Coinduction up to in a fibrational setting

Bisimulation up-to enhances the coinductive proof method for bisimilarity, providing efficient proof techniques for checking properties of different kinds of systems. We prove the soundness of such techniques in a fibrational setting, building on the seminal work of Hermida and Jacobs. This allows us to systematically obtain up-to techniques not only for bisimilarity but for a large class of coinductive predicates modelled as coalgebras. By tuning the parameters of our framework, we obtain novel techniques for unary predicates and nominal automata, a variant of the GSOS rule format for similarity, and a new categorical treatment of weak bisimilarity

Modular coinduction up-to for higher-order languages via first-order transition systems

The bisimulation proof method can be enhanced by employing ‘bisimulations up-to’ techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and bisimilarity, based on abstract fixed-point theory and compatible functions. We transport this theory onto languages whose bisimilarity and LTS go beyond those of first-order models. The approach consists in exhibiting fully abstract translations of the more sophisticated LTSs and bisimilarities onto the first-order ones. This allows us to reuse directly the large corpus of up-to techniques that are available on first-order LTSs. The only ingredient that has to be manually supplied is the compatibility of basic up-to techniques that are specific to the new languages. We investigate the method on the π-calculus, the λ-calculus, and a (call-by-value) λ-calculus with references

Symbolic Algorithms for Language Equivalence and Kleene Algebra with Tests

We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams (BDD). The key idea consists in computing a bisimulation by exploring reachable pairs symbolically, so as to avoid redundancies. This idea can be combined with already existing optimisations, and we show in particular a nice integration with the disjoint sets forest data-structure from Hopcroft and Karp's standard algorithm. Then we consider Kleene algebra with tests (KAT), an algebraic theory that can be used for verification in various domains ranging from compiler optimisation to network programming analysis. This theory is decidable by reduction to language equivalence of automata on guarded strings, a particular kind of automata that have exponentially large alphabets. We propose several methods allowing to construct symbolic automata out of KAT expressions, based either on Brzozowski's derivatives or standard automata constructions. All in all, this results in efficient algorithms for deciding equivalence of KAT expressions

On decidability of concurrent Kleene algebra

Concurrent Kleene algebras support equational reasoning about computing systems with concurrent behaviours. Their natural semantics is given by series(-parallel) rational pomset languages, a standard true concurrency semantics, which is often associated with processes of Petri nets. We use constructions on Petri nets to provide two decision procedures for such pomset languages motivated by the equational and the refinement theory of concurrent Kleene algebra. The contribution to the first problem lies in a much simpler algorithm and an EXPSPACE complexity bound. Decidability of the second, more interesting problem is new and, in fact, EXPSPACE-complete

Algebraic Principles for Rely-Guarantee Style Concurrency Verification Tools

We provide simple equational principles for deriving rely-guarantee-style inference rules and refinement laws based on idempotent semirings. We link the algebraic layer with concrete models of programs based on languages and execution traces. We have implemented the approach in Isabelle/HOL as a lightweight concurrency verification tool that supports reasoning about the control and data flow of concurrent programs with shared variables at different levels of abstraction. This is illustrated on two simple verification examples

Q fever: a new ocular manifestation

Q Fever is a zoonosis caused by Coxiella burnetii. Ocular manifestations are rare in this infection. We describe the case of a man complaining of an intense retro-orbital headache, fever, arthralgia, and bilateral loss of vision, who showed an anterior uveitis accompanied by exudative bilateral inferior retinal detachment and optic disk edema. At the beginning, a Vogt–Koyanagi–Harada (VKH) syndrome was suspected, but the patient was diagnosed with Q fever and treatment with doxycycline was initiated, with complete resolution after 2 weeks. We wondered if Q fever could unleash VKH syndrome or simulate a VKH syndrome by a similar immunological process

On Bisimilarity and Substitution in Presence of Replication

International audienceWe prove a new congruence result for the pi-calculus: bisimilarity is a congruence in the sub-calculus that does not include restriction nor sum, and features top-level replications. Our proof relies on algebraic properties of replication, and on a new syntactic characterisation of bisimilarity. We obtain this characterisation using a rewriting system rather than a purely equational axiomatisation. We then deduce substitution closure, and hence, congruence. Whether bisimilarity is a congruence when replications are unrestricted remains open

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The expansion of OMZs (Oxygen Minimum Zones) due to climate change and their possible evolution and impacts on the ecosystems and the atmosphere are still debated, mostly because of the unability of global climate models to adequatly reproduce the processes governing OMZs. In this study, we examine the factors controlling the oxygen budget, i.e. the equilibrium between oxygen sources and sinks in the northern Arabian Sea OMZ using an eddy-resolving biophysical model. Our model confirms that the biological consumption of oxygen is most intense below the region of highest productivity in the western Arabian Sea. The oxygen drawdown in this region is counterbalanced by the large supply of oxygenated waters originated from the south and advected horizontally by the western boundary current. Although the biological sink and the dynamical sources of oxygen compensate on annual average, we find that the seasonality of the dynamical transport of oxygen is 3 to 5 times larger than the seasonality of the biological sink. In agreement with previous findings, the resulting seasonality of oxygen concentration in the OMZ is relatively weak, with a variability of the order of 15% of the annual mean oxygen concentration in the oxycline and 5% elsewhere. This seasonality primarily arises from the vertical displacement of the OMZ forced by the monsoonal reversal of Ekman pumping across the basin. In coastal areas, the oxygen concentration is also modulated seasonally by lateral advection. Along the western coast of the Arabian Sea, the Somali Current transports oxygen-rich waters originated from the south during summer and oxygen-poor waters from the northeast during winter. Along the eastern coast of the Arabian Sea, we find that the main contributor to lateral advection in the OMZ is the Indian coastal undercurrent that advects southern oxygenated waters during summer and northern low-oxygen waters during winter. In this region, our model indicates that oxygen concentrations are modulated seasonally by coastal Kelvin waves and westward-propagating Rossby waves. Whereas on seasonal time scales the sources and sinks of oxygen are dominated by the mean vertical and lateral advection (Ekman pumping and monsoonal currents), on annual time scales we find that the biological sink is counterbalanced by the supply of oxygen sustained by mesoscale structures (eddies and filaments). Eddy-driven advection hence promotes the vertical supply of oxygen along the western coast of the Arabian Sea and the lateral transport of ventilated waters offshore the coast of Oman and southwest India

Full wave analysis of the image hybrid dielectric/HTS resonator

An analysis of the image hybrid dielectric / high-temperature superconductor (HTS) resonator is carried out. A full-wave radial mode-matching method is used to obtain the electromagnetic fields inside the resonator for single TE01 and dual HE11 modes. Measured resonant frequencies and quality factors of these modes are compared with numerical results of the analysis. The resonator power-handling capability is estimated from the field at the surface of the HTS film, assuming a certain value for the critical field of the HTS film.Peer Reviewe

Checking NFA equivalence with bisimulations up to congruence

16pInternational audienceWe introduce bisimulation up to congruence as a technique for proving language equivalence of non-deterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp. We compare our algorithm to the recently introduced antichain algorithms, by analysing and relating the two underlying coinductive proof methods. We give concrete examples where we exponentially improve over antichains; experimental results moreover show non negligible improvements on random automata