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