Categoral views on computations on trees (Extended abstract)

Computations on trees form a classical topic in computing. These computations can be described in terms of machines (typically called tree transducers), or in terms of functions. This paper focuses on three flavors of bottom-up computations, of increasing generality. It brings categorical clarity by identifying a category of tree transducers together with two different behavior functors. The first sends a tree transducer to a coKleisli or biKleisli map (describing the contribution of each local node in an input tree to the global transformation) and the second to a tree function (the global tree transformation). The first behavior functor has an adjoint realization functor, like in Goguen’s early work on automata. Further categorical structure, in the form of Hughes’s Arrows, appears in properly parameterized versions of these structures

Healthiness from Duality

Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There are several results known for healthiness conditions: for deterministic programs, nondeterministic ones, probabilistic ones, etc. Building upon our previous works on so-called state-and-effect triangles, we contribute a unified categorical framework for investigating healthiness conditions. We find the framework to be centered around a dual adjunction induced by a dualizing object, together with our notion of relative Eilenberg-Moore algebra playing fundamental roles too. The latter notion seems interesting in its own right in the context of monads, Lawvere theories and enriched categories.Comment: 13 pages, Extended version with appendices of a paper accepted to LICS 201

Involutive Categories and Monoids, with a GNS-correspondence

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the so-called Gelfand-Naimark-Segal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive categories

On coalgebras with internal moves

In the first part of the paper we recall the coalgebraic approach to handling the so-called invisible transitions that appear in different state-based systems semantics. We claim that these transitions are always part of the unit of a certain monad. Hence, coalgebras with internal moves are exactly coalgebras over a monadic type. The rest of the paper is devoted to supporting our claim by studying two important behavioural equivalences for state-based systems with internal moves, namely: weak bisimulation and trace semantics. We continue our research on weak bisimulations for coalgebras over order enriched monads. The key notions used in this paper and proposed by us in our previous work are the notions of an order saturation monad and a saturator. A saturator operator can be intuitively understood as a reflexive, transitive closure operator. There are two approaches towards defining saturators for coalgebras with internal moves. Here, we give necessary conditions for them to yield the same notion of weak bisimulation. Finally, we propose a definition of trace semantics for coalgebras with silent moves via a uniform fixed point operator. We compare strong and weak bisimilation together with trace semantics for coalgebras with internal steps.Comment: Article: 23 pages, Appendix: 3 page

Towards learning and verifying invariants of cyber-physical systems by code mutation

Cyber-physical systems (CPS), which integrate algorithmic control with physical processes, often consist of physically distributed components communicating over a network. A malfunctioning or compromised component in such a CPS can lead to costly consequences, especially in the context of public infrastructure. In this short paper, we argue for the importance of constructing invariants (or models) of the physical behaviour exhibited by CPS, motivated by their applications to the control, monitoring, and attestation of components. To achieve this despite the inherent complexity of CPS, we propose a new technique for learning invariants that combines machine learning with ideas from mutation testing. We present a preliminary study on a water treatment system that suggests the efficacy of this approach, propose strategies for establishing confidence in the correctness of invariants, then summarise some research questions and the steps we are taking to investigate them.Comment: Short paper accepted by the 21st International Symposium on Formal Methods (FM 2016

Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review

Enhanced smoking cessation support for newly abstinent smokers discharged from hospital (The Hospital to Home trial): A randomised controlled trial

Background and aimsThe United Kingdom's National Institute for Health and Care Excellence guidance (NICE PH48) recommends that pharmacotherapy combined with behavioural support be provided for all smokers admitted to hospital; however, relapse to smoking after discharge remains common. This study aimed to assess the effect of adding home support for newly?abstinent smokers to conventional NICE?recommended support in smokers discharged from hospital.Designindividually?randomised parallel group trial.SettingOne UK acute hospital.Participants404 smokers aged >18 admitted to acute medical wards between June 2016 and July 2017 were randomised in equal numbers to each treatment group.Interventions and comparatorsThe intervention provided 12 weeks of at?home cessation support which included help in maintaining a smoke?free home, help in accessing and using medication, further behavioural support and personalised feedback on home air quality. The comparator was NICE PH48 care as usual.MeasuresThe primary outcome was self?reported continuous abstinence from smoking validated by an exhaled carbon monoxide level ?6ppm four?weeks after discharge from hospital.FindingsIn an intention?to?treat analysis at the four?week primary endpoint, 38 participants (18.8%) in the usual care group and 43 (21.3%) in the intervention group reported continuous abstinence from smoking (odds ratio 1.17, 95% confidence interval 0.72 to 1.90, Bayes factor 0.33). There were no significant differences in any secondary outcomes, including self?reported cessation at 3 months, having a smoke?free home, or number of cigarettes smoked per day in those who did not quit.ConclusionsProvision of a home visit and continued support to prevent relapse to smoking after hospital discharge did not appear to increase subsequent abstinence rate above usual care in accordance with UK guidance from the National Institute of Health and Care Excellence

Generalized Property-Directed Reachability for Hybrid Systems

Generalized property-directed reachability (GPDR) belongs to the family of the model-checking techniques called IC3/PDR. It has been successfully applied to software verification; for example, it is the core of Spacer, a state-of-the-art Horn-clause solver bundled with Z3. However, it has yet to be applied to hybrid systems, which involve a continuous evolution of values over time. As the first step towards GPDR- based model checking for hybrid systems, this paper formalizes HGPDR, an adaptation of GPDR to hybrid systems, and proves its soundness. We also implemented a semi-automated proof-of-concept verifier, which allows a user to provide hints to guide verification steps.Comment: To appear in VMCAI 202

Multiset Bisimulations as a Common Framework for Ordinary and Probabilistic Bisimulations

Our concrete objective is to present both ordinary bisimulations and probabilistic bisimulations in a common coalgebraic framework based on multiset bisimulations. For that we show how to relate the underlying powerset and probabilistic distributions functors with the multiset functor by means of adequate natural transformations. This leads us to the general topic that we investigate in the paper: a natural transformation from a functor F to another G transforms F-bisimulations into G-bisimulations but, in general, it is not possible to express G-bisimulations in terms of F-bisimulations. However, they can be characterized by considering Hughes and Jacobs’ notion of simulation, taking as the order on the functor F the equivalence induced by the epi-mono decomposition of the natural transformation relating F and G. We also consider the case of alternating probabilistic systems where non-deterministic and probabilistic choices are mixed, although only in a partial way, and extend all these results to categorical simulations