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Discrete Math
Finite-State Machines with Output
eg 100011110101 this numbers of digits REQUIRED be the same as number of states? what if digits are 10 and total states 4
extract:::: // 13.2 Finite-State Machines with Output page 861 Discrete mathematics and its applications / Kenneth H. Rosen. — 7th ed.
I tried solve example 4 but getting output 001010 but is not same as solution 001000
Suppose that the input string is x = x1x2 . . . xk. Then, reading this input takes the machine
from state s0 to state s1, where s1 = f (s0, x1), then to state s2, where s2 = f (s1, x2), and so on,
with sj = f (sj−1, xj ) for j = 1, 2, . . . , k, ending at state sk = f (sk−1, xk). This sequence of
transitions produces an output string y1y2 . . . yk, where y1 = g(s0, x1) is the output corresponding
to the transition from s0 to s1, y2 = g(s1, x2) is the output corresponding to the transition
from s1 to s2, and so on. In general, yj = g(sj−1, xj ) for j = 1, 2, . . . , k. Hence, we can extend
the definition of the output function g to input strings so that g(x) = y, where y is the output
corresponding to the input string x. This notation is useful in many applications.
Finite-State Machines with Output
eg 100011110101 this numbers of digits REQUIRED be the same as number of states? what if digits are 10 and total states 4
extract:::: // 13.2 Finite-State Machines with Output page 861 Discrete mathematics and its applications / Kenneth H. Rosen. — 7th ed.
I tried solve example 4 but getting output 001010 but is not same as solution 001000
Suppose that the input string is x = x1x2 . . . xk. Then, reading this input takes the machine
from state s0 to state s1, where s1 = f (s0, x1), then to state s2, where s2 = f (s1, x2), and so on,
with sj = f (sj−1, xj ) for j = 1, 2, . . . , k, ending at state sk = f (sk−1, xk). This sequence of
transitions produces an output string y1y2 . . . yk, where y1 = g(s0, x1) is the output corresponding
to the transition from s0 to s1, y2 = g(s1, x2) is the output corresponding to the transition
from s1 to s2, and so on. In general, yj = g(sj−1, xj ) for j = 1, 2, . . . , k. Hence, we can extend
the definition of the output function g to input strings so that g(x) = y, where y is the output
corresponding to the input string x. This notation is useful in many applications.
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