Structured Operational Semantics

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Structured Operational Semantics

• Marc Voorhoeve

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Contents

• Introduction
• Definition and Examples
• Bisimulation equivalence
• Congruence

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Introduction
SOS rules are very suitable for defining
semanticsof dynamic components Components
defined as terms. With operators, components are
placed in context.e.g. component C, context D,
together C_at_D Semantics s(C), s(D), s(C _at_D)
transition systems
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Compositionality
Semantics of combination s(C _at_D) should only
depend upon s(C) and s(D) (component and
context) So the following situation should never
occur!
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Compositionality(2)
different subnets
C C
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SOS rules format

• Syntax defines a set T of terms
• SOS rules define transition relation

• SOS rules have the form

• Premises any predicate
• Conclusion of form

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SOS rules example
Set A (actions) given T defined by SOS rules
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Conventions

• TS states terms (syntax)
• TS transitions smallest set satisfying SOS rules

Consequence d is deadlock
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Example derivation
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Term equivalence
Terms d and are equivalent (deadlock)bisimilar
TSs Other equivalences
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Congruence
We want e.g. that f(xy) f(yx) for
any operator f. This imposes restrictions on SOS
rules.
Not e.g.
But e.g.
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Petri Net Components

1. Open Petri nets are transition systems
2. State changes add/remove tokens, fire
3. SOS rules define atoms (unconnectedplaces /
   transitions) and operators

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PNC operator consume
Before
After
.
p
t
t
SOS
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Requirement language
Temporal requirement language L
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Requirement examples
Place a contains 1 token
After a firing of a, a b and c token
become available
Bisimilar iff satisfying same requirements! It is
possible to have non-bisimilar systems that both
satisfy all user requirements!
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Conclusion

• SOS rules suited for dynamic components
• Used to define atoms and operators
• Transition system semantics
• (many choices possible)
• Temporal requirements