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Academic year: 2022

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(1)

Exerie 1: Donnerinq exemples demots dansles langages dénisparles grammaires

suivantes, ainsi que des dérivations le prouvant, et les arbres syntaxiques (dans haque as, le

symboledestartest

X

):

(1) X → aXc | bXc | ε (2) X → aXa | bXb | ε (3)

( X → aXb | aY | ε Y → aY | ε

Danshaqueas,dérireaussilelangageaepté,souslaforme

L =

w ∈ {a, b} ∗ | w

satisfait lapropriété

P

Exerie 2: Donnerdesgrammairesdontlessolutionssontleslangagessuivants:

L 1 =

a n b 2n | n ∈ N L 2 =

w1 n | w ∈ {a, b} ∗ , n ∈ N , n = # a (w) L 3 =

a n b m | n ≤ m ≤ 2n, n ∈ N

Exerie 3: Indiquerpourhaun desmots

abbaaa

,

aabbbab

,

aabaaaaa

s'il appartientau

langagedesgrammairesuivantes :

(1)

 

 

S → aBA | bBS A → SB | BA B → aSS | ε

(2)

 

 

 

 

S → aSbAB | aAb | CCA | ε A → bSSA | ASa | B | ε B → BBS | AS | aAS | ACbb C → aSCa | CbC | aC

Attentionauxnonterminauxinutiles!(inaessiblesounon-génératifs)

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