then l1 and l2 must be regular
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Properties of Regular Languages Example L = {a ba n
L1/L2 = 6 Page 7 Theorem If L1 and L2 are regular then L1/L2 is regular Proof (sketch) ∃ DFA M=(QΣδq0F) s t L1 = L(M) Construct DFA M'=(QΣδq0F |
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1 Closure Properties
Regular Languages are closed under intersection i e if L1 and L2 are regular then L1 ∩ L2 is also regular Proof Observe that L1 ∩ L2 = L1 ∪ L2 |
What is a regular operation?
The regular operations are the operations union, concatenation, and.
Kleene star (or just star, for short), which are defined as follows for any choice of an. alphabet r and languages A, B ⊆ r∗ : 1.Theory of Computation
Regular languages are languages that can be generated from one-element languages by applying certain standard operations a finite number of times.
They are the languages that can be recognized by finite automata.
These simple operations include concatenation, union and kleen closure.
Is L1 L2 regular?
L1 and L2 are regular • L1 ∪ L2 is regular • Hence, L1 ∩ L2 = L1 ∪ L2 is regular.
Is there a direct proof for intersection (yielding a smaller DFA)? Cross-Product Construction Let M1 = (Q1,Σ,δ1,q1,F1) and M2 = (Q2,Σ,δ2,q2,F2) be DFAs recognizing L1 and L2, respec- tively.
What does it mean for a language to be regular?
A regular language is a language that can be expressed with a regular expression or a deterministic or non-deterministic finite automata or state machine.
A language is a set of strings which are made up of characters from a specified alphabet, or set of symbols.
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Problem Set 3 Solutions
11 août 2000 FALSE. Let L1 = ?? and let L2 be any nonregular language over ?. (3) If L1L2 is regular and L1 is finite then ... |
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CS 341 Homework 9 Languages That Are and Are Not Regular
(a) Every subset of a regular language is regular. (b) Let L? = L1 ? L2. If L? is regular and L2 is regular L1 must be regular. (c) If L is regular |
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Formal Languages Automata and Computation Identifying
If L1 ? L2 and L2 is regular then L1 must be regular. (CARNEGIE MELLON UNIVERSITY IN QATAR). SLIDES FOR 15-453 LECTURE 5. SPRING 2011. 17 / |
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Theory of Computation
If L1/L2 and L1 are context free then L2 must be recursive. 6. ..X.. ... If L1 is regular and L2 is context-free |
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1 Closure Properties
Closure under ?. 1. Page 2. Proposition 4. Regular Languages are closed under intersection i.e. |
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Practice Problems for Final Exam: Solutions CS 341: Foundations of
Then A ?P B means there is a polynomial-time computable function f : ??. 1 ? ?? Because L1 and L2 are regular L1 ? L2 must be regular by Theorem 1 ... |
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1 Closure Properties
Closure under ?. 1. Page 2. Proposition 4. Regular Languages are closed under intersection i.e. |
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CS 341 Homework 16 Languages that Are and Are Not Context-Free
1. Show that the following languages are context-free. If there exist languages L1 and L2 such that L(G) = L1 ? L2 then L1 and L2 must both be context. |
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Chapter 4: Properties of Regular Languages?
Then M = (Q |
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Quiz 1: Solutions
1. True or False: If L is a regular language and F is a finite language (i.e. a language with a finite number of words) |
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CS 341 Homework 9 Languages That Are and Are Not Regular
(a) Every subset of a regular language is regular (b) Let L′ = L1 ∩ L2 If L′ is regular and L2 is regular, L1 must be regular (c) If L is regular, then so is L′ |
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Pumping Lemma for Regular Languages - andrewcmued
If L1 ⊆ L2 and L2 is regular, then L1 must be regular (CARNEGIE MELLON UNIVERSITY IN QATAR) SLIDES FOR 15-453 LECTURE 5 SPRING 2011 17 / |
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L1 ∩ L2 - UCSB Computer Science
4 1 Closure Properties of Regular Languages Closure under Simple Set Operators Thm 4 1: If L1 and L2 are regular languages, then so are L1 ∪L2,L1 ∩ |
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1 Closure Properties
If L is regular, then there is a DFA M = (Q,Σ, δ, q0,F) such that L = L(M) • Then Regular Languages are closed under intersection, i e , if L1 and L2 are regular The second state of the last symbol must be in F Holds trivially because L3 only |
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A Proof that if L = L 1 ∩ L2 where L1 is CFL and L2 is Regular then
It is well known that the intersection of a context free language and a regular language is context free This theorem is used in several proofs that certain |
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Solutions - Harry R Lewis - Harvard University
(A) If L1 is regular and L2 ⊆ L1, then L2 is regular We proved in class that L2 is non-regular, and and union, then it must be the case that L is not regular |
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(if any), provide a counter exa
i e L1 ∩ L2 = ∅ Suppose L = L1 ∪ L2 and L is regular (since regular languages 900 states, since no loop is possible other than the sink state 1 You do not have to provide this part, since its proof is essentially like that of (d), with 0 and 1 |
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Finite Automata
all possible transitions on a for each state in S, then taking the set of You do not have to be a declared If L1 and L2 are regular languages, is L1 ∪ L2? start |
