## On the expressiveness of linearity vs persistence in the asychronous pi-calculus (2006)

### Cached

### Download Links

- [www.lix.polytechnique.fr]
- [www.lix.polytechnique.fr]
- [www.lix.polytechnique.fr]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proc. of LICS’06. IEEE Computer Society |

Citations: | 8 - 2 self |

### BibTeX

@INPROCEEDINGS{Palamidessi06onthe,

author = {Catuscia Palamidessi and Frank D. Valencia},

title = {On the expressiveness of linearity vs persistence in the asychronous pi-calculus},

booktitle = {In Proc. of LICS’06. IEEE Computer Society},

year = {2006},

pages = {59--68},

publisher = {IEEE Computer Society}

}

### OpenURL

### Abstract

We present an expressiveness study of linearity and persistence of processes. We choose the π-calculus, one of the main representatives of process calculi, as a framework to conduct our study. We consider four fragments of the π-calculus. Each one singles out a natural source of linearity/persistence also present in other frameworks such as Concurrent Constraint Programming (CCP), Linear CCP, and several calculi for security. The study is presented by providing (or proving the non-existence of) encodings among the fragments, a processes-as-formulae interpretation and a reduction from Minsky machines. 1

### Citations

1000 | A calculus of mobile processes
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...e non-existence of) encodings among the fragments, a processes-as-formulae interpretation and a reduction from Minsky machines. 1 Introduction Several process calculi such as CCS, CSP, the π-calculus =-=[15]-=- and Linear CCP [8, 23] have an obvious source of linearity: Messages (or senders) are consumed upon being received. For example, in the π-calculus, the system x〈z〉 | x(y).P | x(y).Q (1) represents a ... |

588 |
Communicating and Mobile Systems: The π-Calculus
- Milner
- 1999
(Show Context)
Citation Context ... v0, v1 into Pπ, [Ms(v0, v1)], is given below, with the encoding of non-negative numbers in counter c, [(n)]c. The counter values are encoded in a standard fashion (similar to the persistent lists in =-=[14]-=-), and each location Li corresponds to a fresh name li over which the current counter values are passed. Where ever lj〈c, cn⊕1〉 appears, order the objects correctly based on n (⊕ denotes addition modu... |

458 |
L.: Computation: Finite and Infinite Machines
- Minsky
- 1967
(Show Context)
Citation Context ...n this section we show that despite such an impossibility result Pπ is Turing-powerful. We do this by encoding two-counter machines, also called Minsky machines, which are known to be Turing-powerful =-=[16]-=-. Minsky Machines. A two-counter Minsky machine is an imperative program consisting of a sequence of labelled instructions I1; . . . ; Ik which modify the values of two nonnegative counters c0 and c1.... |

440 |
The ⇡-calculus: a Theory of Mobile Processes
- Sangiorgi, Walker
- 2001
(Show Context)
Citation Context ... on channel x. However, in the context of the asynchronous π-calculus in defining the process equivalences it is standard to restrict the observables to be the output barbs; i.e., barbs of the form x =-=[21]-=-. We begin with a basic π process equivalence, sometimes referred to as barbed correspondence [17], which equates processes iff they exhibit the same barbs. In what follows we prefer to refer to this ... |

437 | Concurrent Constraint Programming
- Saraswat, Rinard
- 1990
(Show Context)
Citation Context ...h follow a different pattern: Messages cannot be consumed; they are persistent rather than linear. One of the most prominent representatives of such calculi is Concurrent Constraint Programming (CCP) =-=[22]-=-. In this framework all messages, more precisely items of information, are accumulated in a global store. The messages in the store can be read but, unlike in Linear CCP, they cannot be consumed, i.e.... |

267 |
The classical decision problem
- Borger, Gradel, et al.
- 1997
(Show Context)
Citation Context ..., to the validity of a formula which is in the class of either Bernays-Schönfinkel, Gödel, two-variables, or Monadic FOL formulae without function symbols. All these classes of formulae are decidable =-=[5]-=-. Decidable Classes with Mobility. Let us illustrate briefly the name extrusion capabilities of the “mobile” classes in the above lemma. It is important to recall that input and restriction binders ar... |

140 | On reduction-based process semantics
- Honda, Yoshida
- 1995
(Show Context)
Citation Context ...t be consumed. Properties of [·] : π → PIπ. Our encoding is ideal w.r.t barbed congruence. The proof uses a fundamental property of asynchronous π: Forwarders are barbed congruent to the null process =-=[10]-=-; i.e. !x(�y).x〈�y〉 ≈ 0. Lemma 5.2. Let [·] : π → PIπ be the encoding in Definition 5.1. For every P , [P ] ≈ π P holds. From the above lemma, we get full abstraction w.r.t barbed congruence.sTheorem ... |

