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Register a new userGenerating Witness of Non-Bisimilarity for the pi-Calculus
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Added by
Ki Yung Ahn
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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In the logic programming paradigm, it is difficult to develop an elegant solution for generating distinguishing formulae that witness the failure of open-bisimilarity between two pi-calculus processes; this was unexpected because the semantics of the pi-calculus and open bisimulation have already been elegantly specified in higher-order logic programming systems. Our solution using Haskell defines the formulae generation as a tree transformation from the forest of all nondeterministic bisimulation steps to a pair of distinguishing formulae. Thanks to laziness in Haskell, only the necessary paths demanded by the tree transformation function are generated. Our work demonstrates that Haskell and its libraries provide an attractive platform for symbolically analyzing equivalence properties of labeled transition systems in an environment sensitive setting.
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A (fragment of a) process algebra satisfies unique parallel decomposition if the definable behaviours admit a unique decomposition into indecomposable parallel components. In this paper we prove that finite processes of the pi-calculus, i.e. processes that perform no infinite executions, satisfy this property modulo strong bisimilarity and weak bisimilarity. Our results are obtained by an application of a general technique for establishing unique parallel decomposition using decomposition orders.
We study whether, in the pi-calculus, the match prefix-a conditional operator testing two names for (syntactic) equality-is expressible via the other operators. Previously, Carbone and Maffeis proved that matching is not expressible this way under rather strong requirements (preservation and reflection of observables). Later on, Gorla developed a by now widely-tested set of criteria for encodings that allows much more freedom (e.g. instead of direct translations of observables it allows comparison of calculi with respect to reachability of successful states). In this paper, we offer a considerably stronger separation result on the non-expressibility of matching using only Gorlas relaxed requirements.
Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and structural congruence. Formalisations have been undertaken in a variety of systems, primarily focusing on well-studied (and challenging) properties such as the theory of process bisimulation. We present a formalisation in Agda that instead explores the theory of concurrent transitions, residuation, and causal equivalence of traces, which has not previously been formalised for the pi-calculus. Our formalisation employs de Bruijn indices and dependently-typed syntax, and aligns the proved transitions proposed by Boudol and Castellani in the context of CCS with the proof terms naturally present in Agdas representation of the labelled transition relation. Our main contributions are proofs of the diamond lemma for residuation of concurrent transitions and a formal definition of equivalence of traces up to permutation of transitions.
Message-passing based concurrent languages are widely used in developing large distributed and coordination systems. This paper presents the buffered $pi$-calculus --- a variant of the $pi$-calculus where channel names are classified into buffered and unbuffered: communication along buffered channels is asynchronous, and remains synchronous along unbuffered channels. We show that the buffered $pi$-calculus can be fully simulated in the polyadic $pi$-calculus with respect to strong bisimulation. In contrast to the $pi$-calculus which is hard to use in practice, the new language enables easy and clear modeling of practical concurrent languages. We encode two real-world concurrent languages in the buffered $pi$-calculus: the (core) Go language and the (Core) Erlang. Both encodings are fully abstract with respect to weak bisimulations.
This paper is the first thorough investigation into the coarsest notion of bisimilarity for the applied pi-calculus that is a congruence relation: open barbed bisimilarity. An open variant of labelled bisimilarity (quasi-open bisimilarity), better suited to constructing bisimulations, is proven to coincide with open barbed bisimilarity. These bisimilary congruences are shown to be characterised by an intuitionistic modal logic that can be used, for example, to describe an attack on privacy whenever a privacy property is violated. Open barbed bisimilarity provides a compositional approach to verifying cryptographic protocols, since properties proven can be reused in any context, including under input prefix. Furthermore, open barbed bisimilarity is sufficiently coarse for reasoning about security and privacy properties of cryptographic protocols; in constrast to the finer bisimilarity congruence, open bisimilarity, which cannot verify certain privacy properties.
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