and immediately followed by a b

For the language over Σ = {a, b}, provide a regular expression and a DFA for the language. Your automata should have at most 10 states.The set of strings that contain exactly three as and an even number of bs. For example, abababb is in the language, while ababab is not.