Refusal Graph Construction From a Labelled Transitions System

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Refusal Graph Construction From a Labelled
Transitions System
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Introduction

• Context Robustness test, systems modelling.
• Objective Implementation of a calculating model
  of the refusal sets. Transformation of a Labelled
  Transition System (LTS) to a Refusal Graph (RG).
  
• Tools Delphi software using Pascal as
  programming language.

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Labelled Transition System(LTS)

• A basic structure used to represent a
  communicating system.
• Represented by a quadruple S(S,S,?,s0) where
• S is a finite set of states
• S is a finite set of visible actions
• ? is set of transitions
• out(s) returns the output ( a set of actions ) of
  a state s.

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a
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Refusal Graph (RG)

• A bilabelled graph-structure allowing abstract
  representation of communicating system.
• Represented by 5-tuple (G,S,?,Ref,g0) where
• Ref defines the sets of events that may be
  refused after the sequence leading to one state.
• closing(s) returns a sets of states obtained by
  removing all intern and empty events.

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Difference Between LTS and RG(1)

• Determinism Existence of an isomorphism between
  a state and a transition.

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Difference Between LTS and RG(2)

• There are not any intern event (t) neither empty
  event (e) into a Refusal Graph.

a
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Algorithm

• Initialization
• Define g0 the initial state
• Calculate closing(g0) , out(g0)
• For g Refusal Graph
• Do Newstate(g)
• Newstate(g) Algorithm
• For a out(g)
• -Look for the successor of the states
  Newstate(g) by the event a
• -Calculate their closing
• -if there is g from the Refusal Graph such as
• Newstate(g)nNewstate(g) ? F
• Create transition labelled a such as g ? g
• -else create g such as g ? g by the
  transition labelled a
• Calculate out(g)

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Implementation
Source state Purpose state Action
1 2 a
1 3 b
2 4 e

• Choice of dynamic tables representing LTS and RG.

Source state Purpose state Action
g1 g2 a
g1 g3 b
State NewState Out
g1 1 a,b
g2 2,4 Ø
g3 3 Ø
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Demonstration
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Test(1)
RGraph
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Test(2)
RGraph
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Test(3)
RGraph
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Conclusion

• AimRobustness of a protocol
• Communication protocol TCP , UDP
• Softwares
• Automatic system
• Limits of the software
• Important refusal set
• Specific events