Samenvatting Hoofdstuk 4: Eigenschappen van Reguliere Talen
13 views 0 purchase
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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lennyS. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $3.77. You're not tied to anything after your purchase.
