On the Expressiveness of Polyadicity in Higher-Order Process Calculi - - PowerPoint PPT Presentation

On the Expressiveness of Polyadicity in Higher-Order Process Calculi

Ivan Lanese, Jorge A. P´ erez, Davide Sangiorgi (Univ. di Bologna) Alan Schmitt (INRIA Grenoble - Rhˆ

• ne Alpes)

ICTCS’09 Cremona, September 2009

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 1 / 30

This Talk: Context

Theoretical Computer Science − → Concurrency Theory − → Process Calculi − → Calculi for Mobile Processes

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 2 / 30

Agenda

1

Motivation: Two Approaches for Mobility

2

Polyadic Communication

3

A Core Calculus for Higher-Order Concurrency

4

Polyadicity in Higher-Order Communication

5

Expressiveness Results

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 3 / 30

Roadmap

1

Motivation: Two Approaches for Mobility

2

Polyadic Communication

3

A Core Calculus for Higher-Order Concurrency

4

Polyadicity in Higher-Order Communication

5

Expressiveness Results

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 4 / 30

Motivation: Two Approaches for Mobility

Two agents, A and B, and a resource that A wants to share with B. They share a communication channel c:

PDF A B c c d p e

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 5 / 30

Motivation: Two Approaches for Mobility

Two agents, A and B, and a resource that A wants to share with B. They share a communication channel c:

PDF A B c c d p e

Two approaches for mobility: First-order (or name-passing) concurrency Higher-order (or process-passing) concurrency

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 5 / 30

Motivation: Two Approaches for Mobility

The first-order concurrency approach: send a link to the resource.

PDF A B c c d p e

(a) Before the interaction(s)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 6 / 30

Motivation: Two Approaches for Mobility

The first-order concurrency approach: send a link to the resource.

PDF A B c c d p e

(c) Before the interaction(s)

PDF A B c c d p e

(d) After the interaction(s)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 6 / 30

Motivation: Two Approaches for Mobility

The higher-order concurrency approach: send the resource.

PDF A B c c d p e

(e) Before the interaction(s)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

Motivation: Two Approaches for Mobility

The higher-order concurrency approach: send the resource.

PDF A B c c d p e

(g) Before the interaction(s)

PDF A B c c d p e PDF

(h) After the interaction(s)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

Motivation: Two Approaches for Mobility

The higher-order concurrency approach: send the resource.

PDF A B c c d p e

(i) Before the interaction(s)

PDF A B c c d p e PDF

(j) After the interaction(s)

Upon reception, B can do only two things with the resource:

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

Motivation: Two Approaches for Mobility

The higher-order concurrency approach: send the resource.

PDF A B c c d p e

(k) Before the interaction(s)

PDF A B c c d p e PDF

(l) After the interaction(s)

Upon reception, B can do only two things with the resource:

1

Execute it

2

Forward it

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 7 / 30

Higher-Order Process Calculi

Calculi in which processes can be communicated. Usual operators: parallel composition, input and output prefixes,

• restriction. Infinite behavior can be encoded.

As in the λ-calculus, computation involves term instantiation.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 8 / 30

Roadmap

1

Motivation: Two Approaches for Mobility

2

Polyadic Communication

3

A Core Calculus for Higher-Order Concurrency

4

Polyadicity in Higher-Order Communication

5

Expressiveness Results

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 9 / 30

Polyadic Communication

Communicating tuples of values in a single, atomic interaction

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

Polyadic Communication

Communicating tuples of values in a single, atomic interaction In the (first-order) π-calculus, monadic communication is expressive enough to encode polyadic communication.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

Polyadic Communication

Communicating tuples of values in a single, atomic interaction In the (first-order) π-calculus, monadic communication is expressive enough to encode polyadic communication.

◮ Let x(z1, . . . , zn). P and xa1, . . . , an. P represent input and

• utput prefixes in the π-calculus with n-adic communication.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

Polyadic Communication

Communicating tuples of values in a single, atomic interaction In the (first-order) π-calculus, monadic communication is expressive enough to encode polyadic communication.

◮ Let x(z1, . . . , zn). P and xa1, . . . , an. P represent input and

• utput prefixes in the π-calculus with n-adic communication.

◮ The translation [

[·] ] from polyadic to monadic processes: [ [xa1, . . . , an. P] ] = νw xw. wa1. · · · . wan. [ [P] ] [ [x(z1, . . . , zn). P] ] = x(w). w(z1). · · · . w(zn). [ [P] ] where [ [·] ] is an homomorphism for the other operators.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 10 / 30

Polyadic Communication

Features of [ [·] ]: Robustness with respect to interferences: The encoding relies on a private name that is known by sender and receiver Operational correspondence: One n-adic synchronization is represented as n + 1 monadic synchronizations:

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 11 / 30

Polyadic Communication

Features of [ [·] ]: Robustness with respect to interferences: The encoding relies on a private name that is known by sender and receiver Operational correspondence: One n-adic synchronization is represented as n + 1 monadic synchronizations:

◮ A visible synchronization that mimics the polyadic action ◮ n internal synchronizations on the private name w Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 11 / 30

This Talk

A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

This Talk

A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication. Context: A core calculus for higher-order concurrency.