76 |
On the symbolic reduction of processes with cryptographic functions
- Amadio, Lugiez, et al.
(Show Context)
Citation Context ...e found in the context of calculi for analyzing and describing security protocols. For instance, Crazzolara and Winskel’s SPL [7], the Spi Calculus variants by Fiore and Abadi [9] and by Amadio et al =-=[1]-=-, and the calculus of Boreale and Buscemi [4] are all operationally defined in terms of configurations containing items of information (messages) which cannot be consumed during evolution. The idea is... |

65 | 2000): What Is a ‘Good’ Encoding of Guarded Choice
- Nestmann
(Show Context)
Citation Context ...valences it is standard to restrict the observables to be the output barbs; i.e., barbs of the form x [21]. We begin with a basic π process equivalence, sometimes referred to as barbed correspondence =-=[17]-=-, which equates processes iff they exhibit the same barbs. In what follows we prefer to refer to this equivalence as output equivalence since we only consider output barbs. Recall that a process conte... |

59 | The name discipline of uniform receptiveness
- Sangiorgi
- 1999
(Show Context)
Citation Context ...nother source of linearity in (1): Receivers can also be consumed. For example, in the case in which x(y).P evolves into P {z/y}. Persistent receivers arise, e.g. in the notion of omega receptiveness =-=[20]-=- where the input of a name is always available—but always with the same continuation. In the π-calculus persistent receivers are used, for instance, to model functions, objects, higher-order communica... |

59 | Graph types for monadic mobile processes
- Yoshida
- 1996
(Show Context)
Citation Context ...0 and Q = x.0 | x.0. Clearly, P ≈ Q. Let Ct =!x〈n〉 | !x〈m〉 | !n( r t f ).!m( r ′ t ′ f ′ ).!t. Verify that (Ct | [Q]) ⇓ t but (Ct | [P ]) �⇓ t . Hence, [P ] �≈ [Q]. Nevertheless following the work of =-=[19, 24]-=-, we believe we can provide a type system in order to give a stronger correspondence for the encoding. The type system would allow contexts that may not behave as dictated by the protocol but do not i... |

58 | Events in security protocols
- Crazzolara, Winskel
- 2001
(Show Context)
Citation Context ...rn.victor@it.uu.se Several other frameworks using a persistent store can be found in the context of calculi for analyzing and describing security protocols. For instance, Crazzolara and Winskel’s SPL =-=[7]-=-, the Spi Calculus variants by Fiore and Abadi [9] and by Amadio et al [1], and the calculus of Boreale and Buscemi [4] are all operationally defined in terms of configurations containing items of inf... |

56 | Computing symbolic models for verifying cryptographic protocols
- Fiore, Abadi
- 2001
(Show Context)
Citation Context ...a persistent store can be found in the context of calculi for analyzing and describing security protocols. For instance, Crazzolara and Winskel’s SPL [7], the Spi Calculus variants by Fiore and Abadi =-=[9]-=- and by Amadio et al [1], and the calculus of Boreale and Buscemi [4] are all operationally defined in terms of configurations containing items of information (messages) which cannot be consumed durin... |

31 | Linear concurrent constraint programming: Operational and phase semantics
- Fages, Ruet, et al.
- 2001
(Show Context)
Citation Context ...encodings among the fragments, a processes-as-formulae interpretation and a reduction from Minsky machines. 1 Introduction Several process calculi such as CCS, CSP, the π-calculus [15] and Linear CCP =-=[8, 23]-=- have an obvious source of linearity: Messages (or senders) are consumed upon being received. For example, in the π-calculus, the system x〈z〉 | x(y).P | x(y).Q (1) represents a message with a datum z,... |

30 | Higher-order linear concurrent constraint programming
- Saraswat, Lincoln
- 1992
(Show Context)
Citation Context ...encodings among the fragments, a processes-as-formulae interpretation and a reduction from Minsky machines. 1 Introduction Several process calculi such as CCS, CSP, the π-calculus [15] and Linear CCP =-=[8, 23]-=- have an obvious source of linearity: Messages (or senders) are consumed upon being received. For example, in the π-calculus, the system x〈z〉 | x(y).P | x(y).Q (1) represents a message with a datum z,... |

28 | A Framework for the Analysis of Security Protocols
- Boreale, Buscemi
(Show Context)
Citation Context ...ng and describing security protocols. For instance, Crazzolara and Winskel’s SPL [7], the Spi Calculus variants by Fiore and Abadi [9] and by Amadio et al [1], and the calculus of Boreale and Buscemi =-=[4]-=- are all operationally defined in terms of configurations containing items of information (messages) which cannot be consumed during evolution. The idea is that the persistent store models an attacker... |

