a114← department of mathematics and computer science

PROSE 05-10-06

Checking Properties of Adaptive Workflow

NetsK. van Hee, I. Lomazova, O. Oanea,

A. Serebrenik, N. Sidorova,M. Voorhoeve

Program Systems Institute of the Russsian Academy of Science

a214← department of mathematics and computer science

PROSE 05-10-06

Overview

Workflow (WF) nets and proper termination.

Problems with fixed structure of netsespecially exception modelling.

EWF nets: WF nets with exception transitions.

AWF (adaptive WF) nets: nesting.

Verification of AWF nets.

a314← department of mathematics and computer science

PROSE 05-10-06

Workflow net

Petri net with initial (source) and final (sink) place.All other nodes on directed path from source to sink.

Soundness: every marking reachable from [i] can reach [ f ]

Marking: e.g. [p]+2[q]i

f

b

a

d

c

p

q

r Enabled, firing][][][2][ fqqp d

Reachability: ][][ fi ac

][:][: fMMi ([i] sat AG EF [ f ])

MM Always:

a414← department of mathematics and computer science

PROSE 05-10-06

Problem: modelling exceptionsTypical sound WF net with parallelism(normal flow):

i

f

In one thread an exception may occur.

The other thread should be interrupted.Soundness should be preserved.

superfluousfiring needed

Model becomes unfeasible.

a514← department of mathematics and computer science

PROSE 05-10-06

Reset arcs

i

f

Reset arc empties all places in region.Improves modeling, makes analysis worse.No specific reaction to exceptions.

Problem with adaptivity in general,due to fixed structure!

a614← department of mathematics and computer science

PROSE 05-10-06

EWF nets

i

f

Labelled exception (sink) transitions;upon firing an exception, the net is terminated.

EWF net is sound iff

nTeT e

][:][:* fMMiTn

a714← department of mathematics and computer science

PROSE 05-10-06

AWF nets: definition

e

Adaptive WF (AWF) net:coloured EWF net.Arcs and transitions arelabeled with expressions

n : an EWF net

n final(v)init(n) v

v

e(v)

b

bb

b

b

a814← department of mathematics and computer science

PROSE 05-10-06

AWF nets: allowed expressions

Out-arc expr’s built from: std nets, variables, operators e.g.: . (seq. composition), + (choice), || (parallel composition)

init(n||m).k

In-arc expressions:-b: black,-v (variable): net

We presuppose a set of “standard”sound EWF nets (domain dependent).

v

Transition expressions(guards):- none,- e(v) (e exceptionlabel),- final(v), final(v)

a914← department of mathematics and computer science

PROSE 05-10-06

AWF net firing rules

AWF net and token net can fire independently

e

m

n

init(n+m) v final(v)

v

e(v)

b

bb

b

b

init

e(v)

v

+

t

Transitions in the AWF net can fire,producing black or net tokens.

init +m

marked net tokens

or synchronized on exception label

e

e

or upon token net having reached the final state.

final

a1014← department of mathematics and computer science

PROSE 05-10-06

Adaptivity

Modeling hospital admission; standard cure n.Monitor; if needed extend current cure with m.

e(w)

init(n)

init(c)

v v.m

w init(c)

v

w

final(v)final(w)

ec:

e: extension needed.

a1114← department of mathematics and computer science

PROSE 05-10-06

Circumspectness

AWF net:final(v)

init(n) v

bb

b

b

b b

e

n:

Sound, butcan not reactto exception e intoken net n.(not circumspect)

AWF net N is circumspect:every exception e of token netcan synchronize in any state of N.

a1214← department of mathematics and computer science

PROSE 05-10-06

Circumspect AWF net

Net can synchronize with e before and after firing of t.

init(n+m) v final(v)

v

e(v)

b

bb

b

b

e

init

e(v)

v

m

n

+

t

a1314← department of mathematics and computer science

PROSE 05-10-06

Verification of AWF nets

Colour sets of AWF nets are infinite,so no direct model checking possible.

v. m

v

Abstract interpretation :map token colours tosets of exception labels.

Theorem: AWF net N sound iff all statesreachable in (N) by nonexceptional firings canterminate without synchronising on exceptions.

The set of library net exception labels is finite!

Similar result for circumspectness.

a1414← department of mathematics and computer science

PROSE 05-10-06

Conclusions

EWF nets: WF nets with exceptions.AWF nets: EWF nets with nesting (e.g. reaction to exceptions).Proper termination and circumspectness of AWF nets can be checked.

Extensions:Synchronisation without termination.Checking other temporal properties.

Thank you for your attention!

department of mathematics and computer science