CS206 -Discrete Mathematics II Instructor: Chitoor V.Srinivasan, TA: Xiao Ke. PROBLEM SET 11 SOLUTIONS
We'll draw state table for the finite-state automata.
(a).
The state table of the finite state automaton is
following
where is the start state, and it's a NDFM.
(b).
The state table of the finite state automaton is
following
where is the start state.
(c).
The state table of the finite state automaton is
following
where is the start state.
(a).
For the first machine, the output is 1 .
For the second machine, the output is 0000 .
For the third machine, the output is 0000 .
(b).
For first machine, the output is 001 .
For the second machine, the output is 1000001 .
For the third machine, the output is 11011011 .
(c).
For the first machine, the output is 1 .
For the second machine, the output is 00000000000 .
For the third machine, the output is 00010101010 .
Assume the alphabet for this finite state machine is
. And the states is
, while is the
start state, expresses the state of
having
balance 5i cents, and the is the
final state.
We will draw the state tables for it.
Label the states with the ordered pairs (i,j), i=0,1, j=0,1,2, where i
is the number of zeros mod 2 and j is the number of ones mod 3. (0,0) is the
start state, and (0,0), (1,0), (1,1), and (1,2) are the final states. The
state table is as follows.
Lets draw the state table for FSM.
where is the start state, and
is the final state.
The language for the first machine is
.
The language for the second machine is
.
The language for the third machine is
.