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
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

3
Roadmap

• Global computing
• 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
• Heterogeneity
• Interoperability, coordination
• Mobility
• Openness
• Reconfigurability
• Non-functional requirements

6
Formal methods for GC

• Building models of the system
• Old aims
• Concentrate on a particular aspect
• Abstract from details
• Analyze the properties of the system before
  building it
• 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
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

9
Why comparing models?

• Different models for GC exist
• Process calculi, graphs, UML, categorical models
• 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

10
Which comparisons?

• N models ? 2N comparisons
• Must select some representatives
• Show at a first sight some interesting
  connections
• We have chosen
• Logic programming
• A graph transformation framework SHR
• A process calculus Fusion Calculus

11
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

12
Long background on SHR
13
Very short background on SHR

• Graph transformation formalism
• Productions specify the behaviour of edges
• Synchronization via actions on common nodes
• Hoare, Milner
• Mobility by creating, sending and merging nodes

14
Fusion Calculus

• Calculus for mobility inspired by p-calculus
• Input prefix is not a binder
• When input and output interact a name fusion is
  generated
• The scope of the fusion is determined by an
  explicit scope operator
• Symmetric input/output
• Arbitrary fusions allowed
• Input of p-calculus obtained as inputscope
• Not fully abstract since more powerful contexts
  are available

15
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
• No nested functions
• Transactional application of many clauses
• Exploits function symbols for synchronization
• Similar to tokens in zero-places of zero-safe nets

16
Summary of the comparison

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

17
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
18
Dynamics
S
S
S
19
Dynamics
S
S
S
20
Main results

• Simple (homomorphic) mapping
• Complete correspondance
• Suggests how to introduce restriction in logic
  programming
• What about Milner logic programming?

21
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

22
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.

23
Example
We can also execute both the steps at the same
time
24
Main results

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

25
Milner vs Hoare

• Surprisingly the most difficult step
• Simulating Hoare using Milner
• Must implement n-ary synchronization using binary
  synchronization
• Simulating Milner using Hoare
• Milner synchronization is asymmetric
• In Milner restriction affects the behaviour, in
  Hoare just the observation

26
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
• Not a problem in 2-shared graphs

27
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 system

28
Roadmap

• Global computing
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

29
Synchronization Algebras with Mobility (1)

• 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, treshold
  synchronization

30
Synchronization Algebras with Mobility (2)
31
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

32
Sample synchronization
a
b
c
33
Milner SAM

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

34
Combining SAMs

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

35
Parametric SHR

• The SAM is a parameter of the model
• 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

36
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

37
Take-off transition
univ
univ
chk
inPl
inBo
chk
inPl
38
Specifying the transition (1)
atlte,ltgtgt
inltack,ltatgtgt
atltreq,ltnewatgtgt
chk ltbreq,ltingtgt
inlte,ltgtgt
39
Specifying the transition (2)
atlte,ltgtgt
chk ltbrd,ltnewatgtgt
40
Synchronization in the example
e,ltgt
univ

• Can be obtained using as SAM
• the coproduct of
• Milner SAM for req and ack
• Broadcast SAM for breq and brd

ack,ltunivgt
inBo
e,ltgt
e,ltgt
req,ltnewatgt
e,ltgt
brd,ltnew1gt
breq,ltinPlgt
chk
e,ltgt
brd,ltnew2gt
inPl
41
Effects of the synchronization
e
univ
inBo
t
univ/newat
breq,ltinPlgt
chk
e
inPl/new1,inPl/new2
inPl
42
Result of the transition
univ
chk
inBo
inPl
43
Heterogeneous SHR

• Allows to use different SAMs on different nodes
• Concentrates on dynamic management of SAMs
• SAMs are required to form a commutative monoid
• Node fusions cause SAM composition
• Allows to model heterogeneous systems
• Different primitives in different parts of the
  system
• Example wireless connections with broadcast and
  wired connections with Milner
• Conservative extension of parametric SHR

44
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

45
Modeling the scenario

• Eight different SAMs with all the combinations of
• 4Kb lt 16Kb
• No error detection lt error detection
• Communication lt control
• SAMs provide variants of Milner synchronization
• E.g. action for detecting errors
• SAMs form a partial order (pointwise)
• SAM composition corresponds to glb

46
Building a virtual channel
R
C
4,v
Act
R
16,
16,v
4,
16,v
4,v
C
Act
16,
R
R
47
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

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 included
• Milner PRISMA Calculus is (essentially) Fusion
  Calculus

49
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

50
Roadmap

• Global computing
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

51
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

52
Congruence results for Fusion Calculus

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

53
The idea of the semantics
54
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

55
Congruence properties
56
Congruence properties

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

57
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
• The resulting bisimilarity is a congruence

58
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
• Translations along isomorphisms preserve
  bisimilarity

59
Roadmap

• Global computing
• Comparing models for GC
• Parametric synchronizations with mobility
• Observational semantics and compositionality
• Conclusions

60
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

61
Conclusions on synchronization models

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

62
Conclusions on compositionality

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

63
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

64
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

65
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

66
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

67
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

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
• Moving from Fusion towards p-calculus
• Techniques for proving compositionality
• Bialgebraic techniques requires complex semantics

69
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, to
  appear

70
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

71
End of talk

• Thanks

• Questions?