ETHZ/Intro Tim

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('''.:: System Explanation ::.''')
('''.:: System Explanation ::.''')
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=='''.:: System Explanation ::.'''==
=='''.:: System Explanation ::.'''==
[[Image:FSM.png|thumb|450px|Figure 1: Graph representing the finite state machine.]]
[[Image:FSM.png|thumb|450px|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 described by a 6-tuple, (''Q'', ''q''<sub>0</sub>, Σ, Λ, ''δ'', ''Ω''), with:
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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'' - a set of states, for the proposed system we use five 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
* ''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
* Σ = {AL, A, BL, B} - an input alphabet

Revision as of 09:20, 18 October 2007

.:: System Explanation ::.

Figure 1: Graph representing the finite state machine.

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 five 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.