Question

1. (20 points) Given the following Grammar G,

S->ASB

A -> aAS | a | λ

B -> SbS | A|bb

(a) Identify and remove the λ-productions.

(b) Identify and remove unit-productions from the result of (a).

(c) Convert it to Chomsky Normal Form.

1. (20 points) Given the following Grammar G, S->ASB A -> AS | a 1a B -> Sbs | Albb (a) Identify and remove the -productions. (b) Identify and remove unit-productions from the result of (a). (c) Convert it to Chomsky Normal Form.

Answer 1

Sole To conveat the CFG to CNE Geren Grammare S ASB AaAsalx B SIS | Albb 3 identify and renove the null productions . The null is АНА productions in the above grammoon will ob remove, using replace A with X - we on right hand side of productions If At then: SASB becomes SSB so add this rule aswell to grammar À a AS becomes Stas Add this rule to grammar BA becomes B-A It is a null production again SASB/SB Asa Aslas la B - Sbs/bb (Alx So, again we have a null procluction Beds so eliminate it becomes If Ba ther: S - ASB becomes SAS (Add this rule) SSB (sas] (no need to add this since every raciable is itself) SASB/SB/AS A a Aslasla B - SbS /bb/A So Grammar ies:

sule 2: AaAs lasla Replace à with 'Y' Replace As with a A → Y2 lysla CNF Yta Add 2 rules 2→AS sule 3: B~ 365 / bb la As/as/a Replace 'b' with w wab CNE Add this role BAS6S sws (not (AF), so replace sw with 'v' Tres LENE B VS B - bb becomes B→WW Ja Ba AS becoms (3 - 72 Bas become BOYS So, Final CN Fisc B a SB/SB/As AY2lysla B vs lyzlysla XSB Wb wswg yag AS

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