1. Is the following language A regular or non-regular? A = {1" 0 1" |0 ≤m, n ≤ 3 and m = n + 2} 2. If your answer above is regular, please provide a Regular Expression that recognizes the language. If your answer is non-regular, please prove it by contradiction via Pumping Lemma for Regular Languages. The format and style of the proof using Pumping Lemma are supposed to follow those in the textbook.

1. Is the following language A regular or non-regular? A = {1" 0 1" |0 ≤m, n ≤ 3 and m = n + 2} 2. If your answer above is regular, please provide a Regular Expression that recognizes the language. If your answer is non-regular, please prove it by contradiction via Pumping Lemma for Regular Languages. The format and style of the proof using Pumping Lemma are supposed to follow those in the textbook.

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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Need help in theoretical computer science Given the following language over the alphabet Σ = {a, b, c, d}. • L = {a ^ r b ^ r c ^ r d ^ m | r, m∈IN} Answer the following questions. (i) Are infinitely many words in this language 1-inflatable? If so, include such words. (ii) Are infinitely many words in this language not 1-inflatable? If so, include such words. (iii) Can one use the pumping lemma for context-free languages to show that the language L is not a context-free language? If so, briefly outline how one can then argue. Subtask (b) Now let the following language be given over the alphabet Σ = {a, b, c, d} • L = {a^r b^ r c^r d ^ m | r, m∈IN} ∪ {a^i b ^ j c^k | i, j, k∈IN} (i) Are infinitely many words in this language 1-inflatable? If so, include such words. (ii) Are infinitely many words in this language not 1-inflatable? If so, include such words. (iii) Can one use the pumping lemma for context-free languages to show that the language L is not a context-free…
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