COORDINATION 2005 Namur 20 23 April 2005 Synchronized Hyperedge Replacement for Heterogeneous Systems Ivan Lanese Dipartimento di Informatica Università di Pis

							            COORDINATION 2005, Namur, 20-23 April 2005




Synchronized Hyperedge Replacement
     for Heterogeneous Systems
   Ivan Lanese
   Dipartimento di Informatica
   Università di Pisa

                                 joint work with
                                 Emilio Tuosto
                                 Dipartimento di Informatica
                                 Università di Pisa
Which kind of systems?
    Usually not cats and
     dogs
    Entities on huge
     networks
         applications
         web services
         computers
         …


COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Features of the systems
    Systems composed by interacting
     components
         pre-existing, off-the-shelf
         heterogeneous
              different computational power, features, owner, …
    Interaction via middleware for
     communication
         many primitives for communication
         complex protocols
    Mobile/reconfigurable systems

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Classical formal tools
    Frameworks in literature usually have
     one simple primitive for communication
         e.g. -calculus uses message passing
    Other primitives must be encoded
         not always an easy task
    No primitives modeling complex
     protocols
         useful for abstract models of coordination


COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Our approach
    Two level modeling
    Modeling the primitives provided by the
     middleware
         synchronization algebras with mobility
          (SAMs)
    Modeling the system
         hypergraphs
         evolution via synchronized hyperedge
          replacement (SHR)
         synchronization uses SAMs
COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Roadmap
    Our approach
    A simple example
    A less simple example
    What else?




COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Roadmap
    Our approach
    A simple example
    A less simple example
    What else?




COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Basics of system modeling
    Hyperedges are system components



    Nodes are communication channels
     or ports
    Nodes can be global or local



COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Basics of hyperedge replacement
    Productions rewrite an edge into a
     general graph attached to the same
     nodes

                             
    Context free mechanism
    Limited expressivity
          synchronization is needed
COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Basics of synchronization
    Specified via constraints on nodes
     adjacent to the rewritten edge
    A set of productions can be applied in
     one step iff the constraints are satisfied
    Problems:
         how to specify constraints?
         when constraints are satisfied?



COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Synchronization: general idea
    A production performs actions on nodes
    If the actions can be composed, then
     constraints are satisfied


       a                  ε   
                b

    Defined using a synchronization algebra
     (extends Winskel’s definition)
COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Synchronization algebras
    A tuple <Act,ActComp,ε>
    Act: set of actions
    ActComp: set of triples of actions
         a triple (a,b,c) specifies that a can synchronize with b giving
          c
         associative and commutative
    ε: action
         stands for “not involved in the synchronization”
         neutral element in the synchronization
         c=ε iff a=ε and b=ε
    Allow to specify synchronization, nondeterminism,
     asynchronous execution and incompatibility between
     actions

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Example: Milner (CCS) SA
    Actions {a, a, , ε}
    Synchronizations
         (a,a,) and symmetric
         (,ε,) and symmetric


    Other synchronizations (broadcast,
     mutual exclusion,…) can be easily
     modeled

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Adding mobility
    Each action is equipped with a tuple of
     node references
    During synchronization we
         compute the references attached to the
          resulting action
         compute a fusion among nodes
              mobility in the Fusion Calculus style
         apply the fusion to the graph and to the
          references of the resulting action

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Modeling mobility
    Actions have an arity                       2             3           2

     (number of attached                         a             b           c
     references)
    We extend the tuple
     (a,b,c) to (a,b,(c,Mob))
         Mob: partial function
          {1,…,ar(a)} + {1,…,ar(b)}
           {1,…}
         Parameters of c computed




                                                                           …
          using Mob
              surjective on {1,…,ar(c)}
         Elements that are mapped
          to the same position are
          merged

COORDINATION 2005, 20-23 April, Namur, Belgium       Ivan Lanese and Emilio Tuosto
Other issues
    Some channels are local
         only actions that do not require further
          interactions are meaningful here
         modeled by a subset Fin of actions
    May have many SAMs with the same
     formal structure
         SAMs are named to distinguish them




COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Example: Milner (Fusion) SAM
    Actions {a, a, , ε}
    ar(a)=ar(a), ar()=ar(ε)=0
    Synchronizations
         (a,a,) and symmetric
              corresponding names are merged
         (,ε,) and symmetric
              names of the non-ε action are propagated
    Fin= {, ε}

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Managing multiple SAMs
    SAMs label nodes
    For new nodes a SAM must be specified
    When merging nodes, SAMs must be
     composed
    SAMs form a programmer-defined
     commutative monoid
         monoidal operation used for composition



COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Roadmap
    Our approach
    A simple example
    A less simple example
    What else?




COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Example: graph

                                                 S1

                 Au




                                                 …
                                u:Mil


                      x:Mil                      Sn



                  C



COORDINATION 2005, 20-23 April, Namur, Belgium        Ivan Lanese and Emilio Tuosto
Example: productions

   C
                  x:Mil
                auth,y:Mil                      C
                                                                x:Mil




                                                      y:Mil



  Au
                 u:Mil
                                                Au
                                                                u:Mil



      x                                               x:Mil
auth,u:Mil




COORDINATION 2005, 20-23 April, Namur, Belgium           Ivan Lanese and Emilio Tuosto
Example: synchronization

                                                 S1

                 Au




                                                 …
                                     u:Mil

                    auth,u:Mil
            x:Mil                                Sn
                        auth,y:Mil


                    C



COORDINATION 2005, 20-23 April, Namur, Belgium        Ivan Lanese and Emilio Tuosto
Example: final graph

                                                 S1

                 Au




                                                 …
                                u:Mil


            x:Mil                                Sn



                    C
                                    Assumption: Mil • Mil = Mil


COORDINATION 2005, 20-23 April, Namur, Belgium        Ivan Lanese and Emilio Tuosto
The full power of our approach
    Suppose servers are search engines and
     some clients want to submit the request
     to all of them
    Want to use broadcast synchronization
     between client and servers but Milner
     synchronization to interact with Au
    Just change the production for the
     client with y:Bdc and define Mil • Bdc =
     Bdc
COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Example: synchronization again

                                                 S1

                 Au




                                                 …
                                     u:Mil

                    auth,u:Mil
            x:Mil                                Sn
                        auth,y:Bdc


                    C



COORDINATION 2005, 20-23 April, Namur, Belgium        Ivan Lanese and Emilio Tuosto
Example: final graph again

                                                 S1

                 Au




                                                 …
                                u:Bdc


            x:Mil                                Sn



                    C
                                    Assumption: Mil • Bdc = Bdc


COORDINATION 2005, 20-23 April, Namur, Belgium        Ivan Lanese and Emilio Tuosto
Roadmap
    Our approach
    A simple example
    A less simple example
    What else?




COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
A network example
    Network with routers and clients
    Channels can have
         4Kb/16Kb packets
         error detection/no error detection
    To communicate a client creates a virtual
     communication channel that uses the
     underlying infrastructure
    The communication channel supports 16Kb
     packets/error detection only if all the
     underlying channels do

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Modeling the scenario
    Eight different SAMs with all the combinations
     of
         4Kb < 16Kb
         no error detection < error detection
         communication < control
    SAMs provide variants of Milner
     synchronization
         e.g. action for detecting errors
    SAMs form a partial order (pointwise)
    SAM composition corresponds to glb

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Building a virtual channel

                                                    4,√
           Act
            C                                R                        R


                                                               16,×
         16,√              4,×                   16,√
                                       4,√


                         16,×                                    Act
                                                                  C
                R                      R



comm,16,×

COORDINATION 2005, 20-23 April, Namur, Belgium          Ivan Lanese and Emilio Tuosto
Ideas                        on the productions
    Each production creates a node labelled
     with a SAM
         for communication
         with the features provided by the nearby
          channels
    During synchronization these nodes are
     merged to build the communication
     node
         it is automatically labelled with the desired
          SAM

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Roadmap
    Our approach
    A simple example
    A less simple example
    What else?




COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Behind graphic
    A textual representation for
     hypergraphs, transitions, productions
    A labelled transition system for system
     evolution
    Inference rules to derive transitions
     from productions
    Production schemas to define classes of
     similar productions

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Only for the most proud




COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Conclusions
    A general framework for modeling
     heterogeneous systems
         SAMs to model synchronization/complex
          interaction protocols
         SHR to model system evolution
    Different synchronizations can be used
    Synchronization policy can be changed
     dynamically
    Sound mathematical foundations
COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
Future work
    Use SHR+SAMs to model real
     protocols/heterogeneous systems
    Use SAMs for QoS [see Emilio’s poster]
    Study the expressivity of the framework
    Implement SHR (someone wants to do that?)
    Apply SAMs to process calculi [paper
     submitted to CONCUR]
    Study the relationships between SAMs
     (composition/refinement)

COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto
COORDINATION 2005, 20-23 April, Namur, Belgium   Ivan Lanese and Emilio Tuosto