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How to convert left linear grammar to right linear grammar?
Regular grammar describes a regular language. It consists of four components, which are as follows −
G = (N, E, P, S)
Where,
N: finite set of non-terminal symbols,
E: a finite set of terminal symbols,
P: a set of production rules, each of one is in the forms
S → aB
S → a
S → ∈,
S ∈ N is the start symbol.
The above grammar can be of two forms −
Right Linear Regular Grammar
Left Linear Regular Grammar
Now, let us see the steps to convert left linear grammar to right linear grammar −
Example 1
Consider a left linear grammar as given below −
S→ Sa|Abc A→ Sa|Ab|a
Step 1 − We will convert the given left linear grammar to finite automata.
Step 2 − We will now interchange the initial and final state.
Step 3 − Now we will reverse the direction of all transactions.
Step 4 − We will construct the regular grammar for the above finite automata which will be right linear grammar, as shown below −
C→aA A→bA|cb S→aS
Example 2
Consider another example
The given left linear grammar is −
S→S10|S11|B|e B→B0|0
First eliminate non-deterministic of grammar
S→SA|B|e A→10|11 B→B0|0
So, the right linear grammar is −
S→BS’|S’ S’→e|10S’|11S’ B→0B’ B’→0B’|e
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