1 Ivan Lanese Computer Science Department University of Bologna Italy Exploiting user-definable synchronizations in graph transformation

Roadmap Synchronized Hyperedge Replacement The airport case study Parametric SHR Computing a transition step-by-step Conclusions

Roadmap Synchronized Hyperedge Replacement The airport case study Parametric SHR Computing a transition step-by-step Conclusions

Graph transformation Graphs used to model system structure –(Hyper)edges are components –Nodes are communication channels Graph transformation model system evolution –Rules replace parts of the graph with new parts –Captures in an intuitive way reconfiguration

The SHR approach Traditional graph transformation (e.g., DPO) requires to match large subgraphs –Difficult to implement in a distributed setting The SHR approach –Rules (productions) describe the behaviour of single edges –Productions applied locally –Synchronization to coordinate different productions

Standard SHR presentation Algebra to represent graphs LTS-based semantics Inference rules to derive transitions from productions Apt for developing theory –Induction on the derivation, coinduction Difficult to understand –A transition is a result of many steps of derivation –Heavy technicalities

Our SHR presentation Set-theoretical presentation of graphs LTS-based semantics Algorithm to derive the allowed transitions Each step corresponds to an intuitive check –Choice of the productions, verification of the synchronization constraints, … More easy to guess the resulting transitions More easy to program

More on productions Rewrite an edge into a graph preserving the interface Many productions can be applied concurrently Synchronization constraints must be satisfied Mobility can change the interface at chk L at chk RS

Basics of synchronization & mobility Productions can execute actions on attached nodes Actions executed on each node at each step must be compatible Actions can carry nodes as parameters Parameters of synchronizing actions may be merged Synchronization Mobility

Roadmap Synchronized Hyperedge Replacement The airport case study Parametric SHR Computing a transition step-by-step Conclusions

The airport case study Taken from AGILE project on architectures for mobility Models airplanes taking off and landing at airports and persons traveling using them Modeled inside AGILE using –UML extended with mobility primitives –Synchronized variant of DPO We concentrate on a small part of the case study

Our aim univ inBo chk inPl

Programming using productions (1) at: > in: > chk: > newat in chk at at: > in: > at in

Programming using productions (2) at: > chk: > newat chkat Idle productions always available

Roadmap Synchronized Hyperedge Replacement The airport case study Parametric SHR Computing a transition step-by-step Conclusions

Parametric SHR A member of SHR family Synchronization and mobility patterns not fixed but user-definable –Specified using Synchronization Algebras with Mobility Allows to use each time the most suitable synchronization primitives

Synchronization Algebras with Mobility Specify how actions synchronize –Two at the time, associativity and commutativity required From Winskel’s synchronization algebras –Partial operator ● for action synchronization –Action ε for “not taking part to the synchronization” Added –Arities of actions –Function from parameters of the synchronizing actions to parameters of the result –Set of final actions

Milner SAM Normal actions, coactions, τ, ε l in ● out = τ l a ● ε = a l Final actions: τ, ε inout τ aε a

Broadcast SAM Normal actions, coactions, ε l in ● out = out l in ● in = in l ε ● ε = ε l Final actions: out, ε inout in

And many more SAMs can be defined for many synchronization policies –Mutual exclusion –Priority synchronization –…–… SAMs can be combined –In the example: req and acq interacting using Milner synchronization and breq and brd interacting using broadcast

Applying a SAM SAMs used to synchronize tuples of actions a i carrying parameters p i If synchronization is allowed we can compute –A resulting action c –A substitution σ –A tuple of parameters p

Applying broadcast Broadcast synchronization is allowed if –at most one action is “out” –if there is an ε, then all the actions are ε The result is –ε if all actions are ε –“in” if all the actions are “in” (not allowed on bound nodes) –“out” otherwise Substitution σ computed as mgu of equalities p i =p j for all i, j Parameters p computed as p i σ (any i can be chosen)

Roadmap Synchronized Hyperedge Replacement The airport case study Parametric SHR Computing a transition step-by-step Conclusions

The algorithm (1) One production is chosen for each edge –Idle production for passenger not checked in –Productions shown before for other edges –New nodes are local to productions The actions executed on each node x are synchronized –Action c x, parameters p x and substitution σ x as results If x is bound then c x must be final

Synchronization in the example univ inBo chk inPl ε,<> ack, ε,<> req, ε,<> breq, brd,

Synchronization in the example univ inBo chk inPl ε τ ε breq, brd, univ/newat

Synchronization in the example univ inBo chk inPl ε τ ε breq, univ/newat inPl/new1,inPl/new2

The algorithm (2) Global substitution σ computed by –Merging the substitutions σ x from single nodes Final label contain –The triple for each free x in the LHS Final graph computed by –Merging the RHSs of the productions –Applying the global substitution σ –Hiding nodes unless free in the LHSs or occurring in the label –Deleting isolated nodes

Result of the transition univ inBo newat inPl chk new1 new2 univ/newat, inPl/new1, inPl/new2

Result of the transition univ inBo inPl chk univ/newat, inPl/new1, inPl/new2

Result of the transition univ inBo inPl chk The label is >

Result of the transition univ inBo inPl chk All nodes but univ are hidden

Roadmap Synchronized Hyperedge Replacement The airport case study Parametric SHR Computing a transition step-by-step Conclusions

About SHR –Powerful graph transformation framework –Allows to relate local and global views of the system About PSHR –Allows to simplify the specification of complex transformations About this presentation of PSHR –Less suitable for developing theory –Hopefully more apt for designers/developers –The two views are (nearly) equivalent: the most suitable can be chosen at each time

Future work I have moved, so I’m not sure I will continue working on this Some interesting things on SHR under development –Category of SAMs to compose and compare them –Applying SHR to QoS –Abstract semantics for SHR One thing that is surely missing –Implementation of SHR

End of talk