## Relating State-Based and Process-Based Concurrency through Linear Logic (2006)

Citations: | 12 - 1 self |

### BibTeX

@MISC{Cervesato06relatingstate-based,

author = {Iliano Cervesato and Andre Scedrov},

title = { Relating State-Based and Process-Based Concurrency through Linear Logic},

year = {2006}

}

### OpenURL

### Abstract

This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the well-established state-transformation model inspired to Petri nets and multiset rewriting, and the prolific process-based models such as the π-calculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic. In the second part of the paper, we propose a completely new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic. The resulting interpretation is extended with a majority of linear connectives into the language of ω-multisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous π-calculus to rewrite operators, while the structural equivalence corresponds directly to logically-motivated structural properties of ω-multisets (with one exception).

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Citation Context ...ions, these languages tend to be either process-oriented or state-based. The former include the spi-calculus [1], a security-enhanced version of the π-calculus, strand spaces [29], and others such as =-=[25]-=-. The latter comprises formalisms directly based on multiset rewriting [19, 6321], tool-specific languages [54], inductive definitions [65], colored Petri nets [4, 13], and more. This profusion of fo... |

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Citation Context ...te transition model. In particular, we have enriched it in [16] to support a first-order notion of multiset rewriting with existentials which we have extensively used to model cryptographic protocols =-=[15,17,20]-=-, an eminently subtle type of distributed systems. The alternative process-based model of concurrency identifies each agent with a process and communications between agents replace the global state as... |

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Citation Context ...his purpose, although some issues are not satisfactorily resolved yet. This approach, which goes back to early work by Andreoli and Pareschi [5], has been applied to the π-calculus by several authors =-=[18,39,42]-=- and to the study of security protocols [16]. A few researchers have compared the processas-term and process-as-formulas approaches [39] or used them together [18]. Readers interested in a broader per... |

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Citation Context ...nto the programming language FreshML [71, 76]. Cardelli and Gordon devised two complementary constructs, “revelation” and “hiding”, to study the logical properties of name operators in the π-calculus =-=[17]-=-. More recently, Miller and Tiu introduced the ∇ quantifier to capture the behavior of both ∀ and ∃ in managing names through eigenvariables but away from their handling of substitution [62]. N 16As ... |

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Citation Context ... term constructors so that a process is represented by a term in the logic. Within this process-as-term model, process computation takes the shape of term reduction. Abramsky [2] and Bellin and Scott =-=[10]-=- rely on classical linear logic for this pur3pose. Miller et al. have performed a similar investigation using intuitionistic linear logic [53], and more recently using a refinement of linear logic wi... |

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Citation Context ...Martí-Oliet and Meseguer [37,38] and Brown and Gurr [13] approached the issue from a categorical perspective, motivating the use of additional linear connectives as net operators. Engberg and Winskel =-=[21]-=- reached a similar conclusion using quantales, an early model of linear logic. A few years later, Cervesato [14] compiled a comparison of a number of encodings of linear logic. In this paradigm, concu... |

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Citation Context ... shape of term reduction. Abramsky [2] and Bellin and Scott [9] rely on classical linear logic for this purpose. Miller et al. have performed a similar investigation using intuitionistic linear logic =-=[39]-=-, and more recently using a refinement of linear logic with a new quantifier that resembles name generation [45,57]. Abramsky has recently suggested extracting processes from proofs [3]. The process-a... |

32 | Typed MSR: Syntax and examples
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(Show Context)
Citation Context ...te transition model. In particular, we have enriched it in [16] to support a first-order notion of multiset rewriting with existentials which we have extensively used to model cryptographic protocols =-=[15,17,20]-=-, an eminently subtle type of distributed systems. The alternative process-based model of concurrency identifies each agent with a process and communications between agents replace the global state as... |

31 |
The re exive CHAM and the join-calculus
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(Show Context)
Citation Context ... a process and communications between agents replace the global state as the vehicle of computation. Languages following this model include CSP [29], CCS and the π-calculus [49,55], the join calculus =-=[25]-=-, and a large number of other process algebras, each characterized by subtle differences in behavior. The correlation between logic and process algebra has been investigated along two planes, with occ... |

30 | Higher-order linear concurrent constraint programming
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(Show Context)
Citation Context ...ent of logic, and falls short of endowing it with a rewriting interpretation. Saraswat and Lincoln hint at a similar interpretation for their Higher-order Linear Concurrent Constraint language (HLcc) =-=[49]-=-, interestingly stirring it in the direction of constraint programming (see also [30]). To the extent of our knowledge, ACL and HLcc are the proposals closest to ω in the literature. The semantics of ... |

24 |
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Citation Context ...he first part of the paper and will play an indirect role in later developments. It is conceivable, however, that these and other right rules can be useful query tools, as demonstrated for example in =-=[21,27]-=- relative to Petri nets. This however goes beyond the scope of this work. Derivations are defined as usual, and denoted D. In the second part of this paper, we will emphasize the process of constructi... |

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Citation Context ...e linear context ∆ can be arbitrary rather than a single formula A. We produce an exact correspondence by identifying contexts and formulas, an idea familiar from categorical interpretations of logic =-=[56,10]-=-. More precisely, we identify the tensor ⊗ and its unit 1 with the union “,” and unit “·” constructors of linear contexts, respectively. Therefore, a linear context ∆ is interpreted as the formula � ∆... |