Consider languages over terminal alphabet Σ= = {a, b, c, d}. • Give context-free grammars that generate the following five languages. • In each case, also give a derivation of the specified terminal string using your gram- mar. The derivation beginning from the start variable should indicate each individual derivation step using the notation ⇒. (a) L₁ = {b²i ³k+¹ | k ≥ i ≥ 0} Derivation for the string: 6²cª. (b) L₂ = { a¹b¹c²i | i ≥ 1, k ≥ 1} U {c³kdk | k ≥ 1} Derivation for the string: a²bc¹. (c) L3 = (d) L₁ = a¹b¹c²d² (e) L5 {a²if²i+¹5k+2 | i ≥ 1, k ≥ 1} Derivation for the string: a¹b³c7. {a²f3i+10 +1c³s+1 di+1 -1 = {q³i+¹fi+3²kd²k | i ≥ 0, k ≥ 0} U {a²¹b³c5sdr+¹ | r ≥ 0, s ≥ 0} Derivation for the string: a²bc5d². | i ≥ 1, r ≥ 1, s ≥ 1} Derivation for the string:

Consider languages over terminal alphabet Σ= = {a, b, c, d}. • Give context-free grammars that generate the following five languages. • In each case, also give a derivation of the specified terminal string using your gram- mar. The derivation beginning from the start variable should indicate each individual derivation step using the notation ⇒. (a) L₁ = {b²i ³k+¹ | k ≥ i ≥ 0} Derivation for the string: 6²cª. (b) L₂ = { a¹b¹c²i | i ≥ 1, k ≥ 1} U {c³kdk | k ≥ 1} Derivation for the string: a²bc¹. (c) L3 = (d) L₁ = a¹b¹c²d² (e) L5 {a²if²i+¹5k+2 | i ≥ 1, k ≥ 1} Derivation for the string: a¹b³c7. {a²f3i+10 +1c³s+1 di+1 -1 = {q³i+¹fi+3²kd²k | i ≥ 0, k ≥ 0} U {a²¹b³c5sdr+¹ | r ≥ 0, s ≥ 0} Derivation for the string: a²bc5d². | i ≥ 1, r ≥ 1, s ≥ 1} Derivation for the string:

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

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Concept explainers

Intelligent Machines

Machines that use artificial intelligence to learn from the environment and past experiences to perform better in the presence of variability and uncertainty are called intelligent machines. Intelligence develops according to environment and experience. It is human-like behavior. When the computer system or any programmed machine learns from the inputs and corresponding outputs, it can be called an intelligent machine.

Question

Consider languages over terminal alphabet Σ = {a,b,c,d}.
• Give context-free grammars that generate the following five languages.
• In each case, also give a derivation of the specified terminal string using your gram-
mar. The derivation beginning from the start variable should indicate each individual
derivation step using the notation ⇒.
(a) L₁ = {b²i³k+¹ | k ≥ i ≥ 0} Derivation for the string: 6²c4.
(b) L₂ = { a¹bk c²i | i ≥ 1, k ≥ 1} U {c³k dk | k ≥ 1} Derivation for the string:
a²bc².
(c) L3 = {a²if²i+1c5k+2 | i ≥ 1, k ≥ 1} Derivation for the string: a¹b³c7.
(d) L₁ =
=
{a²f³i+1³s+1di+¹ | i ≥ 1, r ≥ 1, s ≥ 1} Derivation for the string:
2r
a¹b¹c²d²
(e) L5 = {a³i+¹f²+3 ¿2k d²k | i ≥ 0, k ≥ 0} U {a²¹b³c³³d²+¹ | r ≥ 0, s ≥ 0}
Derivation for the string: a²bc5d².

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Dwayne Johnson has got an assignment from his Professor of TOC. He has the alphabet set E = {a, b, (, ), U, *, Ø}. Dwayne Johnson has to make a context-free grammar which generate all string in E* which are regular expressions over the set {a, b}. If Dwayne Johnson can do this he will be promoted to the elite section but if he fails he will be demoted. You have to help Dwayne go to elite section by doing this task for him.
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