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Register a new userOn characterising strong bisimilarity in a fragment of CCS with replication
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Daniel Hirschkoff
Publication date
2008
fields
Informatics Engineering
and research's language is
English
Authors
Daniel Hirschkoff
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We provide a characterisation of strong bisimilarity in a fragment of CCS that contains only prefix, parallel composition, synchronisation and a limited form of replication. The characterisation is not an axiomatisation, but is instead presented as a rewriting system. We discuss how our method allows us to derive a new congruence result in the $pi$-calculus: congruence holds in the sub-calculus that does not include restriction nor sum, and features a limited form of replication. We have not formalised the latter result in all details.
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Higher-order processes with parameterization are capable of abstraction and application (migrated from the lambda-calculus), and thus are computationally more expressive. For the minimal higher-order concurrency, it is well-known that the strong bisimilarity (i.e., the strong bisimulation equality) is decidable in absence of parameterization. By contrast, whether the strong bisimilarity is still decidable for parameterized higher-order processes remains unclear. In this paper, we focus on this issue. There are basically two kinds of parameterization: one on names and the other on processes. We show that the strong bisimilarity is indeed decidable for higher-order processes equipped with both kinds of parameterization. Then we demonstrate how to adapt the decision approach to build an axiom system for the strong bisimilarity. On top of these results, we provide an algorithm for the bisimilarity checking.
We consider the relational characterisation of branching bisimilarity with explicit divergence. We prove that it is an equivalence and that it coincides with the original definition of branching bisimilarity with explicit divergence in terms of coloured traces. We also establish a correspondence with several variants of an action-based modal logic with until- and divergence modalities.
We formalise a general concept of distributed systems as sequential components interacting asynchronously. We define a corresponding class of Petri nets, called LSGA nets, and precisely characterise those system specifications which can be implemented as LSGA nets up to branching ST-bisimilarity with explicit divergence.
We propose a distance between continuous-time Markov chains (CTMCs) and study the problem of computing it by comparing three different algorithmic methodologies: iterative, linear program, and on-the-fly. In a work presented at FoSSaCS12, Chen et al. characterized the bisimilarity distance of Desharnais et al. between discrete-time Markov chains as an optimal solution of a linear program that can be solved by using the ellipsoid method. Inspired by their result, we propose a novel linear program characterization to compute the distance in the continuous-time setting. Differently from previous proposals, ours has a number of constraints that is bounded by a polynomial in the size of the CTMC. This, in particular, proves that the distance we propose can be computed in polynomial time. Despite its theoretical importance, the proposed linear program characterization turns out to be inefficient in practice. Nevertheless, driven by the encouraging results of our previous work presented at TACAS13, we propose an efficient on-the-fly algorithm, which, unlike the other mentioned solutions, computes the distances between two given states avoiding an exhaustive exploration of the state space. This technique works by successively refining over-approximations of the target distances using a greedy strategy, which ensures that the state space is further explored only when the current approximations are improved. Tests performed on a consistent set of (pseudo)randomly generated CTMCs show that our algorithm improves, on average, the efficiency of the corresponding iterative and linear program methods with orders of magnitude.
In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic recently proposed by Mardare, Panangaden, and Plotkin (LICS 2016) that uses equality relations $t equiv_varepsilon s$ indexed by rationals, expressing that `$t$ is approximately equal to $s$ up to an error $varepsilon$. Notably, our quantitative deduction system extends in a natural way the equational system for probabilistic bisimilarity given by Stark and Smolka by introducing an axiom for dealing with the Kantorovich distance between probability distributions. The axiomatization is then used to propose a metric extension of a Kleenes style representation theorem for finite labelled Markov chains, that was proposed (in a more general coalgebraic fashion) by Silva et al. (Inf. Comput. 2011).
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