Expressiveness of Probabilistic π-calculus

In this work we propose a probabilistic extension of the π-calculus. The main novelty is a probabilistic mixed choice operator, that is, a choice construct with a probability distribution on the branches, and where input and output actions can both occur as guards. We develop the operational semantics of this calculus, and then we investigate its expressiveness. In particular, we compare it with the sublanguage with the two separate choices, where input and output guards are not allowed together in the same choice construct. Our main result is that the separate choices can encode the mixed one. Further, we show that input-guarded choice can encode output-guarded choice and viceversa. In contrast, we conjecture that neither of them can encode the pair of the two separate choices.     

Graphical Verification of a Spatial Logic for the π-calculus

The paper introduces a novel approach to the verification of spatial properties for finite π-calculus specifications. The mechanism is based on a recently proposed graphical encoding for mobile calculi: Each process is mapped into a (ranked) graph, such that the denotation is fully abstract with respect to the usual structural congruence (i.e., two processes are equivalent exactly when the corresponding encodings yield the same graph). Spatial properties for reasoning about the behavior and the structure of π-calculus processes are then expressed in a logic introduced by Caires, and they are verified on the graphical encoding of a process, rather than on its textual representation. More precisely, the graphical presentation allows for providing a simple and easy to implement verification algorithm based on the graphical encoding (returning true if and only if a given process verifies a given spatial formula).     

μ-Bases and singularities of rational planar curves

We provide a technique to detect the singularities of rational planar curves and to compute the correct order of each singularity including the infinitely near singularities without resorting to blow ups. Our approach employs the given parametrization of the curve and uses a μ-basis for the parametrization to construct two planar algebraic curves whose intersection points correspond to the parameters of the singularities including infinitely near singularities with proper multiplicity. This approach extends Abhyankar's method of t-resultants from planar polynomial curves to rational planar curves. We also derive the classical result that for a rational planar curve of degree n the sum of all the singularities with proper multiplicity is (n−1)(n−2)/2. Examples are provided to flesh out our results.     

A Third-Order Representation of the λμ-Calculus

Higher-order logical frameworks provide a powerful technology to reason about object languages with binders. This will be demonstrated for the case of the λμ-calculus with two different binders which can most elegantly be represented using a third-order constant. Since cases of third- and higher-order encodings are very rare in comparison with those of second order, a second-order representation is given as well and equivalence to the third-order representation is proven formally.     

Interaction Nets vs. the ρ-calculus: Introducing Bigraphical Nets

The ρ-calculus generalises both term rewriting and the λ-calculus in a uniform framework. Interaction nets are a form of graph rewriting which proved most successful in understanding the dynamics of the λ-calculus, the prime example being the implementation of optimal β-reduction. It is thus natural to study interaction net encodings of the ρ-calculus as a first step towards the definition of efficient reduction strategies. We give two interaction net encodings which bring a new understanding to the operational semantics of the ρ-calculus; however, these encodings have some drawbacks and to overcome them we introduce bigraphical nets—a new paradigm of computation inspired by Lafont's interactions nets and Milner's bigraphs.     

A Spatial Extension to the π Calculus

Spatial dynamics receive increasing attention in Systems Biology and require suitable modeling and simulation approaches. So far, modeling formalisms have focused on population-based approaches or place and move individuals relative to each other in space. SpacePi extends the π calculus by time and space. π processes are embedded into a vector space and move individually. Only processes that are sufficiently close can communicate. The operational semantics of SpacePi defines the interplay between movement, communication, and time-triggered events. A model describing the phototaxis of the Euglena micro-organism is presented as a practical example. The formalism's use and generality is discussed with respect to the modeling of molecular biological processes like diffusion, active transportation in cell signaling, and spatial structures.     

UppDMC: A Distributed Model Checker for Fragments of the μ-Calculus

We present UppDMC, a distributed model-checking tool. It is tailored for checking finite-state systems and μ-calculus specifications with at most one alternation of minimal and maximal fixed-point operators. This fragment is also known as . Recently, efficient game-based algorithms for this logic have been outlined.We describe the implementation of these algorithms within UppDMC and study their performance on practical examples. Running UppDMC on a simple workstation cluster, we were able to check liveness properties of the largest examples given in the VLTS Benchmark Suite, for which no answers were previously known.     

A Behavioural Pseudometric based on λ–Bisimilarity

In order to describe approximate equivalence among processes, the notions of λ–bisimilarity and behavioural pseudometric have been introduced by Ying and van Breugel respectively. Van Breugel provides a distance function induced by λ–bisimilarity, and conjectures that his behavioural pseudometric coincides with this function. This paper is inspired by this conjecture. We give a negative answer for van Breugel's conjecture first. Moreover, we show that the distance function induced by λ–bisimilarity is a pseudometric on states, and provide a fixed point characterization of this pseudometric.     

A Proof Search Specification of the π-Calculus

We present a meta-logic that contains a new quantifier (for encoding “generic judgments”) and inference rules for reasoning within fixed points of a given specification. We then specify the operational semantics and bisimulation relations for the finite π-calculus within this meta-logic. Since we restrict to the finite case, the ability of the meta-logic to reason within fixed points becomes a powerful and complete tool since simple proof search can compute this one fixed point. The quantifier helps with the delicate issues surrounding the scope of variables within π-calculus expressions and their executions (proofs). We shall illustrate several merits of the logical specifications we write: they are natural and declarative; they contain no side conditions concerning names of variables while maintaining a completely formal treatment of such variables; differences between late and open bisimulation relations are easy to see declaratively; and proof search involving the application of inference rules, unification, and backtracking can provide complete proof systems for both one-step transitions and for bisimulation.     

In2O3 + xBaO (x = 0.5-5 at.%) - A novel material for trace level detection of NOx in the ambient

Indium oxide (In₂O₃) doped with 0.5-5 at.% of Ba was examined for their response towards trace levels of NO_x in the ambient. Crystallographic phase studies, electrical conductivity and sensor studies for NO_x with cross interference for hydrogen, petroleum gas (PG) and ammonia were carried out. Bulk compositions with x ≤ 1 at.% of Ba exhibited high response towards NO_x with extremely low cross interference for hydrogen, PG and ammonia, offering high selectivity. Thin films of 0.5 at.% Ba doped In₂O₃ were deposited using pulsed laser deposition technique using an excimer laser (KrF) operating at a wavelength of (λ) 248 nm with a fluence of ∼3 J/cm² and pulsed at 10 Hz. Thin film sensors exhibited better response towards 3 ppm NO_x quite reliably and reproducibly and offer the potential to develop NO_x sensors (Threshold limit value of NO₂ and NO is 3 and 25 ppm, respectively).