◮ Only processes can be communicated. ◮ No links can be passed around. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

This Talk

A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication. Context: A core calculus for higher-order concurrency.

◮ Only processes can be communicated. ◮ No links can be passed around.

Main Result: encodings as in the first-order case do not exist

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

This Talk

A study of the expressive power of higher-order process calculi with respect to their ability to represent polyadic communication. Context: A core calculus for higher-order concurrency.

◮ Only processes can be communicated. ◮ No links can be passed around.

Main Result: encodings as in the first-order case do not exist

A hierarchy of strictly increasingly expressiveness

n-adic communication is strictly less expressive than n + 1-adic communication

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 12 / 30

Roadmap

1

Motivation: Two Approaches for Mobility

2

Polyadic Communication

3

A Core Calculus for Higher-Order Concurrency

4

Polyadicity in Higher-Order Communication

5

Expressiveness Results

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 13 / 30

Hocore: a calculus for higher-order concurrency

P, Q ::= aP

• utput

|

a(x). P input prefix

|

x process variable

|

P Q parallel composition

|

nil

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 14 / 30

Hocore: a calculus for higher-order concurrency

P, Q ::= aP

• utput

|

a(x). P input prefix

|

x process variable

|

P Q parallel composition

|

nil No name passing is allowed. No output prefix: asynchronous calculus. No restriction operator

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 14 / 30

Hocore: a calculus for higher-order concurrency

P, Q ::= aP

• utput

|

a(x). P input prefix

|

x process variable

|

P Q parallel composition

|

nil No name passing is allowed. No output prefix: asynchronous calculus. No restriction operator

◮ Every communication is public. Behavior is exposed. ◮ Dynamic creation of channels is impossible. Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 14 / 30

Main Results for Hocore

[Lanese, P´ erez, Sangiorgi, Schmitt – LICS’08]

Hocore is Turing complete In Hocore, strong bisimilarity is decidable and coincides with a number of behavioral equivalences (including barbed congruence)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 15 / 30

Main Results for Hocore

[Lanese, P´ erez, Sangiorgi, Schmitt – LICS’08]

Hocore is Turing complete In Hocore, strong bisimilarity is decidable and coincides with a number of behavioral equivalences (including barbed congruence)

[Di Giusto, P´ erez, Zavattaro – ICTAC’09]

When communication objects have a “flat” structure based on parallel composition: Termination becomes decidable Convergence remains undecidable

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 15 / 30

Roadmap

1

Motivation: Two Approaches for Mobility

2

Polyadic Communication

3

A Core Calculus for Higher-Order Concurrency

4

Polyadicity in Higher-Order Communication

5

Expressiveness Results

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 16 / 30

Name Passing and Process Passing

Sending a process does not imply sending the names it contains

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 17 / 30

Name Passing and Process Passing

Sending a process does not imply sending the names it contains To the receiver, every received process is a black box, that can

• nly be forwarded or executed

(We can’t “extract” the names contained in a process.)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 17 / 30

Name Passing and Process Passing

Sending a process does not imply sending the names it contains To the receiver, every received process is a black box, that can

• nly be forwarded or executed

(We can’t “extract” the names contained in a process.) Names sent as part of processes cannot be used by the receiver

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 17 / 30

Name Passing and Process Passing

Sending a process does not imply sending the names it contains To the receiver, every received process is a black box, that can

• nly be forwarded or executed

(We can’t “extract” the names contained in a process.) Names sent as part of processes cannot be used by the receiver

Process-passing only cannot represent name-passing

Two agents cannot reach an agreement on a (private) name An encoding of polyadic into monadic communication might not exist in a process-passing setting

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 17 / 30

A variant of Hocore

In what follows, we consider HOm The synchronous variant of Hocore, with polyadicity m ≥ 1 I.e. given an m-tuple R, a

• R. P is a valid process

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 18 / 30

A variant of Hocore

In what follows, we consider HOm The synchronous variant of Hocore, with polyadicity m ≥ 1 I.e. given an m-tuple R, a

• R. P is a valid process

Extended with the construct νr P It allows to define a name r private to the scope of P.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 18 / 30

Roadmap

1

Motivation: Two Approaches for Mobility

2

Polyadic Communication

3

A Core Calculus for Higher-Order Concurrency

4

Polyadicity in Higher-Order Communication

5

Expressiveness Results

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 19 / 30

Expressiveness in A Nutshell

Encoding

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 20 / 30

Expressiveness in A Nutshell

Encoding A translation plus some properties/criteria

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 20 / 30

Expressiveness in A Nutshell

Encoding A translation plus some properties/criteria Criteria include syntactic and semantic considerations

