Behavioral Equivalence

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Behavioral Equivalence

• ECE-548 Sequential Machine Theory
• Prof. K. J. Hintz
• Department of Electrical and Computer Engineering
• Lecture 7

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Behavioral Equivalence

• Black Box View of Machines

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Behavioral Equivalence

• Two machines, M1 and M2, are behaviorally
  equivalent iff
• The sets of inputs are the same, I1 I2,
• The sets of outputs are the same, O1 O2
• and, there exists a behavioral equivalence
  relation (which is not necessarily injective)
  between the states...

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Behavioral Equivalence

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Behavioral Equivalence

• To show that R is a behavioral Equivalence, it is
  necessary to show that

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Behavioral Equivalence

sj
R(s1)
a
a
s1
sk
R
R
M1
M2
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Behavioral Equivalence Example

a
M1
a
B/1
b
A/0
a
b
b
C/0
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Behavioral Equivalence Example

a
M2
a
2/1
b
1/0
b
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Behavioral Equivalence Example

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Behavioral Equivalence Example

• Since This Is a Moore Machine, It Is Only
  Necessary to Check Each State, i.e.,
• For Mealy Machine, Also Need to Check For Each
  Input.

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Equivalence of Outputs

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Verifying Morphism

• Need also to verify relation

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Behav. Equiv. of Moore/Mealy

• Constructive Approach
• Moore to Mealy (easy)

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Moore State

a
a
b
b
c
c
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Mealy State

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Mealy to Moore Conversion

• Construct a New Set of States Consisting of Each
  Present State Combined With Each of the Possible
  Outputs. Some of the States With Outputs May Not
  Be Reachable.
• A More Sophisticated Method Would Generate a New
  Set of States Consisting Only of Those
  State/Output Combinations Reached by the Head of
  an Arrow.

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Mealy to Moore Conversion

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Mealy to Moore Conversion

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Mealy State Table
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Equivalent Moore State Table