Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Convertion of Grammar to Chomsky Normal Form and Greibach Normal Form, Assignments of Discrete Structures and Graph Theory

University of Central Florida (UCF)Discrete Structures and Graph Theory

Solutions for converting given grammars to chomsky normal form and greibach normal form. It includes step-by-step explanations and justifications for each transformation. The document also discusses the elimination of left-recursion and the importance of eliminating recursion on a given non-terminal.

Typology: Assignments

Pre 2010

Uploaded on 02/24/2010

koofers-user-8hw
koofers-user-8hw 🇺🇸

9 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
University of Central Florida
School of Computer Science
COT 4210 Spring 2004
Prof. Rene Peralta
Extra credit HW: answers to selected problems
1. Consider the following grammar over Σ = {a, b}:
•S→AB;
•A→AS +Sb +a;
•B→BS +aA +λ;
Convert the grammar to Chomsky Normal Form (please use rules U→
aand V→b). answer: Besides some simpler transformations, we
must remove unallowed λ-productions and chain rules. The general
technique I taught in class is
to remove a given production P, add redundant productions
until Pitself becomes redundant. Then remove P.
First deal with the mixed (terminals and variables) terms using U→a
and V→b:
•S→AB;
•A→AS +SV +a;
•B→BS +U A +λ;
To make B→λredundant, add S→Aand B→S:
•S→AB +A;
•A→AS +SV +a;
•B→BS +U A +S.
To make S→Aredundant, add S→AS +SV +a. Reasoning: when
the rule S→Ais used in a derivation, the variable Amust at some
point later be substituted for AS or SV or a.
1
pf3
pf4

Partial preview of the text

Download Convertion of Grammar to Chomsky Normal Form and Greibach Normal Form and more Assignments Discrete Structures and Graph Theory in PDF only on Docsity!

University of Central Florida

School of Computer Science

COT 4210 Spring 2004

Prof. Rene Peralta

Extra credit HW: answers to selected problems

  1. Consider the following grammar over Σ = {a, b}:
    • S → AB;
    • A → AS + Sb + a;
    • B → BS + aA + λ;

Convert the grammar to Chomsky Normal Form (please use rules U → a and V → b). answer: Besides some simpler transformations, we must remove unallowed λ-productions and chain rules. The general technique I taught in class is

to remove a given production P , add redundant productions until P itself becomes redundant. Then remove P.

First deal with the mixed (terminals and variables) terms using U → a and V → b:

  • S → AB;
  • A → AS + SV + a;
  • B → BS + U A + λ;

To make B → λ redundant, add S → A and B → S:

  • S → AB + A;
  • A → AS + SV + a;
  • B → BS + U A + S.

To make S → A redundant, add S → AS + SV + a. Reasoning: when the rule S → A is used in a derivation, the variable A must at some point later be substituted for AS or SV or a.

  • S → AB + AS + SV + a;
  • A → AS + SV + a;
  • B → BS + U A + S.

Now we could remove B → S in the same way we removed S → A. Instead, and to show you that there is more than one way to do this, consider the step in a derivation where a new variable B is produced. This can only happen when the production S → AB is used.^1 The only place where B → S can later play a role is in changing this B into an S. So adding the rule A → AS makes B → S redundant. But this rule is already there, so we can simply remove the rule B → S:

  • S → AB + AS + SV + a;
  • A → AS + SV + a;
  • B → BS + U A.

Eliminating recursion on S is simple. The final grammar is

  • S → AB + AT + T V + a;
  • T → AB + AT + T V + a;
  • A → AT + T V + a;
  • B → BT + U A;
  • U → a;
  • V → b.

(^1) Why can we ignore the production B → BS here?

Greibach Normal Form requires expressions on the right-hand side of productions to begin with non-terminals. Simple substitution can be used to obtain

  • S → a + aT ;
  • T → (b + bR)ST + (b + bR)S;
  • A → b + bR;
  • R → (a + aT )R + a + aT.

The text does not allow S in the right-hand side of productions in Greibach Normal Form. However, it was noted in class that there appears to be no good reason for this requirement. So the above is good enough.