ETHZ/Intro Tim

=='''.:: 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'', ''q''<sub>0</sub>, Σ, Λ, ''δ'', ''Ω''), with:
* ''Q'' - a set of states, for the proposed system we use three different states (''q''<sub>0</sub> - not yet trained, ''q''<sub>1</sub> - trained to recognize chemical A,  ''q''<sub>2</sub> - trained to recognize chemical B)
* ''q''<sub>0</sub> - 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, the transition function ''δ'' and the output function ''Ω'' look as follows:
{| class="wikitable" border="1" cellspacing="0" cellpadding="2" style="text-align:left; margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
|-
! inputs/states !! ''q''<sub>0</sub> !! ''q''<sub>1</sub> !! ''q''<sub>2</sub> !!
! inputs/states !! ''q''<sub>0</sub> !! ''q''<sub>1</sub> !! ''q''<sub>2</sub>
|-
! AL            || ''q''<sub>1</sub> || ''q''<sub>1</sub> || ''q''<sub>1</sub> ||
! AL            || nothing           ||  || 
|-
! A             || ''q''<sub>0</sub> || ''q''<sub>1</sub> || ''q''<sub>2</sub> ||
! A             ||  || red               || cyan 
|-
! BL            || ''q''<sub>2</sub> || ''q''<sub>2</sub> || ''q''<sub>2</sub> ||
! BL            || nothing           ||  || 
|-
! B             || ''q''<sub>0</sub> || ''q''<sub>1</sub> || ''q''<sub>2</sub> ||
! B             ||  || green         || yellow
|-
|}


The resulting automaton is represented by Fig. 1.