Let L be a language over the alphabet Σ = {a,b,c}. Prove that L = {abman 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, - ly >0, and - |xy| ≤p. Now consider the following argument: (You finish the rest of the proof.)

Let L be a language over the alphabet Σ = {a,b,c}. Prove that L = {abman 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, - ly >0, and - |xy| ≤p. Now consider the following argument: (You finish the rest of the proof.)

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

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?
Let Σ = {a, b, c}, let L1 be the set of all the strings over Σ which have the same number ofa’s, b’s and c’s, and let L2 the set of strings of Σ where all the a’s precede all the b’s andall the b’s precede all the c’s. What is:(a) L1 ∩ L2?(b) L1 ∪ L2?(c) L1?(d) L2?(e) L1 ⊕ L2?
Let Σ = {x,y,z} be an alphabet and let S be the set of all finite length strings over Σ. Show that S is countable.
Prove that C = {w|w has an equal number of 0s and 1s} is not regular. Considerthe string s=0p1p.
Show that the problem L (M) contains any string that contains at least 3 consecutive a’s is undecidable.
Let Σ = {x,y,z} be an alphabet and let P be the set of all finite length strings over Σ. Prove that P is countable.
Let Σ = {x,y,z} be an alphabet and let P be the set of all finite length strings over Σ. Prove that P is countable by biijection.
Let E={〈M〉| M is a TM and every string in L(M) has even length}. Argue that the property described in E is not trivial – i.e., that Rice’s theorem applies to E.
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 = {(D) | D is a DFA over the binary alphabet, which accepts at least one string that has 100 as a substring}. Prove that L is TM-decidable.
Let Σ={a, b}. Let L be the language of all strings that contain two b's in their middle third. In other words, L= {xyz |x, z ∈ Σ* and y∈ Σ*bΣ*bΣ*, where |x|=|z|>=|y| }. Show that L is not a CFL
Prove that {w | w €e {0,1}*}, the set of all finite strings of 0 and 1, is countable.