Weak bisimulation and open maps

<p>A systematic treatment of weak bisimulation and observational congruence<br />on presheaf models is presented. The theory is developed with<br />respect to a "hiding" functor from a category of paths to observable<br />paths. Via a view of processes as bundles, we are able to account for<br />weak morphisms (roughly only required to preserve observable paths)<br />and to derive a saturation monad (on the category of presheaves over<br />the category of paths). Weak morphisms may be encoded as strong<br />ones via the Kleisli construction associated to the saturation monad.<br />A general notion of weak open-map bisimulation is introduced, and<br />results relating various notions of strong and weak bisimulation are<br />provided. The abstract theory is accompanied by the concrete study<br />of two key models for concurrency, the interleaving model of synchronisation<br /> trees and the independence model of labelled event structures.</p><p>To appear in Proceedings of the 14th Annual IEEE Symposium on Logic<br />in Computer science, LICS'99, IEEE Press, July 1999.</p><p> </p>

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has ``refinement'' operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising Hennessy-Milner logic, which is characteristic for the generalised notion of bisimulation.

Psi-calculi extend the pi-calculus with nominal datatypes to represent data, communication channels, and logics for facts and conditions. This general framework admits highly expressive formalisms such as concurrent higher-order constraints and advanced cryptographic primitives. We here establish the theory of weak bisimulation, where the τ actions are unobservable. In comparison to other calculi the presence of assertions poses a significant challenge in the definition of weak bisimulation, and although there appears to be a spectrum of possibilities we show that only a few are reasonable. We demonstrate that the complications mainly stem from psi-calculi where the associated logic does not satisfy weakening. We prove that weak bisimulation equivalence has the expected algebraic properties and that the corresponding observation congruence is preserved by all operators. These proofs have been machine checked in Isabelle. The notion of weak barb is defined as the output label of a communication action, and weak barbed equivalence is bisimilarity for τ actions and preservation of barbs in all static contexts. We prove that weak barbed equivalence coincides with weak bisimulation equivalence.

Presheaf models for CCS-like languages

A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

The problem of the conceptual unification of the models for concurrent and distributed systems is addressed in terms of categories of graphs with algebraic structure. In this paper, we model the semantics of a concrete process description language, in both its interleaving and its true concurrency versions. As a test case, we consider Milner's Calculus of Communicating Systems (CCS). Instead of defining a single model for CCS, we introduce categories whose objects are models, and where morphisms represent a specification-implementation relation. We start by showing that CCS models can be viewed as ordinary graphs equipped with additional structures over nodes and transitions. Labels are defined using a comma category construction. We then define special classes of morphisms expressing a notion of simplification and we show that observational congruences can be characterized in terms of final universal properties in the sub categories induced by such morphisms. In order to model the truly concurrent aspect of CCS, we write axioms which identify computations obtained by permuting independent transitions. By unfolding the resulting transition system, we obtain the domain of configurations of an event structure.

SUMMARYWe propose a theoretical testing framework and a test generation algorithm for concurrent systems specified with true‐concurrency models, such as Petri nets or networks of automata. The semantic model of computation of such formalisms is labelled event structures, which allow to represent concurrency explicitly. We introduce the notions of strong and weak concurrency: strongly concurrent events must be concurrent in the implementation, while weakly concurrent ones may eventually be ordered. The ioco type conformance relations for sequential systems rely on the observation of sequences of actions and blockings; thus, they are not capable of capturing and exploiting concurrency of non‐sequential behaviours. We propose an extension of ioco for labelled event structures, named co‐ioco, allowing to deal with strong and weak concurrency. We extend the notions of test cases and test execution to labelled event structures and give a test generation algorithm building a complete test suite for co‐ioco. Copyright © 2014 John Wiley & Sons, Ltd.

Modelling concurrent interactions

This paper compares two models of concurrency, Milner's Calculus of Communicating Systems (CCS) and the failures model of Communicating Sequential Processes (CSP) developed by Hoare, Brookes and Roscoe. By adapting Milner's synchronisation trees to serve as notation for both CCS and CSP, we are able to define a representation mapping for CSP processes. We define an equivalence relation on synchronisation trees which corresponds precisely to the notion of failure equivalence. Milner's calculus is founded on a different notion, observation equivalence. We show how these two equivalences are related. Just as Milner's equivalence can be characterised as the smallest relation satisfying a set of axioms, we find a suitable set of axioms for the failures equivalence relation. This again makes explicit the differences between the two systems, as well as revealing that the semantic models underlying CCS and CSP are comparable.

