ETHZ/Intro Tim

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.:: System Explanation ::.

Figure 1: Graph representing the finite state machine.

The proposed system is best described by a [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 defined 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 = {A+L, A, B+L, B} - an input alphabet
  • Λ = {green, red, blue, yellow} - an output alphabet
  • δ : Q × Σ → Q - a state transition function
  • Ω : Q × Σ → Λ - an output function

In detail, the transition function δ and the output function Ω look as follows:

inputs/states q0 q1 q2 inputs/states q0 q1 q2
A+L q1 q1 q1 A+L green green blue
A q0 q0 q0 A green green green
B+L q2 q2 q2 B+L yellow red yellow
B q0 q0 q0 B yellow yellow yellow

The resulting automaton is represented by Fig. 1.