1.0 TABLE 2 Start- Input Input 0,0 State 0.0 FIGURE 2 The state diagram for the finite-state machine shown in Table 2. Another way to represent a finite-state machine is to use a state diagram, which is a directed graph with labeled edges. In this diagram, each state is represented by a circle. Arrows labeled with the input and output pair are shown for each transition. EXAMPLE 2 Construct the state diagram for the finite-state machine with the state table shown in Table 2. Solution: The state diagram for this machine is shown in Figure 2. EXAMPLE 3 Construct the state table for the finite-state machine with the state diagram shown in Figure 3. Solution: The state table for this machine is shown in Table 3. An input string takes the starting state through a sequence of states, as determined by the transition function. As we read the input string symbol by symbol (from left to right), each input symbol takes the machine from one state to another. Because each transition produces an output, an input string also produces an output string. Suppose that the input string is x= x,x2 .. Then, reading this input takes the machine from state s, to state s, where s, = f(Sp, X), then to state s, where s, = f(s, x,), and so on, with 5, = f(s-1 x,) for j = 1, 2, ...k, ending at state s, =f(s- x). This sequence of transitions produces an output string y,y2 ... Ya, where y, = g(sp x) is the output corresponding to the transition from s, to S. y2 = g(5. x2) is the output corresponding to the transition from s, to s. and so on. In general, y, g(s-.X) for j = 1,2.k. Hence, we can extend the definition of TABLE 3 Input Input State 0,0 0.0 Start 1.0 1,0 0,0 1.0
1.0 TABLE 2 Start- Input Input 0,0 State 0.0 FIGURE 2 The state diagram for the finite-state machine shown in Table 2. Another way to represent a finite-state machine is to use a state diagram, which is a directed graph with labeled edges. In this diagram, each state is represented by a circle. Arrows labeled with the input and output pair are shown for each transition. EXAMPLE 2 Construct the state diagram for the finite-state machine with the state table shown in Table 2. Solution: The state diagram for this machine is shown in Figure 2. EXAMPLE 3 Construct the state table for the finite-state machine with the state diagram shown in Figure 3. Solution: The state table for this machine is shown in Table 3. An input string takes the starting state through a sequence of states, as determined by the transition function. As we read the input string symbol by symbol (from left to right), each input symbol takes the machine from one state to another. Because each transition produces an output, an input string also produces an output string. Suppose that the input string is x= x,x2 .. Then, reading this input takes the machine from state s, to state s, where s, = f(Sp, X), then to state s, where s, = f(s, x,), and so on, with 5, = f(s-1 x,) for j = 1, 2, ...k, ending at state s, =f(s- x). This sequence of transitions produces an output string y,y2 ... Ya, where y, = g(sp x) is the output corresponding to the transition from s, to S. y2 = g(5. x2) is the output corresponding to the transition from s, to s. and so on. In general, y, g(s-.X) for j = 1,2.k. Hence, we can extend the definition of TABLE 3 Input Input State 0,0 0.0 Start 1.0 1,0 0,0 1.0
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
Transcribed Image Text:1.0
TABLE 2
1.0
Start-
0,0
Input
Input
State
1
0.0
1.1
FIGURE 2 The state diagram for the
finite-state machine shown in Table 2.
Another way to represent a finite-state machine is to use a state diagram, which is a directed
graph with labeled edges. In this diagram, each state is represented by a circle. Arrows labeled
with the input and output pair are shown for each transition.
EXAMPLE 2 Construct the state diagram for the finite-state machine with the state table shown in Table 2.
Solution: The state diagram for this machine is shown in Figure 2.
EXAMPLE 3 Construct the state table for the finite-state machine with the state diagram shown in Figure 3.
Solution: The state table for this machine is shown in Table 3.
An input string takes the starting state through a sequence of states, as determined by the
transition function. As we read the input string symbol by symbol (from left to right), each input
symbol takes the machine from one state to another. Because each transition produces an output,
an input string also produces an output string.
Suppose that the input string is x = x,x .I. Then, reading this input takes the machine
from state s, to state s,, where s, = f(Sp, X), then to state s, where s, = f(s, x2), and so on, with
s, = f(s-1 x) for j= 1, 2, ..k, ending at state s, = f(s-1. *). This sequence of transitions
produces an output string y,y2 ... ya, where y; = g(sp. X) is the output corresponding to the
transition from s, to s1. y = g(s, X2) is the output corresponding to the transition from s, to s2.
and so on. In general, y, = g(s-1.x,) for j= 1, 2 ..k. Hence, we can extend the definition of
TABLE 3
1, 1
Input
Input
State
1
0,0
0.0
Start
1.0
1,0
1,0
0,0
1.0
- - - 00
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