1 Automated Composition of E-Services: Lookaheads Çağdaş E. Gerede *, Richard Hull , Oscar H. Ibarra *, Jianwen Su * University of California, Santa.

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Automated Composition of

E-Services: Lookaheads

Çağdaş E. Gerede*, Richard Hull, Oscar H. Ibarra*, Jianwen Su*

University of California, Santa Barbara* &

Bell Labs/Lucent Technologies

International Conference on Service Oriented Computing

(ICSOC), September, 2004, NY

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Service Composition

Among the key issues for web services[Tutorial by Hull-Su in SIGMOD ’04]

Automated composition: a holy grail problem[Tutorial by Giacomo-Mecella in ICSOC’04] Planning [e.g., McIlraith ’02, Traverso ’03] Workflow [e.g., van der Aalst ’99, Lu ’02] Synthesis of conversations [e.g., Fu-Bultan-Su, CIAA’03, ICWS

’04, WWW’04] . . .

This paper : Restricted case of the “Roman Model” [Berardi et. al., WES’03,

ICSOC’03, ICSOC04] where services are FSMs as in [ICSOC’03].

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Roman Model

• E-service: software artifact interacting with its clients (human or other e-services) based on activities– Internal Service Schema:

• Internal or Business Logic

– External Service Schema• Published Service Behavior

• Service Instance: – One occurrence of an e-service

• Simple vs. Composite e-service– processing on its own vs. invoke others (delegate)

• Our study focuses on external service schemas represented as Finite State Machines

[Berardi et. al. , ICSOC’03]

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Travel Department of Corp. A:

Travel Dept.

Travel plans

Travel Agency 1

Travel Agency 2itinerary

booking

itinerary

booking

bus flight

hotel

train

Travel Service

Can the Travel Dept. re-use the existing travel services?

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Service Delegation

bus flight

hotel

train train flight

Agency 1hotel

bus(to Newark)

bus flight

hotelAgency 2requests

Delegator

hotel(Hilton)

flight(to JFK)

train(to LAX)

2

111

Desired Service

User A

User Bflight(to LAX)

hotel(Westin)

2 2

request:

delegation:

request:

delegation:

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Service Delegation

bus flight

hotel

train

train flight

Agency 1hotel

bus flight

hotelAgency 2

requests

Delegator

Desired Service

Delegator

train / 1

flight / 1

hotel / 1 hotel / 2

bus / 2

flight / 2

requests

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Can we construct such a delegator?

“Roman” Delegator: Delegation determined with immediate request– can be computed in EXPTIME [Berardi et. al., ICSOC’03]

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Different Scenario: No delegator?

flight hotel

Agency 3train

flight hotel

busAgency 4

busflight

train

Corporation B

hotel

requests

No Roman Delegator What if the delegator could look ahead?

• Broader notion of delegation to allow more re-use of existing services• How to Formulate ? • Decision Problems & Algorithms ?

trainhotelflight

?3

request:

delegation: 3 3

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Main Contributions

• Developed a notion of “lookahead” to enable richer re-use of existing services

• Introduced a broader definition for a delegator that allows the study of lookahead: “functional delegator”– EXPSPACE decision/construction algorithm

• Proved that if there is a k-lookahead functional delegator, then there is a k-lookahead FSM-based delegator– EXPTIME decision/construction algorithm– Roman delegator is 0-lookahead.

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Service Model

• Service: – (Possibly nondetermistic) FSM

• Alphabet, Initial state, Accepting states• Transitions: processing of activities

• Execution model: focus on the interaction between user and service

Composition System: a target service and set of available services (AT, <A1,…,Ar>)

• Results will be presented for deterministic FSMs– Same techniques can be applied to Nondetermistic case (check

the paper)

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Functional Delegators

• f(w,i) = j : service j processes ith activity of w

– a subsequence is assigned to each service

– Actually, f(,) is a subset of {1, …, r}.

• f(,) is a functional delegator for (AT, <A1,…,Ar>) if

for every string w accepted by the target service, each service accepts the assigned (nonempty) subsequence.

• How do we determine if there exist a functional delegator?

w = a1 a2 ….. ai ….. a|w|-1 a|w|

jj j

service j processes a2 ai a|w|-1

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A proof technique for decidability of functional delegators

Product Machine of a system of FSMs: (AT, <A1,…,Ar>) variant of standard product construction FSM with outputs: each state is a configuration of the system

Initial State, Accepting States Each transition produces an output

size: O(|| * 2r * sr * sT) || : alphabet size r, s : number and size of available services sT : size of target service

L(product) = language of FSM (outputs are ignored)

000

110 101 111

a/1a/2

a/1,2

…… …

(AT, <A1, A2>)

b/1b/1

b/2

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Complexity of Decidability

Lemma:

There is a functional delegator for a system, iff L(product) = L(AT).

