Can you please help me go through these problems? 1. Draw a deterministic finite automaton (DFA) for each of the following sets. Remember to always indicate the start and accept states. Try to avoidintroducing redundant states. Use state labels where they would be helpful to indicate the meaning of a state.a. The set of strings in {a, b}* containing a substring of four consecutive b's, eg, strings bbbb, abbabbbb, abbbbab, etc, should be accepted.b. The set of strings in {a}* whose length is evenly divisible by either 3 or 5, eg, aaa, aaaaa, aaaaaa, etc, should be accepted.c. The set of strings in {0, 1}* containing an odd number of Os and an even number of 1s, eg, strings 0, 011, 01010, etc, should be accepted.d. The set of strings in {a, b}* containing at least 2 occurrences of 3 consecutive a's, overlapping permitted, eg, string aaaa should be accepted, as wellas longer strings such as baaababaaab.e. The set of strings in {0, 1, 2}* that are ternary (base 3) representations, leading zeros permitted, of numbers that are not multiples of four (considerthe null string a representation of zero). For example, accepted strings would include 1, 2, 10, 12 (not multiples of four in ternary), whereas rejectedstrings would include 0, 11, 22, 121, etc, (multiples of four in ternary).2. Consider the following two deterministic finite automata with states {1, 2} and input alphabet {a, b}.a ba b--> 1 12 22F 11 1--> 1 11 22F 12 1Use the product construction to give deterministic automata accepting (a) the intersection, and (b) the union of the two sets accepted by theseautomata. Submit drawings of both.3. a. Depict with a drawing the DFA with states Q = {0, 1, 2, 3, 4}, input alphabet {0, 1}, start state 0, final state 0, and transition function8(q, i) (q²i) mod 5, q € Q, i = {0, 1}.=b. What set of bit strings does this DFA accept?

In this question we have to design a Deterministic Finite Automata for each of the following sets.…

1. Draw a deterministic finite automaton (DFA) for each of the following sets. Remember to always indicate the start and accept states. Try to avoid introducing redundant states. Use state labels where they would be helpful to indicate the meaning of a state. a. The set of strings in {a, b}* containing a substring of four consecutive b's, eg, strings bbbb, abbabbbb, abbbbab, etc, should be accepted. b. The set of strings in {a}* whose length is evenly divisible by either 3 or 5, eg, aaa, aaaaa, aaaaaa, etc, should be accepted. c. The set of strings in {0, 1}* containing an odd number of Os and an even number of 1s, eg, strings 0, 011, 01010, etc, should be accepted.

1. Draw a deterministic finite automaton (DFA) for each of the following sets. Remember to always indicate the start and accept states. Try to avoid introducing redundant states. Use state labels where they would be helpful to indicate the meaning of a state. a. The set of strings in {a, b}* containing a substring of four consecutive b's, eg, strings bbbb, abbabbbb, abbbbab, etc, should be accepted. b. The set of strings in {a}* whose length is evenly divisible by either 3 or 5, eg, aaa, aaaaa, aaaaaa, etc, should be accepted. c. The set of strings in {0, 1}* containing an odd number of Os and an even number of 1s, eg, strings 0, 011, 01010, etc, should be accepted.

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

Use of XOR function

XOR function or exclusive OR function was introduced in Excel 2013. This function is available under excel logical functions. For the given statement, the XOR function will return true only when either of the statements is true. It returns false when both the statements are true or when both the statements are false.

Question

Can you please help me go through these problems?

1. Draw a deterministic finite automaton (DFA) for each of the following sets. Remember to always indicate the start and accept states. Try to avoid
introducing redundant states. Use state labels where they would be helpful to indicate the meaning of a state.
a. The set of strings in {a, b}* containing a substring of four consecutive b's, eg, strings bbbb, abbabbbb, abbbbab, etc, should be accepted.
b. The set of strings in {a}* whose length is evenly divisible by either 3 or 5, eg, aaa, aaaaa, aaaaaa, etc, should be accepted.
c. The set of strings in {0, 1}* containing an odd number of Os and an even number of 1s, eg, strings 0, 011, 01010, etc, should be accepted.
d. The set of strings in {a, b}* containing at least 2 occurrences of 3 consecutive a's, overlapping permitted, eg, string aaaa should be accepted, as well
as longer strings such as baaababaaab.
e. The set of strings in {0, 1, 2}* that are ternary (base 3) representations, leading zeros permitted, of numbers that are not multiples of four (consider
the null string a representation of zero). For example, accepted strings would include 1, 2, 10, 12 (not multiples of four in ternary), whereas rejected
strings would include 0, 11, 22, 121, etc, (multiples of four in ternary).
2. Consider the following two deterministic finite automata with states {1, 2} and input alphabet {a, b}.
a b
a b
--> 1 12 2
2F 11 1
--> 1 11 2
2F 12 1
Use the product construction to give deterministic automata accepting (a) the intersection, and (b) the union of the two sets accepted by these
automata. Submit drawings of both.
3. a. Depict with a drawing the DFA with states Q = {0, 1, 2, 3, 4}, input alphabet {0, 1}, start state 0, final state 0, and transition function
8(q, i) (q²i) mod 5, q € Q, i = {0, 1}.
=
b. What set of bit strings does this DFA accept?

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