M bê thế lãnguage over {a, f} accepting all štřings so that: 1. There are precisely two e's in the string. 2. Every a is immediately followed by an even number of f's. 3. Every c is immediately followed by an odd number of b's. 4. b's and f's don't occur except as provided in rules 2 and 3. 5. All a's occur after the first e. 6. All c's occur before the second e. 7. In between the two e's there are exactly half as many a's as c's. onstruct a context-free grammar generating M. You do not need an inductive proof, I ould explain how your construction accounts for each rule. e could eliminate one rule from m to make it regular. Which one? Why?

M bê thế lãnguage over {a, f} accepting all štřings so that: 1. There are precisely two e's in the string. 2. Every a is immediately followed by an even number of f's. 3. Every c is immediately followed by an odd number of b's. 4. b's and f's don't occur except as provided in rules 2 and 3. 5. All a's occur after the first e. 6. All c's occur before the second e. 7. In between the two e's there are exactly half as many a's as c's. onstruct a context-free grammar generating M. You do not need an inductive proof, I ould explain how your construction accounts for each rule. e could eliminate one rule from m to make it regular. Which one? Why?

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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Let Cbe the language over {a, b,c, d, e, f} accepting all strings so that: 1.There are precisely two b’s in the string. 2.Every a is immediately followed by an odd number of e’s. 3.Every d is immediately followed by an even number of f’s. 4.e’s and f’s don’t occur except as provided in rules 2 and 3. 5.All a’s occur after the first b. 6.All d’s occur before the second b. 7.In between the two b’s there are exactly twice as many a’s as d’s.HINT: Don’t be intimidated by the number of rules. The way they interact actually helps you simplify the number of cases you have to deal with while constructing this grammar. a. Construct a context-free grammar generating C.Explain how your construction accounts for each rule. b. We could eliminate one rule from Cand make it regular. Which rule would that be, and why would it work? You do not need a formal proof, but you do need an explanation.
(15) Let M be the language over {a, b, c, d, e, f} accepting all strings so that: 1. There are precisely two e's in the string. 2. Every a is immediately followed by an even number of b's. 3. Every c is immediately followed by an odd number of f's. b's and f's don't occur except as provided in rules 2 and 3. 5. All c's occur after the first e. 4. 6. All a's occur before the second e. 7. In between the two e's there are exactly twice as many c's as a's. Construct a context-free grammar generating M. You do not need an inductive proof, but you should explain how your construction accounts for each rule. 5) We could eliminate one rule from M and make it regular. Which one? Why? (5) Show that the class of context free languages is not closed under intersection by finding two CFLS whose intersection is not a CFL.
1. For each of the following regular expressions find a language (i.e., a set of strings over A = {a,b.c} that can be represented/described by that expression. a. a'bc + bc* b. b'aaac а. b.
a) Give an example of a string containing 11 that is accepted by the following automaton. b) Give an example of a string of length 8 that is rejected by the following automaton. c) Describe the language of this automaton in plain English. d) Describe the language of this automaton using Regular expression.
2- Write a regular expression for each of the following languages over {a,b}: • String of a's and b's that begin with a and end with b. • Strings that have at least two a's. • Strings that have an even number of a's. • Strings that do not have two a's in a row. • Strings that do not end with the substring ab.
Finish the 2 "TODO" in the ASM Language! A palindrome is a word that is spelled the same way forwards and backwards. For example, "radar", "racecar", "civic", "kayak", and "madam" are all palindromes. The definition can be extended to phrases and sentences when ignore case and punctuation, but for this exercise we will stick to a single word. The starter code provided uses the C library functions printf and scanf to prompt for an input a word. The word that is entered from the keyboard is a null-terminated string placed in the byte array at address buf. There are also two output strings provided at addresses str_is_palindrome and str_is_not_palindrome. The starter code provided simply outputs the string at str_is_not_palindrome. The code contains two TODO comments... At the first TODO comment, the byte array at buf is filled with input from the keyboard. This input is a null-terminated character string (i.e. the array contains the characters entered on the keyboard, followed by ASCII…
C++ Consider the language that the following grammar defines: <S> = c | <W> | c<S> <W> = abb|a<W>bb Write all strings that are in this language and that contain seven or fewer characters. If the answer includes multiple strings, you must enter the answers in alphabetical order. A. In alphabetic order, what are the two strings in this language that are 3 characters in length? B. In alphabetic order, what are the two strings in this language that are 4 characters in length? C. In alphabetic order, what are the two strings in this language that are 5 characters in length?
The language composed of all strings over the alphabet {a,b} of the form: zero or more a's followed by zero or more b's, i.e., {"", a, b, aa, ab, bb, aaa, aab, abb, bbb, ...}, where "" is the empty string, is a regular language: show why this is. Note that you may use any line of argument on regular languages, e.g., by showing that it can be constructed using the properties ("Regular Language: a formal definition"), or by drawing the finite state automaton (FSA), or giving its description.
Q No. 1: Write regular expressions and construct NFA for the following languages over the alphabet E ={a, b} a. Write a regular expression that contains at least two a's b. Write a regular expression that contains at least one a and one b c. Write a regular expression that contains exactly two a's d. All strings that do not end with 'aa' e. All strings that contain even number of a's f. All strings which do not contain the substring 'ab' g. All strings that contain odd number of a's and b's
1. Write regular expression for the following languages, alphabet {0,1} a. The set of strings that do not end with 11 b. The set of strings that do not contain substring 01 c. The set of strings having 0 at every 3rd position. d. Describe the language given by the regular expression 0*10*10*1(1|0)* e. Set of all strings that are at least of length 4 and contains an even number of 1's. 2. Draw the DFA for the following languages a. L = {w]w contains substring "aba" and has b in the second last position} b. L = {w[ every 3rd symbol in w is 0} e.g. 110100, 000110001. But 101 won't be accepted since the 3rd symbol is 1. c. Set of all strings that are at least of length 4 and contain an even number of 1's d. L = {w| The 3rd last symbol in w is 0}
1. Write regular expression for the following languages, alphabet {0,1} a. The set of strings that do not end with 11 b. The set of strings that do not contain substring 01 c. The set of strings having 0 at every 3rd position. d. Describe the language given by the regular expression 0*10*10*1(1|0)* e. Set of all strings that are at least of length 4 and contains an even number of 1’s.
Q. Construct DFA’s for FollowingWhen  = {0, 1}v. Machine that accepts the language which has either odd number of 0’s or even number of 1’s but not both together .vi. Machine that accepts the language which has both 01 and 10 as substring .vii. Machine that accepts the language which has neither 00 nor 11 as a substring.