From 2007.igem.org

.:: 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.