====== Lecture 06 ======

{{cc11:l6-cc2011-white.pdf|lecture notes}}

[[cc10:Earley Parser]]

Continued in [[Lecture 07]]

===== Exercise 1 =====

Given the following grammar:

  S → AaB | aBb
  A → a | C
  B → FAb |  bA
  C → CDB | ϵ
  D → A | B | ab
  E → b | A
  F → aF 

  * Remove ϵ-productions, unit productions and useless non-terminals.
  * Put the resulting grammar into Chomsky Normal Form.
  * Argue if it is possible to apply the modifications in the first part in different orders.

===== Exercise 2 =====
A CYK parser is parsing the input "Int , Int => Int".
The incomplete tables for two different grammars are given below.
  * Complete the table.
  * Find the suitable grammar that actually generates the table.
  * Construct the table for "Int , Int => Int , Int".
a)
{{cc10:cyk1.png|}}


b)
{{cc10:cyk2.png|}}



===== Exercise 3 =====

Consider a context-free grammar without unit or ε-productions.
Assume that the maximum number of symbols on the right hand side of any production is $k$.
Show that there exists an equivalent grammar in Chomsky normal form with no more than $(k - 1)|P| +  |T|$ production rules.
The set $P$ is the set of production rules and $T$ is the set of terminals.