Synchronization strategies for global computing models

1
Synchronization strategiesfor global computing
models
Ph.D. thesis discussion
Ivan Lanese Computer Science Department University
of Pisa (moved to Bologna)
Supervisor prof. Ugo Montanari
2
Roadmap

• Global computing
• Background on Synchronized Hyperedge Replacement
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

3
Roadmap

• Global computing
• Background on Synchronized Hyperedge Replacement
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

4
What is global computing?

• Essentially networks deployed on huge areas
• Global computing systems quite common nowadays
• Internet, wireless communication networks,
  overlay networks

5
Features of global computing systems

• Distribution
• Localities may have a semantic meaning
• Mobility
• Heterogeneity
• Interoperability, coordination
• Openness
• Reconfigurability
• Non-functional requirements

6
Formal methods for GC

• Building models of the system
• Old aims
• Analyze the properties of the system before
  building it
• Concentrate on a particular aspect
• Abstract from details
• But new approaches/tools must be used
• Mobility and non-functional requirements must be
  modeled explicitly
• Need for compositionality
• Need for more abstraction

7
High level models

• Models of coordination among components
• Components interact via interfaces
• Declarative specification of synchronization
  constraints
• Possible evolutions derived as solution of system
  of constraints
• Single components may be complex
• We need powerful primitives
• Multiple synchronizations
• Abstractions of full protocols

8
Roadmap

• Global computing
• Background on Synchronized Hyperedge Replacement
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

9
Synchronized Hyperedge Replacement

• A graph transformation approach
• Suitable to deal with distribution,
  synchronization, mobility
• (Hyper)edges are components connected through
  common nodes
• Productions describe the evolution of single
  edges
• Local effect, easy to implement
• Declarative approach
• Synchronization via actions performed on nodes
• Determines which productions can be applied
  concurrently
• Allows to define complex transformations
• Not only binary synchronization

10
Hyperedge Replacement Systems

• A production describes how the hyperedge L is
  rewritten into the graph R

L
R
H
3
3
4
4
2
2
1
1
11
Hyperedge Replacement Systems

• A production describes how the hyperedge L is
  rewritten into the graph R

Many concurrent rewritings are allowed
12
Synchronizing productions

• Synchronization productions execute actions on
  nodes
• A transition is allowed iff the synchronization
  constraints imposed on actions are satisfied
• Two synchronization models existed in the
  literature
• Milner message passing
• Hoare agreement

13
An example Milner SHR

• Pair of edges can synchronize by performing
  complementary actions

14
SHR with mobility

• We use node mobility
• Actions carry tuples of references to nodes (new
  or already existent)
• References associated to synchronized actions are
  matched and corresponding nodes are merged

15
Algebraic presentation of SHR

• Graphs represented as terms
• Edges (applied to nodes) are basic constants
• Operators for parallel composition and hiding of
  nodes
• Node mobility corresponds to name mobility
• Transitions described by a LTS
• Inference rules to derive transitions from
  productions

16
Roadmap

• Global computing
• Background on Synchronized Hyperedge Replacement
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

17
Why comparing models?

• Different models for GC exist
• Process calculi, graphs, UML,
• Each model has strengths and weaknesses
• Compare models to
• Find strengths and weaknesses
• Combine the strengths
• Categorize them
• Move some steps toward a (maybe) unique model

18
Which comparisons?

• N models ? 2N comparisons
• Must select some representatives
• Show at a first sight some interesting
  connections
• We have chosen
• Logic programming
• Synchronized Hyperedge Replacement
• A process calculus Fusion Calculus

19
Logic programming

• Traditionally language for AI and problem solving
• In the GC scenario seen as goal rewriting
  framework
• Unification as synchronization primitive
• Focus on partial computations

20
Fusion Calculus

• Calculus for mobility inspired by p-calculus
• Symmetric input/output
• Arbitrary fusions allowed
• Can simulate p-calculus

21
Hoare SHR vs logic programming

• Hoare synchronization strictly related to
  unification
• Strong relation between Hoare SHR and
  Synchronized Logic Programming
• A subset of logic programming
• Transactional application of many clauses
• Exploits function symbols for synchronization

22
Summary of the comparison

• Hoare SHR SLP
• Graph Goal
• Hyperedge Atom
• Node Variable
• Parallel comp. AND comp.
• Action Function sym.
• Production Clause
• Transition Transaction

