## CCS Semantics via Proved Transition Systems and Rewriting Logic (1998)

Venue: | In Kirchner and Kirchner [47 |

Citations: | 8 - 1 self |

### BibTeX

@INPROCEEDINGS{Carabetta98ccssemantics,

author = {Georgia Carabetta and Pierpaolo Degano and Fabio Gadducci},

title = {CCS Semantics via Proved Transition Systems and Rewriting Logic},

booktitle = {In Kirchner and Kirchner [47},

year = {1998},

pages = {253--272},

publisher = {Elsevier}

}

### Years of Citing Articles

### OpenURL

### Abstract

We consider (a slight variant of) the ccs calculus, and we analyze two operational semantics defined in the literature: the first exploits Proved Transition Systems (pts) and the second Rewriting Logic (rl). We show that the interleaving interpretation of both semantics agree, in that they define the same transitions and exhibit the same nondeterministic structure. In addition, we study causality in ccs computations. We recall the treatment via pts, that exhibits the notion of causality presented in the literature, and we show how to recast it in the rl semantics via suitable axioms. 1 Introduction Concurrency is maybe the basic aspect of the operational interpretation of rewriting logic. And as Jos'e Meseguer says in his lecture at concur'96 [20], . . . my main emphasis in this talk will be on rewriting logic as a semantic framework for concurrency. . . . The goal is . . . to express as faithfully as possible each model [of concurrency] on its own terms, avoiding any encodings or tr...

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Citation Context ...tems to our rewriting logic theory for ccs, obtaining in this way a logic representation of the standard notion of concurrency in process algebras. 2 Some notions on Process Algebras Process Algebras =-=[1,15,21]-=- offer a constructive way to describe concurrent systems, considered as structured entities (the processes) interacting through some synchronization mechanism. A system is then a term of an algebra ov... |

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Citation Context ...and equipping it with a semantics able to describe non standard aspects of concurrent computations, in particular causality. The language we choose is ccs, Milner's Calculus for Communicating Systems =-=[21]-=-, and the starting points are the semantics proposed in [13] and in particular in [18]. Roughly, a ccs process is a term of an algebra over a set of process constructors, under the assumption that the... |

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Citation Context ...at the operators represent basic features of a concurrent system, among which communication is the most relevant. Its original semantics was provided via a transition system, defined in the sos style =-=[24]-=-: the transitions are deduced applying a set of inference rules, driven by the syntax of the terms representing concurrent processes. This semantics describes the evolution of processes in an interlea... |

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Citation Context ...ngs of their proofs. This very concrete representation of process behaviour was used to describe qualitative and quantitative non-interleaving aspects of a variety of calculi, e.g., for the -calculus =-=[23]-=-, a calculus based on naming fairly more complex than ccs [9,11]. Indeed, simple relabellings of proved computations yield the main semantics presented in the literature, in particular the (interleavi... |

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Citation Context ...nents are enabled to perform a rewrite step, which is impossible, according to Lemma 3.4, because they have sort SP . 2 The statement above is equivalent to the usual decomposition property stated in =-=[19]-=- (but see also [4,5]): the main difference is its uniqueness, due to the structure of the proof terms entailed by R ccs . It is not a trivial property, and it is not in general valid for any generic r... |

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Citation Context ...tems to our rewriting logic theory for ccs, obtaining in this way a logic representation of the standard notion of concurrency in process algebras. 2 Some notions on Process Algebras Process Algebras =-=[1,15,21]-=- offer a constructive way to describe concurrent systems, considered as structured entities (the processes) interacting through some synchronization mechanism. A system is then a term of an algebra ov... |

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Citation Context ...)P j !P Hereafter, we usually omit the trailing 0, whenever clear from the context. The reader will notice that we slightly modified the original syntax, by substituting the replication operator ! of =-=[22]-=- in place of the more common definition of constants or recursion. Also, we omitted the relabelling operator, which is irrelevant to our present study. From now onwards, we denote a process P as finit... |

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Citation Context ...ach actionsis a unary operator, and so is each restriction (a) and the bang, while both parallel and non-deterministic choice are binary operators. We denote by \Sigma eccs the order-sorted signature =-=[14]-=- with two sorts, SP and SAP , such that SPsSAP : it contains \Sigma ccs and the additional operatorss: SAP ! SAP for eachs2 A. We refer to active processes, denoted by P a ; Q a ; R a ; : : : 2 AP , a... |

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Citation Context ...computations, in particular causality. The language we choose is ccs, Milner's Calculus for Communicating Systems [21], and the starting points are the semantics proposed in [13] and in particular in =-=[18]-=-. Roughly, a ccs process is a term of an algebra over a set of process constructors, under the assumption that the operators represent basic features of a concurrent system, among which communication ... |

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Citation Context ...the rl semantics via suitable axioms. 1 Introduction Concurrency is maybe the basic aspect of the operational interpretation of rewriting logic. And as Jos'e Meseguer says in his lecture at concur'96 =-=[20]-=-, . . . my main emphasis in this talk will be on rewriting logic as a semantic framework for concurrency. . . . The goal is . . . to express as faithfully as possible each model [of concurrency] on it... |

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Citation Context ...forward to recover the more standard representation of causality as a partial ordering of events, and that of concurrency. Both these notions coincide with those defined in the literature (see, e.g., =-=[7,3]-=-). Roughly, a transition # causally depends on a previous transition # 0 0 if @(# 0 ) is a prefix of @(#) (the tuning needed to cover communications is made precise below). The underlying idea is that... |

