Concurrent and located synchronizations in p-calculus

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Concurrent and located synchronizationsin
p-calculus
Ivan Lanese Computer Science Department University
of Bologna Italy
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Roadmap

• Process calculi
• The standard semantics of p-calculus
• A new located semantics
• A new concurrent semantics
• Conclusions

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Roadmap

• Process calculi
• The standard semantics of p-calculus
• A new located semantics
• A new concurrent semantics
• Conclusions

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Process calculi

• Behavioral models of concurrent interacting
  systems
• Useful to analyze the properties of systems
  before building them
• System satisfies some properties
• Equivalence of different implementations
• Correctness of optimizations
• Systems modeled as terms in a suitable algebra
• Constants for basic behaviours
• Operators of composition (parallel composition,
  declaration of a resource, )

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Operational semantics

• Allows to describe system behaviour
• Two styles reduction semantics and labelled
  semantics
• Reduction semantics
• Describes the evolution of a closed system
• Easy to use and understand
• Rules of the form
• Labelled semantics
• Describes the interactions between the system and
  the environment
• Useful to describe open systems and analyze
  properties
• Rules of the form

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Bisimilarity

• Equivalence relation
• Abstracts from internal details
• Equates systems indistinguishable from the
  outside
• Built on top of a reduction or a labelled
  semantics
• Two processes are bisimilar if one can simulate
  the other (do the same actions going to bisimilar
  processes) and vice versa
• Using reductions requires also context closure
• More distinguishing than trace equivalence
• Bisimilarity is compositional if preserved by
  contexts
• Known as bisimilarity is a congruence property
• Allows to substitute bisimilar processes without
  changing the behaviour (e.g., optimization)

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Which calculus?

• Different process calculi have been proposed,
  focused on different aspects (locations,
  cryptography, wireless communication, )
• We choose the p-calculus
• Apt to model distributed mobile systems in an
  easy way
• Used both in academia and industry
• Basis for BPEL
• Easy to extend to deal with different features
  (spi, dPi, stochastic pi, )

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Roadmap

• Process calculi
• The standard semantics of p-calculus
• A new located semantics
• A new concurrent semantics
• Conclusions

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p-calculus syntax

• Names a,b,x, represent communication channels
• Channel names are the only data
• Enough to encode booleans, integers,

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p-calculus reductions

• is an equivalence relation stating basic
  properties (e.g., parallel composition is
  associative and commutative)

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Example
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Example
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Example
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p-calculus labelled semantics
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Observations on the standard semantics

• The semantics shows inputs, outputs, and
  synchronizations (t)
• All the synchronizations are equal
• On a restricted or on a free channel
• All free channels are equal
• At each step exactly one action is performed
• Concurrency indistinguishable from interleaving
• We want to change these assumptions

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The ideas of our approach

• Many works considered locations and concurrency
  in p-calculus
• Locations explicitly added lP
• Concurrency using mappings to other formalisms
  (Petri nets, graphs, ) or complex algebraic
  structures (event structures, )
• We want to analyze what can be done without
  changing the framework
• Standard p-calculus syntax
• Direct semantics using standard labelled and
  reduction style
• Trying to preserve the good properties of the
  standard framework

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Roadmap

• Process calculi
• The standard semantics of p-calculus
• A new located semantics
• A new concurrent semantics
• Conclusions

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Located synchronizations

• We want to see where a synchronization is
  performed
• Different channels can have different properties
• Accounting
• Security policies

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p-calculus located reductions

• We need labels also for reductions
• Labels show which (free) channel is used

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Properties of the located semantics

• Can be expressed also using the labelled
  semantics
• Label at for a synchronization on free channel a
• Label t for a synchronization on a hidden channel
• Full correspondance between reduction and
  labelled semantics
• Reductions correspond to labelled
  synchronizations
• They induce the same bisimilarity
• Closure under substitutions needed for labelled
  semantics

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Located bisimilarity

• Located bisimilarity refines standard one

• but

• This allows to observe which channels are used
• For instance we can distinguish between
  communication on a local network (free, safe)
  from communication via Internet (under
  accounting, unsafe)

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Roadmap

• Process calculi
• The standard semantics of p-calculus
• A new located semantics
• A new concurrent semantics
• Conclusions

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Concurrent synchronizations

• We want to see which actions can be performed
  concurrently
• Actions can be executed concurrently provided
  that
• they are performed by different sequential
  processes
• they are executed on different channels
• One concurrent transition corresponds to one or
  more located transitions

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p-calculus concurrent reductions

• Labels contain the set of used channels

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Properties of the concurrent semantics

• Can be expressed also using the labelled
  semantics
• Labels are (essentially) multisets of located
  labels
• Full correspondance between reduction and
  labelled semantics
• Reductions correspond to labelled
  synchronizations
• They induce the same bisimilarity

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Concurrent bisimilarity

• Concurrent bisimilarity refines the located one

• but

• This allows to distinguish concurrency from
  nondeterminism
• Actions on the same channel are sequentialized

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Compositionality

• Concurrent bisimilarity is a congruence
• This allows compositional reasoning about system
  behaviour
• Bisimilar subcomponents can be substituted one
  for the other
• This property does not hold for standard or
  located semantics
• Standard and located bisimilarity not preserved
  by contexts that perform substitutions

• but

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Roadmap

• Process calculi
• The standard semantics of p-calculus
• A new located semantics
• A new concurrent semantics
• Conclusions

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Conclusions

• Two new semantics for p-calculus highlighting
• where synchronizations are performed
• which synchronizations can be performed
  concurrently
• The semantics capture these behaviours
• More expressive power
• Many good properties of standard semantics are
  preserved by the extensions
• Correspondance between reduction and labelled
  semantics
• Bisimilarities refine standard one
• Additional property concurrent bisimilarity is
  compositional

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Future work

• Further analysis on the new semantics
• Weak semantics (first results in the paper)
• Analysis techniques
• Applications
• Looking for semantics in the same style for other
  calculi
• Analysing the effects of more concurrency
• What happens if many actions are allowed on the
  same channel?

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End of talk

• Thanks!

• Questions?