## Section: New Results

### Expressive power of models and formalisms for concurrency

Participants : Jesus Aranda, Romain Beauxis, Catuscia Palamidessi, Frank Valencia.

#### On the Expressive Power of Restriction in CCS with Replication

Busi et al. [40] showed that CCS! (CCS with replication instead of recursion) is Turing powerful by providing an encoding of Random Access Machines (RAMs) which preserves and reflects convergence (i.e., the existence of terminating computations). The encoding uses an unbounded number of restrictions arising from having restriction operators under the scope of replication. On the other hand, in [39] they had shown that there is no encoding of RAMs into CCS! which preserves and reflects divergence.

In [23] we have studied the expressive power of restriction and its interplay with replication. We have done this by considering several syntactic variants of CCS! which differ from each other in the use of restriction with respect to replication. We have considered three syntactic variations which do not allow the use of an unbounded number of restrictions: is the fragment of CCS! not allowing restrictions under the scope of a replication. is the restriction-free fragment of CCS! . The third variant is which extends CCS with PhillipÕs priority guards. We have shown that the use of unboundedly many restrictions in CCS! is necessary for obtaining Turing expressiveness in the sense of Busi et al. We have done this by showing that there is no encoding of RAMs into CCS which preserves and reflects convergence. We have also proved that up to failures equivalence, there is no encoding from CCS! into CCS nor from CCS into CCS . As lemmata for the above results we have proved that convergence is decidable for CCS and that language equivalence is decidable for CCS . As corollary it follows that convergence is decidable for restriction-free CCS. Finally, we have shown the expressive power of priorities by providing an encoding of RAMs in CCS : Not only does the encoding preserve and reflect convergence but it also preserves and reflects divergence (the existence of infinite computations). This is to be contrasted with the result of Busi et al. mentioned above.

#### Linearity vs persistence

In his PhD thesis [11] Aranda has presented an expressiveness study of linearity vs persistence in the asynchronous -calculus (A ), a representative process calculus, w.r.t. De Nicola and Hennessy's testing scenario which is sensitive to divergence. The work considers A and three sub-languages of it, each capturing one source of persistence: the persistent-input A -calculus (PI ), the persistent-output A -calculus (PO ) and the persistent A -calculus (P ). It is shown that, under some general conditions related to compositionality of the encoding and preservation of the infinite behaviour, there cannot be an encoding from A into a (semi)-persistent calculus preserving the must testing semantics. It also shown that, unlike for A , convergence and divergence are decidable for PO (and P ). As a consequence there is no encoding preserving and reflecting divergence or convergence from A into PO (and P ). This work confirms informal expressiveness claims in the literature of CCP.

#### Expressiveness of ntcc

In the context of the modeling expressiveness of process calculi, in [31] we have studied the suitability of the ntcc (nondeterministic timed concurrent constraint) calculus for modeling, simulating and analyzing biological systems. In particular, we have explored if it is possible to model membrane systems in ntcc. As the main contribution of this paper, we have proposed a general mechanism for modeling membrane systems in ntcc. The application of this mechanism has been illustrated with a model for the LDL cholesterol degradation pathway using membrane systems defined in ntcc. We have simulated the model of the LDL cholesterol degradation pathway by using ntccSim, a tool to run program specifications in ntcc.

#### Fairness

In [16] we have defined fair computations in the -calculus. We have followed Costa and Stirling's approach for CCS-like languages [44] , [45] but exploited a more natural labeling method of process actions to filter out unfair process executions. The new labeling has allowed us to prove all the significant properties of the original one, such as unicity, persistence and disappearance of labels. It has also turned out that the labeled -calculus is a conservative extension of the standard one. We have contrasted the existing fair testing notions [38] , [48] with those that naturally arise by imposing weak and strong fairness. This comparison provides the expressiveness of the various fair testing-based semantics and emphasizes the discriminating power of the one already proposed in the literature.

#### On the asynchronous nature of the asynchronous -calculus

In [12] and [37] we have addressed the question of what kind of asynchronous communication is exactly modeled by the asynchronous -calculus (a ). To this purpose we have defined a calculus where channels are represented explicitly as special buffer processes. The base language for is the (synchronous) -calculus, except that ordinary processes communicate only via buffers. We have compared this calculus with a , and we have shown that there is a strong correspondence between a and in the case that buffers are bags: there are indeed encodings which map each a process into a strongly asynchronous bisimilar process, and each process into a weakly asynchronous bisimilar a process. In case the buffers are queues or stacks, on the contrary, the correspondence does not hold. We have shown indeed that it is not possible to translate a stack or a queue into a weakly asynchronous bisimilar a process. Actually, for stacks we have shown an even stronger result, namely that they cannot be encoded into weakly (asynchronous) bisimilar processes in a -calculus without mixed choice.

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