Complexity: O(||2 * 2r * sr * s2T) space (i.e., EXPSPACE)

language equivalence of two FSMs: polynomial space in size of FSMs

What if we put a bound on the amount of lookahead?

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Subclass: k-lookahead (functional) delegators

f(,): LAk (functional) delegator

Observation: Roman delegator corresponds to an LA0 delegator.

How can we determine the existence of a k-lookahead delegator?

w = a1 ... ai ai+1 … ai+k ai+k+1… a|w|

x y z

f(xyz, i) = f(xyz’, i) for all z, z’

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Decidability of functional LAk

• Reduction of a problem with LAk to ||k problems with LA0

• Roman delegator (LA0)• can be determined in exponential time in the total size of the

input (satisfiability of description logic formula) [Berardi et. al. ICSOC’03]

• Why if we use FSMs directly?• We achieved a finer characterization of the complexity.

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Existence of functional LA0

Theorem: For a system, there is an LA0 delegator iff there is a

deterministic submachine S such that L(S) = L(AT) where AT is the target service.

Proof idea: Existence of functional LA0 implies the existence of an FSM-based

delegator. Splicing argument

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Algorithm: Existence of LA0

Algorithm: Existence Check & Construction Construct the product Remove “bad” configurations

Configurations that a delegator shouldn’t enter

Find a deterministic submachine (same language with target) Pick one delegation arbitrarily, ignore others

Submachine is an LA0 delegator

Exponential

a/i

…

… …

…

a/ja/k a/m

a/pWhich one is correct delegation?

If none is bad, any choice is correct

Linear

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Analysis for LA0, LAk Checks

LA0

Complexity: O(|| * 22r * sr * sT) - time- | | : alphabet size- r, s : number and size of available services

- sT : size of target service

Details: product machine construction: O(|| * 2r * sr * sT) time submachine construction: polynomial in size of the product machine

LAk: Complexity: use | |rk+k instead of | |

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Summary

• Introduced a more general class of delegators: – functional delegators

• Examined decision problems on functional delegators

– decision algorithm: O(|2 * 2r * sr * s2T) space

• subclass: k-lookahead delegators– Enables a richer form of delegation and broader re-use of

existing services

– decision/construction algorithm: O(||rk+r * 22r * sr * sT) time

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Current and Future Work

• Extension to FSM model [Dang-Ibarra-Su, ISAAC’04]– FSMs augmented with restricted counters and stacks– decidability/undecidability results

• Extension on delegation [submitted]– Cost function associated with each activity in each service– For a given word, computing the cheapest delegation minimizing

the total cost is linear time in the length of the word.

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Thanks

Questions and Comments

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Backup Slides

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Example of a functional delegator

flight hotel

Agency 3train

flight hotel

busAgency 4

busflight

train

hotel

◦ f(flight hotel train, 1) = 3

◦ f(flight hotel bus, 1) = 4

◦ f(flight hotel train flight hotel bus, 4) = 4

◦ f(flight hotel train flight hotel bus, 1) = 3

◦ f(flight hotel train flight hotel bus, 1) = 3

…

Corporation B

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Delayed delegation: How to represent?

flight / -

hotel / -

train / 1 bus / 2

flight / 1

hotel / 1# / 1

# / 1 # / 2

# / 2 flight / 2

hotel / 2

bus

flight

train

hotel flight hotel

Agency 3

train

flight hotel

bus

Agency 4Corp. B

FSM with outputs (Mealy)

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Functional Delegators• f(w,i) = j : service j processes ith activity of w

– a subsequence is assigned to each service

– Actually, f(,) is a subset of {1, …, r}.

• f(,) is a functional delegator for (AT, <A1,…,Ar>) if

for every string w accepted by the target service, each service accepts the assigned (nonempty) subsequence.

• f has “full knowledge” of word w for each delegation decision. Does the amount of knowledge (lookahead) matter?

w = a1 a2 ….. ai ….. a|w|-1 a|w|

jj j

service j processes a2 ai a|w|-1

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Strict hierarchy on the amount of lookahead

• Required amount of lookahead:

(a) 1-lookahead, (b) 2-lookahead, (c) unbounded (full-knowledge)

Services

Desired Service

• How do we determine if there is a functional delegator?