23
Main results

• Simple (homomorphic) mapping from Hoare SHR to
  SLP
• Complete correspondance
• Suggests how to introduce restriction in logic
  programming

24
Milner SHR vs Fusion Calculus

• Many common features
• Synchronization in Milner style
• Mobility using fusions
• LTS semantics
• Straightforward mapping of Fusion into Milner SHR
• SHR adds
• Graphical presentation
• Multiple synchronizations
• Concurrent semantics

25
Summary of the comparison

• Fusion Milner SHR
• Processes Graphs
• Sequential processes Hyperedges
• Names Nodes
• Parallel comp. Parallel comp.
• Scope Restriction
• Prefixes Productions
• Transitions Interleaving tr.

26
Example
We can also execute both the steps at the same
time
27
Main results

• Simple (homomorphic) mapping
• Complete correspondance
• Suggests many generalizations of Fusion
• A concurrent semantics
• PRISMA Calculus

28
Milner vs Hoare

• Surprisingly the most difficult step
• Expressiveness as sets of reconfigurations that
  can be specified
• Simulating Hoare using Milner
• Must implement n-ary synchronization using binary
  synchronization
• Simulating Milner using Hoare
• Milner synchronization is asymmetric
• Milner restriction affects the behaviour, Hoare
  restriction just the observation

29
Some results

• Not equivalent in general
• In closed 2-shared graphs Milner is more powerful
  than Hoare
• Hoare implemented by dropping the distinction
  between actions and coactions
• A translation of graphs can be used to bridge the
  gap in many cases
• Amoeboids to simulate synchronization
• Hoare amoeboids are broadcasters
• Milner amoeboids are routers
• Mutual exclusion can not be enforced

30
And so?

• Synchronization and mobility strategies are an
  important characteristic of a model
• Difficult to simulate a strategy using another
  one
• Have strategies as parameters of the model

31
Roadmap

• Global computing
• Background on Synchronized Hyperedge Replacement
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

32
Synchronization Algebras with Mobility (1)

• Abstract formalization of a synchronization model
• Extend Winskels synchronization algebras to deal
  with name mobility and local resources
• Allow to have synchronization strategies as
  first-class citizens
• Can be used to have models with parametric
  synchronization policies
• Many synchronization policies in the same model
• Different policies can be compared and combined
• Common policies can be expressed as SAMs
• Simple ones Milner, Hoare, broadcast
• More complex ones with priority,

33
Synchronization Algebras with Mobility (2)
34
Synchronization Algebras with Mobility (2)

• SAs specify composition of actions
• (a,a,t) a synchronizes with a producing t
• SAMs also provide
• Arities for actions
• Mapping from parameters of synchronizing actions
  to parameters of the result
• Fusions among parameters
• Final actions (can be performed on local
  channels)
• Some more technical stuff

35
Sample synchronization
a
b
c
36
Milner SAM

• Normal actions, coactions, t, e
• (in, out, t)
• (a, e, a)
• Final actions t, e

37
Combining SAMs

• SAMs form a category
• Standard constructions can be used to compose
  SAMs
• Coproduct makes different protocols available
• Product applies two protocols concurrently

38
Parametric SHR

• Application of SAMs to SHR
• Different models obtained via instantiation
• Allows to recover Hoare and Milner SHR
• and to easily define new models
• Properties can be proved in general
• Allows to highlight relations between properties
  of SAMs and properties of the model

39
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
• We concentrate on a small part of the case study

40
Take-off transition
univ
univ
chk
inPl
inPi
chk
inPl
41
Specifying the transition (1)
atlte,ltgtgt
at
inltack,ltatgtgt
in
atltreq,ltnewatgtgt
chk ltbreq,ltingtgt
inlte,ltgtgt
42
Specifying the transition (2)
atlte,ltgtgt
chk ltbrd,ltnewatgtgt
43
Synchronization in the example

• The productions define exactly the wanted kind of
  transitions
• The used SAM is the coproduct of a Milner SAM and
  a broadcast SAM
• Defining the same transition using, e.g., only
  Milner is far more difficult

