T-homotopy and refinement of observation (III) : Invariance of the branching and merging homologies

This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this third part, it is proved that the generalized T-homotopy equivalences preserve the branching and merging homology theories of a flow. These homology theories are of interest in computer science since they detect the non-deterministic branching and merging areas of execution paths in the time flow of a higher dimensional automaton. The proof is based on Reedy model category techniques.Comment: 30 pages ; final preprint version before publication ; see http://nyjm.albany.edu:8000/j/2006/Vol12.ht

T-homotopy and refinement of observation (II) : Adding new T-homotopy equivalences

This paper is the second part of a series of papers about a new notion of T-homotopy of flows. It is proved that the old definition of T-homotopy equivalence does not allow the identification of the directed segment with the 3-dimensional cube. This contradicts a paradigm of dihomotopy theory. A new definition of T-homotopy equivalence is proposed, following the intuition of refinement of observation. And it is proved that up to weak S-homotopy, a old T-homotopy equivalence is a new T-homotopy equivalence. The left-properness of the weak S-homotopy model category of flows is also established in this second part. The latter fact is used several times in the next papers of this series.Comment: 20 pages, 3 figure

Antipode formulas for some combinatorial Hopf algebras

Motivated by work of Buch on set-valued tableaux in relation to the K-theory of the Grassmannian, Lam and Pylyavskyy studied six combinatorial Hopf algebras that can be thought of as K-theoretic analogues of the Hopf algebras of symmetric functions, quasisymmetric functions, noncommutative symmetric functions, and of the Malvenuto-Reutenauer Hopf algebra of permutations. They described the bialgebra structure in all cases that were not yet known but left open the question of finding explicit formulas for the antipode maps. We give combinatorial formulas for the antipode map for the K-theoretic analogues of the symmetric functions, quasisymmetric functions, and noncommutative symmetric functions.Comment: 26 page

A MDE-based optimisation process for Real-Time systems

The design and implementation of Real-Time Embedded Systems is now heavily relying on Model-Driven Engineering (MDE) as a central place to define and then analyze or implement a system. MDE toolchains are taking a key role as to gather most of functional and not functional properties in a central framework, and then exploit this information. Such toolchain is based on both 1) a modeling notation, and 2) companion tools to transform or analyse models. In this paper, we present a MDE-based process for system optimisation based on an architectural description. We first define a generic evaluation pipeline, define a library of elementary transformations and then shows how to use it through Domain-Specific Language to evaluate and then transform models. We illustrate this process on an AADL case study modeling a Generic Avionics Platform

Mapping RT-LOTOS specifications into Time Petri Nets

RT-LOTOS is a timed process algebra which enables compact and abstract specification of real-time systems. This paper proposes and illustrates a structural translation of RT-LOTOS terms into behaviorally equivalent (timed bisimilar) finite Time Petri nets. It is therefore possible to apply Time Petri nets verification techniques to the profit of RT-LOTOS. Our approach has been implemented in RTL2TPN, a prototype tool which takes as input an RT-LOTOS specification and outputs a TPN. The latter is verified using TINA, a TPN analyzer developed by LAAS-CNRS. The toolkit made of RTL2TPN and TINA has been positively benchmarked against previously developed RT-LOTOS verification tool

Branch merging on continuum trees with applications to regenerative tree growth

We introduce a family of branch merging operations on continuum trees and show that Ford CRTs are distributionally invariant. This operation is new even in the special case of the Brownian CRT, which we explore in more detail. The operations are based on spinal decompositions and a regenerativity preserving merging procedure of $(\alpha, \theta)$-strings of beads, that is, random intervals $[0, L_{\alpha, \theta}]$ equipped with a random discrete measure $dL^{-1}$ arising in the limit of ordered $(\alpha, \theta)$-Chinese restaurant processes as introduced recently by Pitman and Winkel. Indeed, we iterate the branch merging operation recursively and give an alternative approach to the leaf embedding problem on Ford CRTs related to $(\alpha, 2-\alpha)$-regenerative tree growth processes.Comment: 40 pages, 5 figure

On Redundancy Elimination Tolerant Scheduling Rules

In (Ferrucci, Pacini and Sessa, 1995) an extended form of resolution, called Reduced SLD resolution (RSLD), is introduced. In essence, an RSLD derivation is an SLD derivation such that redundancy elimination from resolvents is performed after each rewriting step. It is intuitive that redundancy elimination may have positive effects on derivation process. However, undesiderable effects are also possible. In particular, as shown in this paper, program termination as well as completeness of loop checking mechanisms via a given selection rule may be lost. The study of such effects has led us to an analysis of selection rule basic concepts, so that we have found convenient to move the attention from rules of atom selection to rules of atom scheduling. A priority mechanism for atom scheduling is built, where a priority is assigned to each atom in a resolvent, and primary importance is given to the event of arrival of new atoms from the body of the applied clause at rewriting time. This new computational model proves able to address the study of redundancy elimination effects, giving at the same time interesting insights into general properties of selection rules. As a matter of fact, a class of scheduling rules, namely the specialisation independent ones, is defined in the paper by using not trivial semantic arguments. As a quite surprising result, specialisation independent scheduling rules turn out to coincide with a class of rules which have an immediate structural characterisation (named stack-queue rules). Then we prove that such scheduling rules are tolerant to redundancy elimination, in the sense that neither program termination nor completeness of equality loop check is lost passing from SLD to RSLD.Comment: 53 pages, to appear on TPL

A heuristic-based approach to code-smell detection

Encapsulation and data hiding are central tenets of the object oriented paradigm. Deciding what data and behaviour to form into a class and where to draw the line between its public and private details can make the difference between a class that is an understandable, flexible and reusable abstraction and one which is not. This decision is a difficult one and may easily result in poor encapsulation which can then have serious implications for a number of system qualities. It is often hard to identify such encapsulation problems within large software systems until they cause a maintenance problem (which is usually too late) and attempting to perform such analysis manually can also be tedious and error prone. Two of the common encapsulation problems that can arise as a consequence of this decomposition process are data classes and god classes. Typically, these two problems occur together – data classes are lacking in functionality that has typically been sucked into an over-complicated and domineering god class. This paper describes the architecture of a tool which automatically detects data and god classes that has been developed as a plug-in for the Eclipse IDE. The technique has been evaluated in a controlled study on two large open source systems which compare the tool results to similar work by Marinescu, who employs a metrics-based approach to detecting such features. The study provides some valuable insights into the strengths and weaknesses of the two approache