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 20 / 30

Expressiveness in A Nutshell

Encoding A translation plus some properties/criteria Criteria include syntactic and semantic considerations No agreement on how a “good” encoding should be. Many suitable criteria —an open research problem.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 20 / 30

Expressiveness in A Nutshell

Encoding A translation plus some properties/criteria Criteria include syntactic and semantic considerations No agreement on how a “good” encoding should be. Many suitable criteria —an open research problem. One says that language A is more expressive than language B if

◮ an encoding [

[·] ] : B → A exists

◮ but an encoding [

[·] ] : A → B doesn’t —an impossibility result

For impossibility results, one seeks the most relaxed criteria possible —this is to ensure generality.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 20 / 30

Our Notion of Encoding (Informally)

Follows standard proposals excepting... Synchronizations on public names are considered visible actions. Example:

• aT. P a(x). Q

aτ

− − → P Q{T/x} Visible action

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 21 / 30

Our Notion of Encoding (Informally)

Follows standard proposals excepting... Synchronizations on public names are considered visible actions. Example:

• aT. P a(x). Q

aτ

− − → P Q{T/x} Visible action νr (rT. P r(x). Q)

τ

− − → νr (P Q{T/x}) Internal action

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 21 / 30

Our Notion of Encoding (Informally)

Follows standard proposals excepting... Synchronizations on public names are considered visible actions. Example:

• aT. P a(x). Q

aτ

− − → P Q{T/x} Visible action νr (rT. P r(x). Q)

τ

− − → νr (P Q{T/x}) Internal action A visible action in the source language has to be matched by exactly one visible action in the target language, possibly surrounded by zero or more internal actions (as above)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 21 / 30

Our Notion of Encoding (Formally)

Language: processes, behavioral equivalence, semantics. L = (P, ≈, − →)

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 22 / 30

Our Notion of Encoding (Formally)

Language: processes, behavioral equivalence, semantics. L = (P, ≈, − →) Translation: Injective function from a source language Ls into a target language Lt.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 22 / 30

Our Notion of Encoding (Formally)

An encoding is a translation [ [·] ] from Ls into Lt that satisfies:

1

Compositionality: given an operator op, and a set of names N [ [op(S1, . . . , Sk)] ] = C N

• p[[

[S1] ], . . . , [ [Sk] ]].

2

Name invariance: if [ [σ(P)] ] = σ([ [P] ]), for any injective permutation

• f names σ.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 23 / 30

Our Notion of Encoding (Formally)

An encoding is a translation [ [·] ] from Ls into Lt that satisfies:

1

Compositionality: given an operator op, and a set of names N [ [op(S1, . . . , Sk)] ] = C N

• p[[

[S1] ], . . . , [ [Sk] ]].

2

Name invariance: if [ [σ(P)] ] = σ([ [P] ]), for any injective permutation

• f names σ.

3

Completeness: ∀S, S′ ∈ Ps such that S

α

= ⇒s S′, it holds that [ [S] ]

α

= ⇒t ≈t [ [S′] ]

4

Soundness: ∀S ∈ Ps, T ∈ Pt such that [ [S] ]

α

= ⇒t T there exists an S′ ∈ Ps such that both S

α

= ⇒s S′ and T

α

= ⇒t≈t [ [S′] ].

5

Adequacy: if P ≈s Q then [ [P] ] ≈t [ [Q] ].

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 23 / 30

Impossibility Results

Using this notion of encoding, we have shown an impossibility result that characterizes an expressiveness hierarchy

Theorem (Generalized case)

For every n > 0, there is no encoding of HOn+1 into HOn.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 24 / 30

Impossibility Results

Using this notion of encoding, we have shown an impossibility result that characterizes an expressiveness hierarchy

Theorem (Generalized case)

For every n > 0, there is no encoding of HOn+1 into HOn.

Key of the proof: Disjoint Forms

The fact that the set of private names of a process remains invariant along higher-order interactions That is, a process cannot “obtain” new private names through communication As such, a sender and a receiver can’t agree on a name for safe communication

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 24 / 30

Disjoint Forms

Intuition: Consider two processes P and Q which do not share private names

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 25 / 30

Disjoint Forms

Intuition: Consider two processes P and Q which do not share private names T = ν n(a

• R. P) a(x). Q

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 25 / 30

Disjoint Forms

Intuition: Consider two processes P and Q which do not share private names T = ν n(a

• R. P) a(x). Q

aτ

− − → ν n(P C[ R]) = T ′

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 25 / 30

Disjoint Forms

Intuition: Consider two processes P and Q which do not share private names T = ν n(a

• R. P) a(x). Q

aτ

− − → ν n(P C[ R]) = T ′ In T ′, the names of P and R are disjoint wrt those of context C.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 25 / 30

Disjoint Forms

Intuition: Consider two processes P and Q which do not share private names T = ν n(a

• R. P) a(x). Q

aτ

− − → ν n(P C[ R]) = T ′ In T ′, the names of P and R are disjoint wrt those of context C.

