ETHZ/Intro Tim

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.:: System Explanation ::.

The proposed system is best described by a Mealy machine [http://en.wikipedia.org/wiki/Mealy_machine Mealy machine], a special type of [http://en.wikipedia.org/wiki/Finite_state_machine finite state machines] (FSM). Mealy machines are described by a 6-tuple, (Q, q0, Σ, Λ, δ, Ω), with:

  • Q - a set of states, for the proposed system we use three different states (q0 - not yet trained, q1 - trained to recognize chemical A, q2 - trained to recognize chemical B)
  • q0 - a start state, here we assume we start in a state where the system is not yet trained
  • Σ = {AL, A, BL, B} - an input alphabet
  • Λ = {green, red, cyan, yellow, nothing} - an output alphabet
  • δ : Q × Σ → Q - a state transition function
  • Ω : Q × Σ → Λ - an output function

In detail, δ looks as follows:

State transition function δ
inputs/states q0 q1 q2
AL q1 q1 q1
A q0 q1 q2
BL q2 q2 q2
B q0 q1 q2

And Ω looks as follows:

Output function Ω
inputs/states q0 q1 q2
AL nothing
A red cyan
BL nothing
B green yellow

The resulting automaton is represented by Fig. 1.