10.3 Finite State Machines

A machine system can accept input and possibly produce output. The complete internal condition of the machine and all of its memory, at any particular time, is said to constitute the state of the machine at any given time. A finite state machine = (S,I,F) S = state-set. The elements are called states, denoted by s (similar to a vertex). I = input set (similar to an edge). F = State Transition Function. The effect the input set has on the machine

f0(S0) = S0 function 0 of state 0 = state 0 (input is 0) Example: S = {S0, S1} I = {0,1} f0(S0) = S0 function 0 of state 0 = state 0 (input is 0) f0(S1) = S1 function 0 of state 1 = state 1 (input is 0) f1 (S0) = S1 function 1 of state 0 = state 1 (input is 1) f1 (S1) = S0 function 1 of state 1 = state 0 (input is 1) Transition table Rm Digraph Rm = Relation of a Machine 1 S0 S1 1 S0 S1 1

Given the state transition table, create the RmDigraph a and b are the inputs (edges) There are 3 states (verticies): S0 ,S1, S2 This table shows us: fa(S0) = S0 function a of state 0 = state = 0 fa(S1) = S2 function a of state 1 = state = 2 fa(S2) = S1 function a of state 2 = state = 1 fb(S0) = S1 function b of state 0 = state = 1 fb(S1) = S0 function b of state 1 = state = 0 fb(S2) = S2 function b of state 2 = state = 2 a b S0 S1 S2 b S1 a S0 S2 a a b b Starting point End point