Parse tree /Derivation tree:

The process of generating string from given grammar is called as derivation . The derivation in a CFG can be represented using tree, such tree representing derivations are called derivation /parse trees. While deriving a string w from S ,if every derivation is considered to be step in the tree construction, then we get a graphical display of derivation of a string w as a tree ,called as derivation The purpose of CFG is used to generate the string.

The CFG that are not linear, a derivation may involve sentential form with more than one variables/ non-terminals. In such cases, we have a choice in the order in which variables are replaced. So there are following two order of derivation –
1. Left most derivation (LMD)
2. Right most derivation (RMD)
1. Left most derivation (LMD): A derivation is said to be left most, if in each step the left most variable in the sentential form is replaced is called as left most derivation(LMD).
2. Right most derivation (RMD): A derivation is said to be right most, if in each step the right most variable in the sentential form is replaced is called as right most derivation(RMD).

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