a 14← department of mathematics and computer science PROSE Checking Properties of Adaptive Workflow Nets K. van Hee, I. Lomazova, O. Oanea, A. Serebrenik, N. Sidorova, M. Voorhoeve Program Systems Institute of the Russsian Academy of Science

a 14← department of mathematics and computer science PROSE Overview Workflow (WF) nets and proper termination. Problems with fixed structure of nets especially exception modelling. EWF nets: WF nets with exception transitions. AWF (adaptive WF) nets: nesting. Verification of AWF nets.

a 14← department of mathematics and computer science PROSE 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 Reachability: ([ i ] sat AG EF [ f ]) Always:

a 14← department of mathematics and computer science PROSE Problem: modelling exceptions Typical 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. superfluous firing needed Model becomes unfeasible.

a 14← department of mathematics and computer science PROSE 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!

a 14← department of mathematics and computer science PROSE EWF nets i f Labelled exception (sink) transitions; upon firing an exception, the net is terminated. EWF net is sound iff

a 14← department of mathematics and computer science PROSE AWF nets: definition Adaptive WF (AWF) net: coloured EWF net. Arcs and transitions are labeled with expressions n : an EWF net n final( v ) init( n ) v v e(v)e(v) b b b b b 

a 14← department of mathematics and computer science PROSE 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 exception  label), - final( v ), final( v )

a 14← department of mathematics and computer science PROSE AWF net firing rules AWF net and token net can fire independently m n init( n+m ) v final( v ) v e(v)e(v) b b b b b init  e(v)e(v) v + t Transitions in the AWF net can fire, producing black or net tokens. init+m+m marked net tokens or synchronized on exception label e e or upon token net having reached the final state. final

a 14← department of mathematics and computer science PROSE Adaptivity Modeling hospital admission; standard cure n. Monitor; if needed extend current cure with m. e(w)e(w) init( n ) init( c ) vv.m w init( c ) v w final( v )  final( w ) c:c: e: extension needed.

a 14← department of mathematics and computer science PROSE Circumspectness AWF net: final( v ) init( n ) v b b b b  b b n:n: Sound, but can not react to exception e in token net n. (not circumspect) AWF net N is circumspect: every exception e of token net can synchronize in any state of N.

a 14← department of mathematics and computer science PROSE Circumspect AWF net Net can synchronize with e before and after firing of t. init( n+m ) v final( v ) v e(v)e(v) b b b b b init  e(v)e(v) v m n + t

a 14← department of mathematics and computer science PROSE 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 to sets of exception labels. Theorem: AWF net N sound iff all states reachable in  ( N ) by nonexceptional firings can terminate without synchronising on exceptions. The set of library net exception labels is finite! Similar result for circumspectness.

a 14← department of mathematics and computer science PROSE 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