44
Heterogeneous SHR

• Allows to model heterogeneous systems
• Different primitives in different parts of the
  system
• Example wireless connections with broadcast and
  wired connections with Milner
• Technical trick use different SAMs on different
  nodes
• Concentrates on dynamic management of SAMs
• Conservative extension of parametric SHR

45
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

46
Modeling the scenario

• Eight different SAMs with all the combinations of
• 4Kb or 16Kb
• No error detection or error detection
• Communication or control
• SAMs provide variants of Milner synchronization
• E.g. actions for detecting errors

47
Building a virtual channel
R
C
4,v
Act
R
16,
16,v
4,
16,v
4,v
C
Act
16,
R
R
48
PRISMA Calculus

• SAM-based process calculus
• Prefixes of the form x a y . P
• Synchronization ruled by the SAM
• Mobility using fusions
• Standard operators can be defined
• Milner PRISMA Calculus is (essentially) Fusion
  Calculus

49
Comparison with parametric SHR

• The two frameworks are at the same level of
  abstraction
• SHR more apt as architectural model
• PRISMA Calculus more apt to experiment new
  primitives
• Can be enriched following standard process
  calculi techniques

50
Hints on technical difficulties

• In some SAMs (e.g., Hoare) a set of processes
  must interact to allow a synchronization on x
• All the processes
• All the processes that know x
• All the processes able to synchronize on x
• We have chosen the last approach

51
Roadmap

• Global computing
• Background on Synchronized Hyperedge Replacement
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

52
Observational semantics and compositionality

• Allows to have an abstract description of system
  behaviour
• Compositionality useful to
• Compute abstract behavior of the system from the
  behavior of the components
• Compute the behavior of a system when plugged in
  its execution environment
• Bisimilarity is a standard tool
• Bisimilarity is a congruence is a key property

53
Abstract semantics for parametric SHR

• Bisimulation can be defined in a standard way for
  SHR
• Under reasonable conditions on the SAM
  bisimilarity is a congruence for parametric SHR
• Milner, Hoare and many others satisfy the
  conditions
• Proof exploits bialgebraic techniques

54
Congruence results for Fusion Calculus

• Bisimilarity is not a congruence for Fusion
  Calculus (not closed under substitutions)
• The comparison with SHR shows why congruence
  fails and suggests how to solve the problem
• We have proposed a new concurrent semantics which
  is compositional

55
The idea of the semantics
56
The idea of the semantics

• Allowing many actions in the same transition but
  on different channels
• Process ab can execute a and b concurrently
  going to 0 (but can also execute either a or b)
• Process aa is bisimilar to a.a
• Process aab can perform t and b concurrently
  going to 0
• Allows to observe the degree of parallelism of a
  process

57
Congruence properties
58
Congruence properties

• no more a
  counterexample since the two terms are not
  bisimilar

59
Congruence properties

• no more a
  counterexample since the two terms are not
  bisimilar
• Observing where a synchronization is performed
  becomes important
• Otherwise congruence non preserved by context
  a-
• Actions at in addition to normal t

60
Observational semantics of PRISMA

• Hyperbisimilarity is a congruence
• Common axioms bisimulate for each SAM
• A translation along a morphism can be used to
  change the used SAM
• Some classes of translations preserve
  observational properties

61
Roadmap

• Global computing
• Background on Synchronized Hyperedge Replacement
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

62
Conclusions on SHR

• SHR is an interesting model for GC
• Deals well with distribution, synchronization,
  mobility
• Can be extended to deal with eterogeneity
• Good compositionality features have been proved
• Some extensions for dealing with non-functional
  requirements are under analysis Hirsch Tuosto
• Strong connections with process calculi
• Allow cross-fertilization

63
Conclusions on synchronization models

• Synchronization and mobility patterns are a
  dimension in the space of GC models
• Can be factored out
• Parametric models help the modeling phase
• Different SAMs can
• be composed
• interoperate

64
Conclusions on compositionality

• General and original result on compositionality
  for graph transformations
• Interesting result for Fusion Calculus
• Connection between concurrency and
  compositionality

65
Future work

• Further analysis required in many directions
• Exploiting the mappings for cross-fertilization
• Comparing SHR with other graph transformation
  frameworks
• Analyzing the properties of the new models
• Moving from Fusion towards p-calculus
• Techniques for proving compositionality

