Probabilistic π-Calculus and Event Structures

This paper proposes two semantics of a probabilistic variant of the π-calculus: an interleaving semantics in terms of Segala automata and a true concurrent semantics, in terms of probabilistic event structures. The key technical point is a use of types to identify a good class of non-deterministic probabilistic behaviours which can preserve a compositionality of the parallel operator in the event structures and the calculus. We show an operational correspondence between the two semantics. This allows us to prove a “probabilistic confluence” result, which generalises the confluence of the linearly typed π-calculus.     

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.     

On the ω-language Expressive Power of Extended Petri Nets

In this paper, we study the expressive power of several monotonic extensions of Petri nets. We compare the expressive power of Petri nets, Petri nets extended with non-blocking arcs and Petri nets extended with transfer arcs, in terms of ω-languages. We show that the hierarchy of expressive powers of those models is strict. To prove these results, we propose original techniques that rely on well-quasi orderings and monotonicity properties.     

Handling Liveness Properties in (ω-)Regular Model Checking

Since the topic emerged several years ago, work on regular model checking has mostly been devoted to the verification of state reachability and safety properties. Though it was known that liveness properties could also be checked within this framework, little has been done about working out the corresponding details, and experimentally evaluating the approach. This paper addresses these issues in the context of regular model checking based on the encoding of states by finite or infinite words. It works out the exact constructions to be used in both cases, and solves the problem resulting from the fact that infinite computations of unbounded configurations might never contain the same configuration twice, thus making cycle detection problematic. Several experiments showing the applicability of the approach were successfully conducted.     

Strong normalisation in the π-calculus

We introduce a typed π-calculus where strong normalisation is ensured by typability. Strong normalisation is a useful property in many computational contexts, including distributed systems. In spite of its simplicity, our type discipline captures a wide class of converging name-passing interactive behaviour. The proof of strong normalisability combines methods from typed λ-calculi and linear logic with process-theoretic reasoning. It is adaptable to systems involving state, non-determinism, polymorphism, control and other extensions. Strong normalisation is shown to have significant consequences, including finite axiomatisation of weak bisimilarity, a fully abstract embedding of the simply typed λ-calculus with products and sums and basic liveness in interaction. Strong normalisability has been extensively studied as a fundamental property in functional calculi, term rewriting and logical systems. This work is one of the first steps to extend theories and proof methods for strong normalisability to the context of name-passing processes.     

A Partition Refinement Algorithm for the π-Calculus

The partition refinement algorithm is the basis for most of the tools for checking bisimulation equivalences and for computing minimal realisations of CCS-like finite state processes. In this paper, we present a partition refinement algorithm for the π-calculus, a development of CCS where channel names can be communicated. It can be used to check bisimilarity and to compute minimal realisations of finite control processes—the π-calculus counterpart of CCS finite state processes. The algorithm is developed for strong open bisimulation and can be adapted to late and early bisimulations, as well as to weak bisimulations. To arrive at the algorithm, a few laws, proof techniques, and four characterizations of open bisimulation are proved.     

Open Bisimulation, Revisited

In the context of the π-calculus, open bisimulation is prominent and popular due to its congruence properties and its easy implementability. Motivated by the attempt to generalise it to the spi-calculus, we offer a new, more refined definition and show in how far it coincides with the original one.     

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 Model in κ for DNA Addition

DNA computing is a hot research topic in recent years. Formalization and verification using theories(π-calculus, bioambients, κ-calculus and etc.) in Computer Science attract attention because it can help prove and predict to a certian degree various kinds of biological processes. Combining these two aspects, formal methods can be used to verify algorithms in DNA computing, including basic arithmetic operations if they are to be included in a DNA chip. In this paper, we first introduce a newly-designed algorithm for solving binary addition with DNA, which contributes to a unit in DNA computer processor, and then formalize the algorithm in κ-calculus(a formal method well suited for describing protein interactions) to show the correctness of it in a sense, and a sensible example is provided. Finally, some discussion on the described model is made, in addition to a few possible future improvement directions.     

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.     

Divide and Congruence Applied to η-Bisimulation

We present congruence formats for η- and rooted η-bisimulation equivalence. These formats are derived using a method for decomposing modal formulas in process algebra. To decide whether a process algebra term satisfies a modal formula, one can check whether its subterms satisfy formulas that are obtained by decomposing the original formula. The decomposition uses the structural operational semantics that underlies the process algebra.     

Preparation and characterization of nanocrystalline α-Fe2O3 by a sol-gel process

α-Fe₂O₃ ultra-fine powder with an average particle size of 6–26nm has been prepared by a sol-gel process. Thermal analysis, X-ray diffraction and transmission electron microscope were used to study its formation process and micro-structure. The temperature dependence of the electric conductance of the elements made of nanocrystalline α-Fe₂O₃ shows that the gas-sensing properties are strongly related to its surface. The elements exhibited good sensitivity and selectivity to ethyl alcohol, indicating it is a promising alcohol-sensing material.     

On discrete lower π-strategies

Two-person zero-sum differential games of survival are investigated. It is assumed that player I, as well as player II, can employ during the course of the game any lower π-strategy [2], π(t_i) being a finite partition of [t₀, ∞). The concept of a discrete lower π-strategy is introduced and it is shown that if player I (II) confines himself to the space of discrete lower π-strategies, being a subset of the space of lower π-strategies, then he will be able to force the same lower (upper) value as if he could employ any lower π-strategy. Since we do not use any deep facts about differential games, the results contained here might be extended to continuous games.     

A Process Model of Rho GTP-binding Proteins in the Context of Phagocytosis

At the early stages of the phagocytic signalling, Rho GTP-binding proteins play a key role. With the stimulus from the cell membrane and with the help from the regulators (GEF, GAP, Effector, GDI), these proteins serve as switches that interact with their environment in a complex manner. We present a generic process model for the Rho GTP-binding proteins, and compare it with a previous model that uses ordinary differential equations. We then extend the basic model to include the behaviour of the GDIs. We discuss the challenges this extension brings and directions of further research.     

On the representation of McCarthy's in the -calculus

We study the encoding of , the call-by-name λ-calculus enriched with McCarthy's amb operator, into the π-calculus. Semantically, amb is a challenging operator, for the fairness constraints that it expresses. We prove that, under a certain interpretation of divergence in the λ-calculus (weak divergence), a faithful encoding is impossible. However, with a different interpretation of divergence (strong divergence), the encoding is possible, and for this case we derive results and coinductive proof methods to reason about that are similar to those for the encoding of pure λ-calculi. We then use these methods to derive the most important laws concerning amb. We take bisimilarity as behavioural equivalence on the π-calculus, which sheds some light on the relationship between fairness and bisimilarity.     

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.