Samenvatting Hoofdstuk 4: Eigenschappen van Reguliere Talen
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Course
Automaten en Berekenbaarheid
Institution
Vrije Universiteit Brussel (VUB)
Book
An Introduction to Formal Languages and Automata
Dit is de samenvatting van het vierde hoofdstuk van het vak Automaten en Berekenbaarheid. In deze samenvatting werd alle relevante informatie uit de slides alsook uit eigen notities opgenomen.
Eindresultaat: 16/20
Hoofdstuk 4: Eigenschappen van reguliere
talen
1 Eigenschappen
• Zijn alle talen regulier?
• Indien we 2 reguliere talen combineren, krijgen we dan een nieuwe reguliere taal?
• Hoe kunnen we aantonen dat een taal regulier is?
• Hoe kunnen we aantonen dat een taal niet regulier is?
1.1 Closure under simple set operations
Eigenschap:
Als 𝐿1 en 𝐿2 reguliere talen zijn, dan zijn 𝐿1 ∪ 𝐿2 , 𝐿1 ∩ 𝐿2 , 𝐿1 𝐿2 , ̅̅̅̅
𝐿1 en 𝐿∗1 ook reguliere talen.
Bewijs:
1
, Voorbeeld:
1.2 Closure under reversal
Eigenschap:
The family of regular languages is closed under reversal.
Bewijs:
1.3 Other closure properties
• Closed under arbitrary homomorphisms
o Replace each symbol in vocabulary by a certain string
• Closed under right quotient
𝐿1
o 𝐿2
= {𝑥: 𝑥𝑦 ∈ 𝐿1 𝑓𝑜𝑟 𝑠𝑜𝑚𝑒 𝑦 ∈ 𝐿2 }
2 Elementary questions about regular languages
2
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