66
Future work

• Further analysis required in many directions
• Exploiting the mappings for cross-fertilization
• Milner logic programming
• Multiple synchronizations in process calculi
• Comparing SHR with other graph transformation
  frameworks
• Analyzing the properties of the new models
• Moving from Fusion towards p-calculus
• Techniques for proving compositionality

67
Future work

• Further analysis required in many directions
• Exploiting the mappings for cross-fertilization
• Comparing SHR with other graph transformation
  frameworks
• DPO
• Bigraphs
• Analyzing the properties of the new models
• Moving from Fusion towards p-calculus
• Techniques for proving compositionality

68
Future work

• Further analysis required in many directions
• Exploiting the mappings for cross-fertilization
• Comparing SHR with other graph transformation
  frameworks
• Analyzing the properties of the new models
• Concurrent Fusion
• PRISMA Calculus
• Moving from Fusion towards p-calculus
• Techniques for proving compositionality

69
Future work

• Further analysis required in many directions
• Exploiting the mappings for cross-fertilization
• Comparing SHR with other graph transformation
  frameworks
• Analyzing the properties of the new models
• Moving from Fusion towards p-calculus
• Concurrent p-calculus
• Parametric p-calculus
• Techniques for proving compositionality

70
Future work

• Further analysis required in many directions
• Exploiting the mappings for cross-fertilization
• Comparing SHR with other graph transformation
  frameworks
• Analyzing the properties of the new models
• Moving from Fusion towards p-calculus
• Techniques for proving compositionality
• Bialgebraic techniques difficult to apply

71
Bibliography of the thesis

• A Graphical Fusion Calculus, I. Lanese and U.
  Montanari, Proceedings of CoMeta Computational
  Metamodels Final Workshop, ENTCS 104
• Mapping Fusion and Synchronized Hyperedge
  Replacement into Logic Programming, I. Lanese
  and U. Montanari, TPLP, special issue, to appear
• Synchronization Algebras with Mobility for Graph
  Transformations, I. Lanese and U. Montanari,
  Proceedings of FGUC 2004 Workshop on
  Foundations of Global Ubiquitous Computing, ENTCS
  138
• Insights Emerged while Comparing Three Models
  for Global Computing, I. Lanese and U.
  Montanari, Proceedings of Dagstuhl seminar 05081
  on Foundations of Global Computing, Electronic
  proceedings, 2005
• Synchronized Hyperedge Replacement for
  Heterogeneus Systems, I. Lanese and E. Tuosto,
  Proceedings of COORDINATION 2005, LNCS 3454
• "Hoare vs Milner Comparing Synchronizations in a
  Graphical Framework with Mobility", I. Lanese and
  U. Montanari, Proceedings of GT-VC05, ENTCS
  154(2)

72
Other publications

• Software Architecture, Global Computing and
  Graph Transformation via Horn Clauses, I. Lanese
  and U. Montanari, Proceedings of SBES 2002 16th
  Brazilian Symposium on Software Engineering
• On Graph(ic) Encodings, R. Bruni and I. Lanese,
  Proceedings of Dagstuhl seminar 04241 on Graph
  transformations and process algebras for modeling
  distributed and mobile systems, Electronic
  proceedings, 2004
• New Insights on Architectural Connectors, R.
  Bruni, J. Fiadeiro, I. Lanese, A. Lopes and U.
  Montanari, Proceedings of IFIP TCS04, Kluwer
• Complete Axioms for Stateless Connectors, R.
  Bruni, I. Lanese and U. Montanari, Proceedings of
  CALCO05, LNCS 3629
• A Basic Algebra of Stateless Connectors, R.
  Bruni, I. Lanese and U. Montanari, TCS, to appear
• "Exploiting User-Definable Synchronizations in
  Graph Transformation",I. Lanese, Proceedings of
  GT-VMT'06, ENTCS, to appear

73
End of talk

• Thanks

• Questions?

74
Example
75
An example
y
y
C(x,y)?C(x,z),C(z,y)
C
C
x
z
C
x
rltwgt
y
y
C(r(x,w),r(y,w))?S(y,w)
C
S
w
x
x
rltwgt
76
Dynamics
S
S
S
77
Dynamics
S
S
S
78
Ideas on the derivation

• Each production poses some constraints on the
  features of the resulting channel
• During synchronization the constraints are
  composed according to the specified pattern
• The characteristics of the resulting channel are
  automatically computed