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Citation Context ... literature reports a lot of work on non-interleaving semantics for ccs. The most similar to the original are those provided via transition systems that express the causality between transitions (see =-=[3,7--9,16]-=- to mention only a few references). Remarkably, all these semantics agree on the notion of causality they define and conservatively extend the original interleaving semantics. We first provide ccs wit... |

48 |
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Citation Context ...uents with source c(P ). 6 In fact, while the others are more specific, the first axiom schemata could be considered analogous to the conditions required for permutation equivalence on term rewriting =-=[2]-=-, since the rewrites occur on disjoint parts of a process. For general results on the relationships between rewriting logic and permutation equivalence, see [17,6,12]. Proof sketch We proceed like in ... |

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Citation Context ...oms should be added to the theory for the interleaving case in order to capture causality and concurrency. The causal model for ccs that better drives our intuition is the proved transition system of =-=[9]-=-, pts for short. This is because the labels of proved transitions, call them enhanced, have an algebraic structure, that reflect the structure of processes. More precisely, the transitions are labelle... |

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Citation Context ... we lift the notion of concurrency from one, or some computations to the whole transition system. We omit here the precise statement of this theorem, and refer the interested reader to Theorem 6.4 of =-=[10]-=-. An immediate consequence is that we feel free to call equivalent (w.r.t. concurrency) computationssands0 that only differ in the order in which concurrent transitions occur, in symbolssis0 ; disrega... |

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Citation Context ...ess behaviour was used to describe qualitative and quantitative non-interleaving aspects of a variety of calculi, e.g., for the -calculus [23], a calculus based on naming fairly more complex than ccs =-=[9,11]-=-. Indeed, simple relabellings of proved computations yield the main semantics presented in the literature, in particular the (interleaving and the) causal one which is of main interest here. It will b... |

24 | B.: Sesqui-pushout rewriting
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(Show Context)
Citation Context ... characterization of the class of active proof terms (and associated sequents), roughly denoted as those closed proof terms of sort SAP such that the sequential composition operator never occurs (see =-=[4,5]). Definit-=-ion 3.3 Let ff be a closed proof term. Then ff is ffl one-step, if it does not contain the composition operator "\Delta"; ffl active, if it is one-step and contains just one occurrence of an... |

24 | On the Algebraic Approach to Concurrent Term Rewriting
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Citation Context ...rmutation equivalence on term rewriting [2], since the rewrites occur on disjoint parts of a process. For general results on the relationships between rewriting logic and permutation equivalence, see =-=[17,6,12]-=-. Proof sketch We proceed like in the proof of Theorem 4.1: we first find a normal form for both equivalent proved computations and concurrent proof terms, and we show then thatsc andsff c are inverse... |

18 | Relating two categorical models of term rewriting
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Citation Context ...rmutation equivalence on term rewriting [2], since the rewrites occur on disjoint parts of a process. For general results on the relationships between rewriting logic and permutation equivalence, see =-=[17,6,12]-=-. Proof sketch We proceed like in the proof of Theorem 4.1: we first find a normal form for both equivalent proved computations and concurrent proof terms, and we show then thatsc andsff c are inverse... |

14 | Tiles, rewriting rules and CCS
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(Show Context)
Citation Context ...ard aspects of concurrent computations, in particular causality. The language we choose is ccs, Milner's Calculus for Communicating Systems [21], and the starting points are the semantics proposed in =-=[13]-=- and in particular in [18]. Roughly, a ccs process is a term of an algebra over a set of process constructors, under the assumption that the operators represent basic features of a concurrent system, ... |

12 |
Axiomatizing permutation equivalence in the - calculus
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Citation Context ...rmutation equivalence on term rewriting [2], since the rewrites occur on disjoint parts of a process. For general results on the relationships between rewriting logic and permutation equivalence, see =-=[17,6,12]-=-. Proof sketch We proceed like in the proof of Theorem 4.1: we first find a normal form for both equivalent proved computations and concurrent proof terms, and we show then thatsc andsff c are inverse... |

10 | Cpo models for infinite term rewriting
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(Show Context)
Citation Context ... characterization of the class of active proof terms (and associated sequents), roughly denoted as those closed proof terms of sort SAP such that the sequential composition operator never occurs (see =-=[4,5]). Definit-=-ion 3.3 Let ff be a closed proof term. Then ff is ffl one-step, if it does not contain the composition operator "\Delta"; ffl active, if it is one-step and contains just one occurrence of an... |

4 |
A partial ordering semantics for CCS. Theoret
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(Show Context)
Citation Context ...a process to produce as (finitely) many copies of itself as needed. 2.2 Proved Transition System We present now an enrichment over the labels of the standard transition system of ccs, in the style of =-=[3,8]-=-. This additional structure is used to encode some information on the derivation of the transitions, that is, on the inference rules actually used to obtain that derivation. We define jointly the noti... |

4 |
Comparing causality and locality based equivalences
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(Show Context)
Citation Context ... literature reports a lot of work on non-interleaving semantics for ccs. The most similar to the original are those provided via transition systems that express the causality between transitions (see =-=[3,7--9,16]-=- to mention only a few references). Remarkably, all these semantics agree on the notion of causality they define and conservatively extend the original interleaving semantics. We first provide ccs wit... |