NFA without epsilon moves to Deterministic Finite Automata (DFA).NFA with epsilon moves to without epsilon moves.RE to Non-deterministic finite automata (NFA) with epsilon moves.The above figure explains that it is easy to convert The relationship between FA and RE is as follows − Now that we have learnt about these terminologies, let us understand the relation between them. δ: Q × Σ → Q is the transition function.It is a mathematical model of a system with discrete inputs, outputs, states and a set of transitions from state to state that occurs on input symbols from the alphabet Σ. Finite Automataįinite automata is an abstract computing device. The r* is known as Kleen closure or closure which indicates occurrence of r for an infinite number of times. If r and s regular expressions denoting the language.ε is a regular expression and denotes the set.Φ is a regular expression which denotes the empty set.The regular expression over Σ can be defined as follows − Let Σ be an alphabet which denotes the input set. Regular expressions are the most effective way to represent any language. Regular expression is the language which is used to describe the language and is accepted by finite automata. The above automata will accept all string which have ‘ab’ as substring. We can construct finite automata as shown in Figure 2. String with ‘ab’ as substring : The regular expression for strings with ‘ab’ as substring is (ab)ab (ab). Let us begin by understanding what is a regular expression. So, it will accept all strings with even number of a’s. Nondeterministic Finite Automata We’ve been looking at deterministic finite automata (DFAs) so far. In order to understand the relationship between finite automata (FA) and regular expression (RE), we need to understand these terminologies. is the only accepting state, the automaton accepts strings if and only if they contain an odd number of 0s and end with a 1.