Web services composition is decidable

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Web services composition is decidable

• Ramy RAGAB HASSEN Lhouari Nourine
• Farouk Toumani
• LIMOS, France

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Web services protocoles

• WSDL
• SelectVehicle
• ModifySelection

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Composition (Protocol Synthesis)

• Input
• A target protocol.
• A registry of available services protocols.
• Question synthesize a composite protocol which
  
• Has the same behavior as the target protocol
• Delegates all its actions to protocols from the
  registry.
• Conforms the used protocols.

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Web services registry
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Composition (Protocol Synthesis)
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Agenda

• Web services synthesis problem
• Decidability of the composition

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Existing works

• Berardi al. 2003
• PDL-based framework .
• 2Exp-time upper bound.
• Musholl al. 2007
• Simulation based framework.
• Exp-time complete lower bound.
• ? Strong assumption only one instance of each
  available service can be involved.

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Simulation - Example
s0
q0 ltlt s0
q0
b
a
q2 ltlt s2
q1 ltlt s1
b
a
b
a
c
q3? ltlt s3
s2
s1
q2
q1
d
c
c
s3
s4
q3
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Composition as a simulation problem

• Input
• S a target service
• RS1,,Sn a set of services
• Notation ?(R) USi1,,Sik?R Si1xxSik
• Question does there exist a simulation of S by
  a part of the product of existing services?
• Composition of S using R iff S ?(R), i.e.
• Some part of?(R) behaves as S from a client
  perspective.
• ? Extensible to k instances S ?(R) x x ?(R)
  (k-times) (?(R))?k

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The unbounded case

• In practice, simple compositions can not be
  computed (for any k)

Open problem in theory.
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The unbounded case
S (S)?

• Recall that
• Composition with k instances, S (?(R))?k
• Assuming an unbounded instance number
• K8 S (?(R))?8 (?(R))?
• What is new?
• ?(R) is an FSM
• ? k?N (?(R))?k is still an FSM
• (?(R))? is not an FSM any more

Need of a model ?
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Agenda

• Web services synthesis problem
• Decidability of the composition

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Product Closure State Machine(PCSM)

• Runs an (unbounded) parallel/sequential instances
  of a given FSM.
• Relies on notion of configuration
• Each component informs the token number of each
  state of the FSM.
• A configuration is final iff each intermediate
  state has no tokens.
• Intermediate states not final with at least
  one incoming transition
• Hybrid states final with at least one outgoing
  transitions
• Only hybrid and intermediate states are present
  in a configuration

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PCSM - Example
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Simulation FSM / PCSM
q0 ltlt (0,0)
a
q1 ltlt (1,0)
q0
c
b
q2 ltlt (0,0)
q1 ltlt (1,1)
a
b
a
c
b
b
q2 ltlt (0,1)
q1 ltlt (1,2)
s2
s1
q1
b
q1 ltlt (1,3)
d
c
c
b
q2
Services registry
q1 ltlt (1,8)
Target service
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Configuration cover

• Let C and C be two configurations
• C is covered by C iff
• C C,
• For all intermediate q Cq Cq
• Intuition
• All what we can run from C, is enabled from C.

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Simulation and cover
q0 ltlt (0,0)
a
q1 ltlt (1,0)
e
q0
c
b
q2 ltlt (0,0)
q1 ltlt (1,1)
a
b
a
b
s2
s1
q1
q1 ltlt (1,0)
d
c
c
q2
Services registry
Target service
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Decidability result

• Theorem
• Web services composition is decidable in
  presence of an unbounded number of instances.

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Discussion Conclusion

• Main contributions
• Formalization of the problem in the settings of
  shuffle closure
• Decidability proof (see the online report)
• A PCSM is a Petri net, and hence
• Similar decidability results does exist but not
  the same
• No complexity bound at the moment
• Proof based on Dickson lemma ? not primitive
  recursive