Exploiting user-definable synchronizations in graph transformation

1
Exploiting user-definable synchronizationsin
graph transformation
Ivan Lanese Computer Science Department University
of Bologna Italy
2
Roadmap

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

3
Roadmap

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

4
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

5
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

6
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

7
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

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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

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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
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Roadmap

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

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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

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Our aim
univ
univ
chk
inPl
inBo
chk
inPl
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Programming using productions (1)
atlte,ltgtgt
inltack,ltatgtgt
atltreq,ltnewatgtgt
chk ltbreq,ltingtgt
inlte,ltgtgt
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Programming using productions (2)
atlte,ltgtgt
chk ltbrd,ltnewatgtgt
Idle productions always available
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Roadmap

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

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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

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Synchronization Algebras with Mobility

• Specify how actions synchronize
• Two at the time, associativity and commutativity
  required
• From Winskels synchronization algebras
• Partial operator ? for action synchronization
• Action e 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

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Milner SAM

• Normal actions, coactions, t, e
• in ? out t
• a ? e a
• Final actions t, e

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Broadcast SAM

• Normal actions, coactions, e
• in ? out out
• in ? in in
• e ? e e
• Final actions out, e

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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

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Applying a SAM

• SAMs used to synchronize tuples of actions ai
  carrying parameters pi
• If synchronization is allowed we can compute
• A resulting action c
• A substitution s
• A tuple of parameters p

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Applying broadcast

• Broadcast synchronization is allowed if
• at most one action is out
• if there is an e, then all the actions are e
• The result is
• e if all actions are e
• in if all the actions are in (not allowed on
  bound nodes)
• out otherwise
• Substitution s computed as mgu of equalities
  pipj for all i, j
• Parameters p computed as pis (any i can be chosen)

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Roadmap

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

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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 cx, parameters px and substitution sx as
  results
• If x is bound then cx must be final

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Synchronization in the example
e,ltgt
univ
ack,ltunivgt
inBo
e,ltgt
e,ltgt
req,ltnewatgt
e,ltgt
brd,ltnew1gt
breq,ltinPlgt
chk
e,ltgt
brd,ltnew2gt
inPl
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Synchronization in the example
e
univ
inBo
t
univ/newat
brd,ltnew1gt
breq,ltinPlgt
chk
e
brd,ltnew2gt
inPl
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Synchronization in the example
e
univ
inBo
t
univ/newat
breq,ltinPlgt
chk
e
inPl/new1,inPl/new2
inPl
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The algorithm (2)

• Global substitution s computed by
• Merging the substitutions sx from single nodes
• Final label contain
• The triple ltx, cx, pxsgt for each free x in the
  LHS
• Final graph computed by
• Merging the RHSs of the productions
• Applying the global substitution s
• Hiding nodes unless free in the LHSs or occurring
  in the label
• Deleting isolated nodes

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Result of the transition
univ
newat
chk
inBo
inPl
univ/newat, inPl/new1, inPl/new2
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Result of the transition
univ
chk
inBo
inPl
univ/newat, inPl/new1, inPl/new2
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Result of the transition
univ
chk
inBo
inPl
The label is ltx,e,ltgtgt
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Result of the transition
univ
chk
inBo
inPl
All nodes but univ are hidden
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Roadmap

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

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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

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Future work

• I have moved, so Im 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

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End of talk

• Thanks

• Questions?