Lecture Notes in Computer Science 3472

190 Machiel van der Bijl and Fabien Peureux
Implementation I1
q1
q2
q3
q4
?button
?button
Implementation I2
q1
q2
?button
?button
?button
?button q3 ?button q3 ?button
!tea !coffee !tea !coffee !tea !soup
q4
?button
q5
?button ?button
q4
Implementation I3
q1
q2
q5
?button
q6
?button ?button ?button
Fig. 7.9. Examples of IOSM implementation of coffee machine
Implementation I4
q1
q2
q3
?button
?button
?button
The conformance is then defined as a relation, called implementation relation,
between the implementation and its relevant specification. The next definition
formally expresses this relation by means of IOSM as introduced by M. Phalippou.
Definition 7.24 (Implementation relation on IOSM).
An implementation relation on IOSM is a relation R on IOSM × IOSM .Given
an implementation I and a specification S such as I , S ∈ IOSM ,ifR(I , S) holds
then we say that I conforms to S.
The choice of an implementation relation is generally arbitrary, although
some minimal properties have to be respected according to the conformance
objectives [PBD93]. To elaborate such relations, we place ourselves in a testing
situation where all that we can do is to send interactions towards a black box
system to be tested, and to analyze the outputs returned by the black box.
Definition 7.25 (Outputs authorized by the specification).
Given σ ∈ Tr (S) andL a finite non empty set of labels, O =(σ, S) ={a ∈ L |
σ!a ∈ Tr (S)} denotes the set of all the outputs authorized by the specification
S after the trace σ.
All the definitions needed to present implementation relations on IOSM are
now described. M. Phalippou defines five implementation relations adapted to
the IOSM (these examples illustrate the variety of the arbitrary choices) [Pha93].
A first idea, to ensure that an implementation conforms to a specification,
consists in verifying that the outputs returned by the implementation never
contradict what is envisaged by the specification when something is envisaged.
The goal of applying this kind of implementation relation, is not to know what
it occurs when interactions, that are not specified by the specification, are send
to the implementation. This implementation relation is known as R1.
Definition 7.26 (Relation R1).
R1(I , S) iff(∀ σ ∈ Tr (S))(σ ∈ Tr (I ) ⇒ O(σ, I ) ⊆ O(σ, S))