Assume that we want to use the Pumping Lemma to prove the language L is not a regular language. Here are the steps we follow: 1. We assume that L is a regular laguage with a pumping length value of P. 2. We define a string in the language L, called S such that |S| 3. We consider all different cases that string S can be divided into three segments: S=x.y.z for all these cases, the following conditions can not be satisfied at the same time: |y|>0; │x.y| ; x.yi.ze for all i=0,1,2,3,... therefore L cannot be a regular language.

Assume that we want to use the Pumping Lemma to prove the language L is not a regular language. Here are the steps we follow: 1. We assume that L is a regular laguage with a pumping length value of P. 2. We define a string in the language L, called S such that |S| 3. We consider all different cases that string S can be divided into three segments: S=x.y.z for all these cases, the following conditions can not be satisfied at the same time: |y|>0; │x.y| ; x.yi.ze for all i=0,1,2,3,... therefore L cannot be a regular language.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Let E = {0,1} and La be the language of all strings that represent binary numbers that are not divisible by 4. L, be the language of all strings that end with 0. d) We know that La and L, are both regular. But what about their complements, La and L,? Justify your answer. e) Show that (L. n L,), the intersection between La and Lp, is also a regular language.
Let Σ be the alphabet {a,b}. Let L be the language describe by Σ∗ − (ε|Σ∗b)aa(ε|bΣ∗), where the hyphen denotes set difference and ε de- notes the empty string. (Hint: L consists of the strings over Σ in which no maximal substring consisting solely of a’s is of length 2.) Draw a finite automa- ton that accepts L.
Suppose L is a subset of {a, b}*. If xo, x1,... is a sequence of distinct strings in {a, b}* such that for every n20, xn and xn+1 are L-distinguishable, does it follow that the strings xo, X1,... are pairwise L- distinguishable?
e3q4 Pumping Lemma for Regular Languages Here are three incorrect statements of the Pumping Lemma for regular languages. In each case, explain why the statement is not correct. Try to identify the most serious problem. (a) Suppose L is a regular language over the alphabet Σ. Then the following property must be true. For every string w € L, there exists a constant n such that |w| ≥n, and it is possible to write w as w = xyz such that i. y ‡ λ ii. |xy| ≤ n and iii. for every integer k ≥ 0, the string xyz is also in L. (b) Suppose L is a regular language over the alphabet Σ. Then there exists a constant n and a string w € L such that |w| ≥n, and it is possible to write w as w = xyz such that i. y X
(V, E) be a connected, undirected graph. Let A = V, B = V, and f(u) = neighbours of u. Select all that are true. Let G = a) f: AB is not a function Ob) f: A B is a function but we cannot always apply the Pigeonhole Principle with this A, B Odf: A B is a function but we cannot always apply the extended Pigeonhole Principle with this A, B d) none of the above
Design a deterministic finite state automaton (DFA) that accepts exactly the strings over the alphabet {A, B, ...,Z} that contain at least two R, at most one T, and where every E comes after some S (there may be other letters in between). For instance, your DFA should accept the strings: • MYSTICWARRIORS • MARSMATRIX • SHOCKTROOPERS • CONTRAHARDCORPS STRIDER but not the strings • CRAZYTAXI (it does not contain at least two Rs) LASTRESORT (it contains more than one T) AFTERBURNER (there are Es without a S somewhere before them) • BATTLECIRCUIT (all of these at the same time) Clearly indicate the meaning of each state. One way to do this is to number the states and have a numbered list of their meanings, but any readable method you use to label and explain your states is fine. Hint: there are three separate conditions accepted strings must meet; states will need to encode whether or not each one is met (or perhaps partially met). You can label an edge with the word “else" to indicate it…
1. Show that the language of even strings over (0,1} that begin and end with 0 is regular. Give both the regular expression and finite automaton.
Let L be a strict subset of LACC (i.e. L c LACC). Then L is ( always / sometimes / never ) decidable.
Let LPrime = {I the number of strings accepted by M is prime}. Classify this language as either (i) decidable, (ii) recognizable but not decidable, or (iii) not recognizable. Prove your answer. You may give a high-level description of any TM programs used in your proof. ( You should not use Rice's theorem.)
LetΣ={a,b}. Let L be the set of all strings over Σ that end in the substring bbbb. Give three strings in Σ∗ that are pairwise distinguishable with respect to L. Show that they are pairwise distinguishable by providing appro- priate distinguishing strings.
Let L be a language over the alphabet Σ = {a, b, c}. Prove that L = {aªbman for any positive integers n ‡m} is not regular. Proof: Assume that L is regular, so that the pumping lemma applies. Therefore L has a pumping length p. Let Since s belongs to L and S = This string is a member of L because has length longer than p, there exist strings x, y, and z such that s = xyz, where xz is a member of L, xyz is a member of L for all positive integers i, − [y] >0, and − |xy| ≤ p. Now consider the following argument: (You finish the rest of the proof.)
Let A={+,x,a,b}. Show that (a*V ba)+ b is regular over A.