Lecture 7 - Finite Automata and Regular Expressions Flashcards
Closure theorems, Main Theorem, Generalized Automaton
What is the main theorem?
A language L is regular:
- iff. it is accepted by a finite automaton
- (i.e.) iff. there is a finite automaton M, such that L = L(M)
What is the closure theorem? Are the class of regular languages also closed under this?
The class of languages accepted by a finite automata is closed under:
1. Union
2. Concatenation
3. Kleene’s Star
4. Complementation
5. Intersection
Yes, class of regular languages are closed under these operations.
*The class of languages accepted by ______ ________ ________ is the same as the class of _______ _________
finite automata DFA/NDFA; regular languages
*A language is regular iff. ____ ________ __ _ ______ _________
it’s accepted by a finite automaton
Languages are sets so we have the operations:
(Sets) Union, Intersection, Complementation
(Language specific operations) Concatenation, and Kleene’s Star
What is a schema diagram?
Diagram of M with no names on states
In the concatenation operation, why can’t the transaction
(q, e, s2) be skipped?
Skipping these transactions b/w M1 & M2 leads to automata accepting different languages
Theorem 1 of Main Theorem?
For any regular language L, there is a finite automata M such that L = L(M)
Theorem 2 of Main Theorem?
For any finite automata M, the language L(M) is regular; there is a regular expression
r ∈ R,
such that L(M) = r
What is the Generalized Automaton used for?
To construct a regular expression r ∈ R that defines L(M), such that L(M) = r; Construction of a sequence of GM that are all equivalent to M
How does the GM work? What is the final outcome?
- States of M are eliminated one by one
- GM is reduced to single transition between the 2 states initial and final
What is a regular language?
Those that can be described by regular expressions
