A Denotational Study of Mobility Jo el-Alexis Bialkiewicz and Fr - PowerPoint PPT Presentation

Basics: Locations Mobility Equivalence & Refinement A Denotational Study of Mobility Jo¨ el-Alexis Bialkiewicz and Fr´ ed´ eric Peschanski November 2, 2009 J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 1 / 16

Basics: Locations Mobility Equivalence & Refinement Introduction Two Main Points of View on Modelling Processes Operational POV ( π -calculus. . . ) Low level, double-edged: easy mobility but difficult to abstract unsettled theory so many variants issues with compositionality: bound prefixes and guards denotations exist but not practical Denotational POV (CSP) denotational (tr, fail, div) and compositional by design supports refinement but no easy way to account for mobility Our Approach: Mobility in a Denotational Way Heavily inspired by CSP but integrated model (decorated traces) π -like mobility but compositional = ⇒ fully denotational model Support for refinement J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 2 / 16

Basics: Locations Mobility Equivalence & Refinement Introduction Two Main Points of View on Modelling Processes Operational POV ( π -calculus. . . ) Low level, double-edged: easy mobility but difficult to abstract unsettled theory so many variants issues with compositionality: bound prefixes and guards denotations exist but not practical Denotational POV (CSP) denotational (tr, fail, div) and compositional by design supports refinement but no easy way to account for mobility Our Approach: Mobility in a Denotational Way Heavily inspired by CSP but integrated model (decorated traces) π -like mobility but compositional = ⇒ fully denotational model Support for refinement J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 2 / 16

Basics: Locations Mobility Equivalence & Refinement Outline 1 Basics: Locations 2 Mobility 3 Equivalence & Refinement J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 3 / 16

Basics: Locations Mobility Equivalence & Refinement Outline 1 Basics: Locations 2 Mobility 3 Equivalence & Refinement J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 4 / 16

Basics: Locations Mobility Equivalence & Refinement Representing Behaviours The problem Full representation of behaviour? branching structure (LTS) Set of process traces: information lost Traces + failures,divergences: hard to introduce mobility What we wanted Traces but with as much information as the LTS How: link observations to where and when in LTS = ⇒ locations ! LTS can be rebuilt from decorated traces: no information lost J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 5 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) What does this process do? Behaviour LTS Traces coin ? button 1? coin ? { � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } out ! coffee J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) What does this process do? Behaviour LTS Traces coin ? button 1? coin ? { � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } out ! coffee J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) What does this process do? Behaviour LTS Traces coin ? button 1? coin ? { � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } out ! coffee J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) What does this process do? Behaviour LTS Traces coin ? button 1? coin ? { � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } out ! coffee J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) What does this process do? Behaviour LTS Traces coin ? button 1? coin ? { � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } out ! coffee J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) What does this process do? Behaviour LTS Traces coin ? button 1? coin ? { � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } out ! coffee J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) What does this process do? Behaviour LTS Traces coin ? button 1? coin ? { � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } out ! coffee J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Basic Example The basics Observation (::location): input channel ? output channel ! value , or � ⋄ j Location: origin: ǫ , next: ⊲ and choice: ⋄ number of branches , weak variants � ⊲ and � branch number i Process ( not mobile) coin ? . ( button 1? . out ! tea + coin ? . button 2? . out ! coffee ) Which locations why? What is an absolute location? Behaviour LTS Traces ǫ coin ? ⊲ button 1? coin ? { ⋄ 2 ⋄ 2 � coin ?:: ⊲, button 1?:: ⋄ 2 1 , out ! tea :: ⊲ � , 1 2 � coin ?:: ⊲, coin ?:: ⋄ 2 2 , button 2?:: ⊲, out ! coffee :: ⊲ � out ! tea button 2? } ⊲ ⊲ out ! coffee ⊲ J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 6 / 16

Basics: Locations Mobility Equivalence & Refinement Outline 1 Basics: Locations 2 Mobility 3 Equivalence & Refinement J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 7 / 16

Basics: Locations Mobility Equivalence & Refinement About Mobility Physical vs Logical Mobility A process is mobile if it changes neighbours How Can a Process Change Neighbours? ν d ν c c c A B d C J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 8 / 16

Basics: Locations Mobility Equivalence & Refinement About Mobility Physical vs Logical Mobility A process is mobile if it changes neighbours How Can a Process Change Neighbours? ν d ν c c c A B d C J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 8 / 16

Basics: Locations Mobility Equivalence & Refinement About Mobility Physical vs Logical Mobility A process is mobile if it changes neighbours How Can a Process Change Neighbours? ν d ν c c c d A B d C J.-A. Bialkiewicz and F. Peschanski A Denotational Study of Mobility 8 / 16