Problem 1. the regular expression a* bc* d. Consider the language of strings over the alphabet {a,b,c,d}, described a. Use the Thompson's construction method to derive a non-deterministic finite automat (NFA) recognizing the language. b. Use the powerset construction method to derive an equivalent deterministic finite autom ton (DFA). Use the partitioning method to derive an equivalent, minimal DFA. C.

Problem 1. the regular expression a* bc* d. Consider the language of strings over the alphabet {a,b,c,d}, described a. Use the Thompson's construction method to derive a non-deterministic finite automat (NFA) recognizing the language. b. Use the powerset construction method to derive an equivalent deterministic finite autom ton (DFA). Use the partitioning method to derive an equivalent, minimal DFA. C.

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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Question 2 1. Let L by a language over E. For each of the following statements about L, determine whether or not the statement is stronger, weaker or equivalent to L being regular i.e. does the state- ment (i) imply that L is regular, (ii) follow from L being regular, or (iii) both? You should justify your answer. (a) Lis finite. (b) E*\L is regular. (c) L* is regular. (d) L contains a regular language i.e. there exists a regular language Li C E* such that L C L. (e) Lis contained in a regular language i.e. there exists a regular language L2 C £* such that L C L2. 2. Suppose that Land M are two languages over the same alphabet E. Show that the following statements hold: (a) LC L* (b) If LC M* then L* C M* (c) (L*)* = L* (d) If L CM then L* C M*
1. Is the following language A regular or non-regular? A = {1" 0m 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.
2. [Based on Problem 2.26, page 157 in Sipser's 3rd Edition] Suppose G is a context-free grammar in Chomsky normal form. This exercise will help you prove that for any string w e L(G) of length n 2 1, exactly 2n - 1 steps are required for any derivation of w. To make the proof simple, we define: a variable rule is any rule of the form A BC, where A, B,C are variables, • a terminal rule is any rule of the form A → a, where A is a variable and a is a terminal. Now consider a derivation in G that starts with the start variable and applies apply variable rules s times (may not be consecutive) and applies terminal rules t times, and let r be the string generated by the derivation (z can contain both variables and terminals). (a) Prove that the string r contains t terminals. (b) Prove that the string r contains (1+s – t) variables. (c) Prove that if r E L(G) and |2| = n, then s +t = 2n – 1. %3D
Problem 1: Considering the alphabet E {a,b} derive a Non-Deterministic-Finite Automaton (NFA) using the Thompson construction that is able to recognize the sentences generated by the regular expression b*(ab|ba)b*. Does the sentence w = "abbb" belong to the language generated by this regular expression? Justify.