Definition (Disjoint Form)

Let T ≡ ν n(P C[ R]) be a HOm process where

1

n is a set of names such that n ⊆ fn(P, R) and n ∩ fn(C) = ∅;

2

C is a k-ary (multihole) context;

3

• R contains k guarded, closed processes.

Then T is in k-adic disjoint form with respect to n, R, and P.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 25 / 30

Properties of Disjoint Forms

Disjoint forms are preserved by Internal actions Output actions that do not extrude names The definition of encoding

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 26 / 30

The base case of the hierarchy

Theorem (Biadic case)

There is no encoding of HO2 into HO1. Proof Sketch. By contradiction.

1

Suppose an encoding [ [·] ] : HO2 → HO1 indeed exists.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 27 / 30

The base case of the hierarchy

Theorem (Biadic case)

There is no encoding of HO2 into HO1. Proof Sketch. By contradiction.

1

Suppose an encoding [ [·] ] : HO2 → HO1 indeed exists.

2

Take a HO2 process P whose behavior depends on private names

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 27 / 30

The base case of the hierarchy

Theorem (Biadic case)

There is no encoding of HO2 into HO1. Proof Sketch. By contradiction.

1

Suppose an encoding [ [·] ] : HO2 → HO1 indeed exists.

2

Take a HO2 process P whose behavior depends on private names

3

Show that [ [P] ] eventually becomes a disjoint form

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 27 / 30

The base case of the hierarchy

Theorem (Biadic case)

There is no encoding of HO2 into HO1. Proof Sketch. By contradiction.

1

Suppose an encoding [ [·] ] : HO2 → HO1 indeed exists.

2

Take a HO2 process P whose behavior depends on private names

3

Show that [ [P] ] eventually becomes a disjoint form

4

Since the behavior of P depends on internal actions, and [ [P] ] is not able to acquire new private names, it fails to represent the behavior of P faithfully

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 27 / 30

The base case of the hierarchy

Theorem (Biadic case)

There is no encoding of HO2 into HO1. Proof Sketch. By contradiction.

1

Suppose an encoding [ [·] ] : HO2 → HO1 indeed exists.

2

Take a HO2 process P whose behavior depends on private names

3

Show that [ [P] ] eventually becomes a disjoint form

4

Since the behavior of P depends on internal actions, and [ [P] ] is not able to acquire new private names, it fails to represent the behavior of P faithfully

5

As a result, the operational correspondence between P and [ [P] ] is broken: contradiction.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 27 / 30

The Expressiveness Hierarchy

We have seen an outline of the proof for the biadic-monadic case. All the notions and properties extend to the n-adic case.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 28 / 30

The Expressiveness Hierarchy

We have seen an outline of the proof for the biadic-monadic case. All the notions and properties extend to the n-adic case. Hence, we have

Theorem (Generalized case)

For every n > 0, there is no encoding of HOn+1 into HOn.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 28 / 30

Concluding Remarks

Process-passing is not enough to model effective name passing Protocols based on agreeing upon a distinguished name might not be faithfully modeled

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 29 / 30

Concluding Remarks

Process-passing is not enough to model effective name passing Protocols based on agreeing upon a distinguished name might not be faithfully modeled We studied a particular protocol, aimed at representing polyadic communication with monadic one.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 29 / 30

Concluding Remarks

Process-passing is not enough to model effective name passing Protocols based on agreeing upon a distinguished name might not be faithfully modeled We studied a particular protocol, aimed at representing polyadic communication with monadic one. The same idea could be applied to other protocols.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 29 / 30

Concluding Remarks

Process-passing is not enough to model effective name passing Protocols based on agreeing upon a distinguished name might not be faithfully modeled We studied a particular protocol, aimed at representing polyadic communication with monadic one. The same idea could be applied to other protocols. The proof relies on characterizing the conditions under which private names remain invariant along interactions.

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 29 / 30

Thanks!

References On the Expressiveness and Decidability of Higher-Order Process Calculi In Proc. of LICS 2008. IEEE Computer Society, 2008. On the Expressiveness of Forwarding in Higher-Order Communication In Proc. of ICTAC 2009, Springer, 2009. Separation Results for Higher-Order Process Calculi Forthcoming Technical Report, UNIBO, 2009.

More info on Hocore (new results, extended versions): www.cs.unibo.it/~perez/hocore

Jorge A. P´ erez (Univ. di Bologna) Polyadicity in Higher-Order Concurrency ICTCS’09 30 / 30