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Design finite automata from a given regular expression.
Finite automata (FA) is an abstract computing device. It can be represented in the following −
- Graphical (Transition diagrams)
- Tabular (Transition table)
- Mathematical (Transition function)
The formal definition of FA is that it is a five tuples.
M=(Q, Σ, δ, q0, F)
Where,
- Q: Finite set called states
- Σ: Finite set called alphabets
- δ: Q × Σ → Q is the transition function
- q0 ∈ Q is the start or initial state
- F: Final or accept state
Regular expression
The regular expression can be used to describe a sequence of patterns that defines a string. It is used to match character combinations in strings.
The language accepted by some regular expression are referred to as regular language
Now let’s consider RE 10+(0+11)0*,
Construct finite automata for this regular expression −
Step 1
Initially consider two states q0 and qf. Also, consider the initial and final states, q0 to qf and the given regular expression 10+(0+11)0*1
Step 2
Now applying the union operation, q0 on 10 goes to qf and q0 on (0+11)0*1 goes to qf.
Step 3
Now, divide the expression by applying concatenation i.e. let L1=0, L2=1. Concatenate both and we get L= L1.L2.
Applying this formula on regular expression, so q0 on 1 goes to q1 and q1 on 0 goes to qf. Similarly, q0 on (0+1) goes to q2 and q2 on 0*1 goes to qf.
Step 4
q0 on 1 goe to q1 and q1 on 0 goes to qf, q0 on (0+1) goes to q2, q2 on 0 goes to q2 itself and on 1 goes to qf.
Step 5
The final finite automata for the given regular expression is as follows −
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