From 2007.igem.org

Finite State Machine View on the System

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	cyan	cyan	green
A	q0	q0	q0		A	cyan	cyan	cyan
B+L	q2	q2	q2		B+L	yellow	red	yellow
B	q0	q0	q0		B	yellow	yellow	yellow

The resulting automaton is shown in Fig. 1.
In its native state (q₀), the system reacts on the presence of either chemical A or B by fluorescing cyan or yellow, respectively. The system itself remains in state q₀. Only when the input chemical is combined with a learning signal (chemical L), it changes its state either to q₁ (in presence of chemical A) or q₂ (in presence of chemical B). In these two states, the system is able to distinguish between changing input: while the system is in state q₁, the system starts fluorescing red if confronted with chemical B and vice versa when the system is in state q₂ and confronted with chemical A (it fluoresces green). In order to maintain the states q₁ and q₂, the learning signal L has to be present all the time.