- Trending Categories
- Data Structure
- Operating System
- MS Excel
- C Programming
- Social Studies
- Fashion Studies
- Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Explain the elimination of epsilon productions in CFG
All grammars are not always optimized, which means the grammar may consist of some extra symbols (non-terminals) which increase the length of grammar.
So, we have to reduce the grammar by removing the useless symbols.
The properties to reduce grammar are explained below −
- Each non-terminal and terminal of G appears in the derivation of some word in L.
- There should not be any production as X->Y where X and Y are non-terminals.
- If epsilon is not in language L then there need not be in the production X-> ε.
The diagram given below depicts the use of reduce grammar−
The productions of type S-> ε are called ε productions
These types of production can only be removed from the grammars that do not generate ε
First find all null-able non terminals which derive.
For each production A->a construct all productions A. where X is obtained from 'a' by removing 1 or more non-terminals from step 1.
Now combine the result of step 2 with the original production and remove ε production.
While removing ε production we are deleting the rule X-> ε and Y-> ε
To preserve the meaning of CFG we are placing ε at right hand side wherever X and Y appear
If the first X at the right hand side is ε
Similarly, if the last X at the right hand side is ε
If Y= ε,
If both Y and X are ε,
If both x are replaced,
Now let us consider,
If we replace ε at right hand side for X then,
The CFG with removal of epsilon production as follows,
- Related Articles
- Explain the concept of state elimination method in TOC
- Explain removing unit productions in context free grammar
- Explain NFA with epsilon transition.
- Explain how to convert CFG to CNF
- Explain if the CFG is recognized by Non-deterministic push down automata
- How to convert NFA with epsilon to without epsilon?
- Elimination Disorders
- Elimination Game in C++
- Construct a pair of languages by using CFG
- What is an epsilon closure in TOC?
- Design an unambiguous CFG in CNF that generates E?
- What is an acceptance of language by NFA with Epsilon?
- How to convert CFG to Greibach Normal Form?
- Derive the string “00101” using LMD and RMD while using CFG
- How to convert NFA with epsilon to DFA in TOC?