(a) Construct a finite state automaton which recognizes strings over {0, 1} that begins with101 and ends with 0110.(b) Determine the output for a finite state machine, which is represented by the state tablebelow if the input is 00110001010. Show the transitioning states and output at each input.StateSoS₁S₂0SofS₁1S₁S₂ S₁So0110g1011

To construct a finite state automaton we first need to define states and transitions.State q0: Initial state before any input is read.State q1: Represents the beginning of the string "101."State q2: Represents any subsequent characters after "101."State q3: Represents the last character of the required ending "0110."State q4: Final accepting state.State q0 (Initial State):Transition on reading '1' to state q1.Stay in q0 on reading '0.'State q1:Transition on reading '0' to state q2.Stay in q1 on reading '1.'Stay in q1 on reading '0.'State q2:Transition on reading '1' to state q1.Transition on reading '0' to state q2.Transition on reading '1' to state q2.Transition on reading '0' to state q3.State q3:Transition on reading '0' to state q4.Stay in q3 on reading '1.'State q4 (Final Accepting State):No transitions out of this state.Diagram:

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(a) Construct a finite state automaton which recognizes strings over {0, 1} that begins with 101 and ends with 0110.

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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Recurrence relation

A recurrence relation or recursive relation is an equation that represents a function in terms of the values of its smaller inputs. Every recurrence relation T(n) is a recursive function of integer n and consists of a base case and a recursive case.

Question

(a) Construct a finite state automaton which recognizes strings over {0, 1} that begins with
101 and ends with 0110.
(b) Determine the output for a finite state machine, which is represented by the state table
below if the input is 00110001010. Show the transitioning states and output at each input.
State
So
S₁
S₂
0
So
f
S₁
1
S₁
S₂ S₁
So
0
1
1
0
g
1
0
1
1

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