ETHZ/Intro Tim

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('''.:: Finite State Machine view on the System ::.''')
('''.:: Finite State Machine View on the System ::.''')
 
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=='''.:: Finite State Machine View on the System ::.'''==
 
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[[Image:FSM.png|thumb|350px|Figure 1: Graph representing the finite state machine.]]
 
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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'', ''q''<sub>0</sub>, Σ, Λ, ''δ'', ''Ω''), with:
 
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* ''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)
 
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* ''q''<sub>0</sub> - a start state, here we assume we start in a state where the system is not yet trained
 
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* Σ = {A+L, A, B+L, B} - an input alphabet
 
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* Λ = {''green'', ''red'', ''blue'', ''yellow''} - an output alphabet
 
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* ''δ'' : ''Q'' × Σ → ''Q'' - a state transition function
 
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* ''Ω'' : ''Q'' × Σ → Λ - an output function
 
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In detail, the transition function ''δ'' and the output function ''Ω'' look as follows:
 
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{| 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;"
 
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|-
 
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! inputs/states !! ''q''<sub>0</sub> !! ''q''<sub>1</sub> !! ''q''<sub>2</sub> !!
 
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! inputs/states !! ''q''<sub>0</sub> !! ''q''<sub>1</sub> !! ''q''<sub>2</sub>
 
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|-
 
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! A+L          || ''q''<sub>1</sub> || ''q''<sub>1</sub> || ''q''<sub>1</sub> ||
 
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! A+L          || ''green''        || ''green''        || ''blue''
 
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|-
 
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! A            || ''q''<sub>0</sub> || ''q''<sub>0</sub> || ''q''<sub>0</sub> ||
 
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! A            || ''green''        || ''green''        || ''green''
 
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|-
 
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! B+L          || ''q''<sub>2</sub> || ''q''<sub>2</sub> || ''q''<sub>2</sub> ||
 
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! B+L          || ''yellow''        || ''red''          || ''yellow'' 
 
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|-
 
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! B            || ''q''<sub>0</sub> || ''q''<sub>0</sub> || ''q''<sub>0</sub> ||
 
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! B            || ''yellow''        || ''yellow''        || ''yellow''
 
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|-
 
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|}
 
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The resulting automaton is shown in Fig. 1. <br />
 
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In its native state (''q''<sub>0</sub>), the system reacts on the presence of either chemical A or B by fluorescing ''green'' or ''yellow'', respectively. The system itself remains in state ''q''<sub>0</sub>. Only when the input chemical is combined with a learning signal (chemical L), it changes its state either to ''q''<sub>1</sub> (in presence of chemical A) or ''q''<sub>2</sub> (in presence of chemical B). In these two states, the system is able to distinguish between changing input: while the system is in state ''q''<sub>1</sub>, the system starts fluorescing ''red'' if confronted with chemical B and vice versa when the system is in state ''q''<sub>2</sub> and confronted with chemical A (it fluoresces ''blue''). In order to maintain the states ''q''<sub>1</sub> and ''q''<sub>2</sub>, the learning signal L has to be present all the time.
 

Latest revision as of 12:04, 18 October 2007