ETHZ/Intro Tim

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(→'''.:: System Explanation ::.''')
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* ''Ω'' : ''Q'' × Σ → Λ - an output function
* ''Ω'' : ''Q'' × Σ → Λ - an output function
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In detail, ''δ'' looks as follows:
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In detail, the transition function ''δ'' and the output function ''Ω'' look as follows:
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{| class="wikitable" style="text-align:center" border = "1"
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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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|+ State transition function ''δ''
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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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|-
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! AL            || ''q''<sub>1</sub> || ''q''<sub>1</sub> || ''q''<sub>1</sub>
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|-
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! A            || ''q''<sub>0</sub> || ''q''<sub>1</sub> || ''q''<sub>2</sub>
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|-
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! BL            || ''q''<sub>2</sub> || ''q''<sub>2</sub> || ''q''<sub>2</sub>
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|-
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! B            || ''q''<sub>0</sub> || ''q''<sub>1</sub> || ''q''<sub>2</sub>
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|-
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|}
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And ''Ω'' looks as follows:
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{| class="wikitable" style="text-align:center" border = "1"
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|+ Output function ''Ω''
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|-
|-
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! 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>
! inputs/states !! ''q''<sub>0</sub> !! ''q''<sub>1</sub> !! ''q''<sub>2</sub>
|-
|-
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! AL            || ''q''<sub>1</sub> || ''q''<sub>1</sub> || ''q''<sub>1</sub> ||
! AL            || nothing          ||  ||  
! AL            || nothing          ||  ||  
|-
|-
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! A            || ''q''<sub>0</sub> || ''q''<sub>1</sub> || ''q''<sub>2</sub> ||
! A            ||  || red              || cyan  
! A            ||  || red              || cyan  
|-
|-
 +
! BL            || ''q''<sub>2</sub> || ''q''<sub>2</sub> || ''q''<sub>2</sub> ||
! BL            || nothing          ||  ||  
! BL            || nothing          ||  ||  
|-
|-
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! B            || ''q''<sub>0</sub> || ''q''<sub>1</sub> || ''q''<sub>2</sub> ||
! B            ||  || green        || yellow
! B            ||  || green        || yellow
|-
|-
|}
|}
 +
The resulting automaton is represented by Fig. 1.
The resulting automaton is represented by Fig. 1.

Revision as of 12:27, 16 October 2007

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

inputs/states q0 q1 q2 inputs/states q0 q1 q2
AL q1 q1 q1 AL nothing
A q0 q1 q2 A red cyan
BL q2 q2 q2 BL nothing
B q0 q1 q2 B green yellow


The resulting automaton is represented by Fig. 1.

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