Majority of mammalian transcriptomes encode long noncoding RNAs (lncRNAs) that are not translated into proteins. LncRNAs are mRNA-like transcripts that are longer than 200 nucleotides, transcribed by RNA-Pol-II and undergo post-transcriptional modifications and splicing. Although they are less evolutionary conserved than protein-coding genes, lncRNAs have been shown to regulate several biochemical and cellular processes at a transcriptional level. Yet to date, the mechanism of only a handful of them has been studied in mammalian organisms. Therefore, in order to understand the function of lncRNAs in the mouse, we have performed large-scale RNA-sequencing of whole E14.5 mouse embryos. Results obtained revealed ~7000 putative lncRNA transcripts expressed at this developmental stage. From this list, we focused our attention on a small group of divergent lncRNAs that are transcribed in close proximity to physiologically important protein-coding genes and that showed significant evolutionary conservation in mammals. Our RNA in situ hybridization (ISH) data in mouse embryos confirmed that a few of these divergent lncRNAs genes share similar expression profiles with their neighboring protein-coding genes. From this list, we selected an uncharacterized and mammalian conserved divergent lncRNA Gm14204 that has an expression similar to its adjacent neurotransmitter transporter gene Slc32a1. Gm14204 is divergently transcribed with respect to Slc32a1 on the opposite strand with a distance of ~50 bp between the two genes. Keeping in mind the prevailing idea in the literature, we hypothesized that Gm14204 lncRNA might regulate Slc32a1 transcription. First, we performed an in-depth molecular characterization of Gm14204 expression using RNA-ISH and observed that it has a nervous system-specific expression pattern in the developing mouse embryos and an ubiquitous expression throughout the adult brain, which is broadly comparable to Slc32a1 mRNA expression. Next, using a series of RNA-FISH and single-molecule (sm) FISH experiments, we showed that Gm14204 lncRNA and Slc32a1 mRNA transcripts are co-expressed in a subset of GABAergic interneuron population in the adult mouse brain. To investigate the function of Gm14204, we have generated the first genetic mouse model for Gm14204 by knock-in of transcription termination sequences into the first intron of this gene. LncRNA gene deletion was not advisable because Gm14204 and Slc32a1 genes are situated very close to each other and deleting a region of Gm14204 might disrupt cis-regulatory elements in that locus. Thus, our novel strategy prematurely terminated the transcription of all Gm14204 lncRNA isoforms, leaving an intact Slc32a1 gene locus. Furthermore, using quantitative RT-PCR analysis of embryonic mouse brains, we showed that the expression of Slc32a1 gene is not altered in the lncRNA mutants. Contrary to the general notion in the field that divergent lncRNAs regulate their adjacent genes, in this study, we provide evidence that the divergent Gm14204 lncRNA does not regulate Slc32a1 despite the fact that they share similar expression patterns. Additionally, this lncRNA also does not regulate other protein-coding genes in the Gm14204 genomic region. Moreover, our smFISH data in adult brain have clearly indicated that Gm14204 localizes to multiple locations inside the nucleus in a subset of neurons, suggesting a trans function of the lncRNA. Identification of these neurons with molecular markers might provide us with a deeper knowledge about the possible function of lncRNA. Only a few lncRNA knockouts in mouse have been shown to be lethal whereas many others have reported the presence of subtler phenotypes. In our study, we found that genetic deletion of Gm14204 was not lethal. The mice were viable, healthy, showed no visible abnormalities and were born at a normal Mendelian ratio. We still search for a subtle phenotype in the nervous system where Gm14204 shows strong expression during mouse development and in the adult.

Event structures and trace monoids

Reversibility and Models for Concurrency

This paper addresses the subject of linking functional specifications to performance analysis in a process algebraic context. It presents a timed, probabilistic extension of a process algebraic formalism and its application to performance analysis. More specifically, an extension of a subset of LOTOS is presented equipped with a truly concurrent semantical model based on bundle event structures. It is investigated how semi-Markov chains can be obtained from functional speciications using this semantical model. The use of a true concurrency model enables us to distinguish between non-determinism and parallelism, to reduce the state explosion problem and, moreover, to analyse part of the system wi thout considering other (irrelevant) parts. An example illustrates the proposed approach.

Recently, the formal approach of I-Systems has been newly established through an abstract axiomatic system where events in system components are solely derived and defined from their bilateral interaction with other components as well as from the autonomy as found in decentralized systems. As a major difference to other concurrency models we do not assume that simultaneity or coincidence of events are observable in distributed systems. (This is a fundamental practical problem in autonomous decentralized systems.) We respect this by defining concurrency of events as a system-wide or global concept of causal independence which will be given and characterized by bilateral interaction properties about the components involved, detectable through local checks only. A novel concept of conflicting actions will be given as well. While not complementary to concurrency (as often understood in the area of Petri Nets) concurrency and conflict will be complemented to constitute fundamental relationships between distributed events, through a new relation termed ’event funneling’. Practicerelated issues related to this fine-grained event structure will be discussed.

Timed transition systems are one of the most popular real-time models for concurrency. In the paper, various behavioral equivalences of timed transition systems are defined and studied. In particular, categories of this model are constructed, and their properties are studied. In addition, based on the open maps concept, abstract characterization of the considered equivalences is given. Such an approach makes it possible to develop a metatheory designed for unified definition and study of timed behavioral equivalences in the “linear time-branching time” spectrum of semantics.