21 | A Logical View of Concurrent Constraint Programming
- Mendler, Panangaden, et al.
- 1995
(Show Context)
Citation Context ...sults. We also show that Pπ admits a processes-as-formulae compositional interpretation, building on the translation of π to linear logic in [13, 23] and the logical characterization of CCP languages =-=[11, 12]-=-. Specifically, we characterize the standard π-calculus notion of barbed observability (for Pπ) as entailment in First-Order Logic (FOL). Indeed, Pπ can be seen as a CCP language over the Gentzen cons... |

18 |
The Classical Decision Problem
- örger, ädel, et al.
- 1997
(Show Context)
Citation Context ...5, to the validity of a formula which is in the class of either Bernays-Schönfinkel, Gödel, twovariables, or Monadic FOL formulae without function symbols. All these classes of formulae are decidable =-=[5]-=-. See [18] for details. Decidable Classes with Mobility. Let us illustrate briefly the name extrusion capabilities of the “mobile” classes in the above lemma. Recall that input and restriction binders... |

17 |
Comparing recursion, replication, and iteration in process calculi
- Busi, Gabbrielli, et al.
- 2004
(Show Context)
Citation Context ...sible) with only two names. E.g., P and Q above belong to the class since P ≡ (νz)(!x〈z〉 | !z(x).!x) and Q ≡!x(u).(νx)!u〈x〉. Decidability Result for Barbed Congruence. It is easy to adapt the results =-=[6]-=- to prove that (weak) barbed congruence is undecidable for the zero-adic version of the π, in our notation π 0 . In contrast, here we prove that (weak) barbed congruence is decidable for the zero-adic... |

14 | Partial order and SOS semantics for linear constraint programs
- Best, Boer, et al.
- 1997
(Show Context)
Citation Context ...llowing the attacker to remove messages from the network may rule out the specification of a possible attack to a given protocol. (Note that the claims of extra expressivity of Linear CCP over CCP in =-=[2, 8]-=- are based on discrimination introduced by divergence that is ignored by the standard notion of weak bisimulation.) There is another source of linearity in (1): Receivers can also be consumed. For exa... |

6 |
Proofs as concurrent processes: A logical interpretation of concurrent constraint programming
- Lincoln, Saraswat
- 1991
(Show Context)
Citation Context ...sults. We also show that Pπ admits a processes-as-formulae compositional interpretation, building on the translation of π to linear logic in [13, 23] and the logical characterization of CCP languages =-=[11, 12]-=-. Specifically, we characterize the standard π-calculus notion of barbed observability (for Pπ) as entailment in First-Order Logic (FOL). Indeed, Pπ can be seen as a CCP language over the Gentzen cons... |

4 |
From linear to classical logic by abstract interpretation
- Blanchet
- 2005
(Show Context)
Citation Context ...s to model the fact that every message can be remembered by the spy). In fact, the approach of specifying protocols in a persistent setting, with an unbounded number of sessions, has been explored in =-=[3]-=- by using a classic logic Horn clause representation of protocols (rather than a linear logic one). In this paper, we present our expressiveness study of linearity and persistence in a well-establishe... |

3 |
On encoding pπ in mπ
- Quaglia, Walker
- 1998
(Show Context)
Citation Context ...0 and Q = x.0 | x.0. Clearly, P ≈ Q. Let Ct =!x〈n〉 | !x〈m〉 | !n( r t f ).!m( r ′ t ′ f ′ ).!t. Verify that (Ct | [Q]) ⇓ t but (Ct | [P ]) �⇓ t . Hence, [P ] �≈ [Q]. Nevertheless following the work of =-=[19, 24]-=-, we believe we can provide a type system in order to give a stronger correspondence for the encoding. The type system would allow contexts that may not behave as dictated by the protocol but do not i... |

2 |
The pi-calculus as a theory in linear-logic
- Miller
- 1992
(Show Context)
Citation Context ...dic version of Pπ. Table 1 summarizes these decidability results. We also show that Pπ admits a processes-as-formulae compositional interpretation, building on the translation of π to linear logic in =-=[13, 23]-=- and the logical characterization of CCP languages [11, 12]. Specifically, we characterize the standard π-calculus notion of barbed observability (for Pπ) as entailment in First-Order Logic (FOL). Ind... |

2 |
On the expressiveness of linearity and persistence in the asynchronous π-calculus
- Palamidessi, Saraswat, et al.
- 2006
(Show Context)
Citation Context ...ted input processes) are willing to run unboundedly many times, as those studied in [3] . Due to space limitations most proofs will be omitted. They can be found in the extended version of this paper =-=[18]-=-.sPAR: COM: x〈�z〉 | x(�y).P −→ P {�z/�y} if |�z| = |�y| P −→ P ′ P | Q −→ P ′ | Q 2 The Calculi RES: STRUCT: P ≡ P ′ −→ Q ′ ≡ Q P −→ Q Table 2. Reduction Rules. P −→ P ′ (νx)P −→ (νx)P ′ Here we defin... |

2 | if and only if v - P |