### A discrete-time software reliability-growth model and its application for predicting the number of errors encountered during program testing

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We combine a new data model, where the random classification is subjected to rather weak restrictions which in turn are based on the Mammen−Tsybakov [E. Mammen and A.B. Tsybakov, Ann. Statis. 27 (1999) 1808–1829; A.B. Tsybakov, Ann. Statis. 32 (2004) 135–166.] small margin conditions, and the statistical query (SQ) model due to Kearns [M.J. Kearns, J. ACM 45 (1998) 983–1006] to what we refer to as PAC + SQ model. We generalize the class conditional constant noise (CCCN) model introduced by Decatur...

Among several alternative viewpoints for building software quality metrics, evaluating the consistency between different models in a software specification or implementation appears to be fruitful. An obvious difficulty is that different models are usually expressed by means of different concepts, and then, confronting heterogeneous representations is not straightforward. In this paper, we propose a solution for measuring the consistency between the architecture and the communication models. After...

We study in this paper the electromagnetic field generated in a conductor by an alternating current density. The resulting interface problem (see Bossavit (1993)) between the metal and the dielectric medium is treated by a mixed–FEM and BEM coupling method. We prove that our BEM-FEM formulation is well posed and that it leads to a convergent Galerkin method.

Computing the image of a regular language by the transitive closure of a relation is a central question in regular model checking. In a recent paper Bouajjani et al. [IEEE Comput. Soc. (2001) 399–408] proved that the class of regular languages $L$ – called APC – of the form ${\cup}_{j}$${L}_{0...}$

Computing the image of a regular language by the transitive closure of a relation is a central question in regular model checking. In a recent paper Bouajjani et al. [IEEE Comput. Soc. (2001) 399–408] proved that the class of regular languages L – called APC – of the form UjL0,jL1,jL2,j...Lkj,j, where the union is finite and each Li,j is either a single symbol or a language of the form B* with B a subset of the alphabet, is closed under all semi-commutation relations R. Moreover a recursive...

In the context of object-oriented systems, algorithms for building class hierarchies are currently receiving much attention. We present here a characterization of several global algorithms. A global algorithm is one which starts with only the set of classes (provided with all their properties) and directly builds the hierarchy. The algorithms scrutinized were developped each in a different framework. In this survey, they are explained in a single framework, which takes advantage of a substructure...

We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system...

We present an abstract equational framework for the specification of systems having both observational and computational features. Our approach is based on a clear separation between the two categories of features, and uses algebra, respectively coalgebra to formalise them. This yields a coalgebraically-defined notion of observational indistinguishability, as well as an algebraically-defined notion of reachability under computations. The relationship between the computations yielding new system states...

The organizational structure is usually defined using the best experience and there is a minimum of formal approach involved. This paper shows the possibilities of the theory of concept analysis that can help to understand organizational structure based on solid mathematical foundations. This theory is extended by the concept of knowledge sharing and diversity that enables to evaluate the organizational structure. The alternative approach based on the hierarchical methods of cluster analysis is...

A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation...

This paper sketches the state of the art in the application of mechanical theorem provers to the verification of commercial computer hardware and software. While the paper focuses on the theorem proving system ACL2, developed by the two authors, it references much related work in formal methods. The paper is intended to satisfy the curiosity of readers interested in logic and artificial intelligence as to the role of mechanized theorem proving in hardware and software design today. In addition,...