A lower bound on web service composition

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A lower bound on web service composition

• Anca Muscholl
• Igor Walukiewicz

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Web services

• Working definition (R. Hull)
• Network-resident software services accessible
  via standardized protocols
• P2P systems asynchronous communication
• Data-driven (Vianu)

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Formal models for services
Vianu et al. data-driven (PODS 04)

• DB fixed through the run
• states change depending on clients input
• web page schemas
• input choices determined by DB queries
• Transitions, choices etc. are relational schemas
• Verification of LTL-FO properties
• PSPACE verification algorithm
• bounded part of DB

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Formal models for services
Hull et al. automata-oriented

• Roman model
• (de Giacomo, Calvanese ICSOC 03)
• asynchronous composition of services
• Conversation model
• (Bultan, Fu, Su WWW 03) synthesis of
• message passing automata (CFM)

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Here (Simple) roman model
U

• Messaging not explicitly modeled
• Out edges set of options that will be presented
  to the user

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Desired service
Available services
Web store
search
Juke
Bank
search
order
init
listen
buy
search
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Delegator
???
Available services
Web store
search
Juke
Bank
search
order
init
listen
buy
search
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Roman composition

• In general delegator means simulation
• Given (service) DFA A1,, An
• (goal) DFA B
• Question
• Does the asynchronous product
  
• A1 An simulate B?

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Previous results

• ExpTime algorithm for delegator synthesis
• de Giacomo, Calvanese, Hull ICSOC 03
• Open lower bound
• ExpTime lower bound for deciding simulation
• for non-flat systems (synchronous products of
  automata with binary synchronization)
• Laroussinie, Schnoebelen FoSSaCS 00

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Our result

• EXPTIME lower bound for deciding simulation
• B A1 A2 ? An
• PSPACE-completeness in the case where the input
  alphabets are pairwise disjoint

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Proof ideas

• Reduction from poly space TM
• B A1 A2 ? An iff
• TM never stops
• DFA Ak for each tape cell k, with states
• tape symbols
• pairs (state, tape symbol)
• garbage state ?

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Proof ideas

• Alphabet of Ak ?k
• q ak, q ak L, q ak R state q, symbol
  a
• Transitions of Ak

a
b
?
q,a
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Proof ideas

• DFA B enforces the head move state consistency
• L(B) (k q bk R q ck1 q bk L q
  ck-1)
• Garbage runs of B simulated by ?-states

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Proof ideas ExpTime

• Simulating a poly space ATM
• Universal transitions all runs of B must be
  simulated by the product
• Existential transitions
• 2 automata for each tape cell, sharing
• common action choice
• the automaton performing choice
  determines the transition

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Further reading

• Different standards for web services
• WSDL (XML I/O signatures, ports)
• BPEL (flowcharts with fork/join, data)
• WSCL (service interaction)
• Roman model Colombo (CFM)
• Simulation for CFM?
• P2P service composition CFM synthesis