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From Branching to Linear Time, Coalgebraically
Corina Cirstea
Computer Science , 2013, DOI: 10.4204/EPTCS.126.2
Abstract: We consider state-based systems modelled as coalgebras whose type incorporates branching, and show that by suitably adapting the definition of coalgebraic bisimulation, one obtains a general and uniform account of the linear-time behaviour of a state in such a coalgebra. By moving away from a boolean universe of truth values, our approach can measure the extent to which a state in a system with branching is able to exhibit a particular linear-time behaviour. This instantiates to measuring the probability of a specific behaviour occurring in a probabilistic system, or measuring the minimal cost of exhibiting a specific behaviour in the case of weighted computations.
Rewriting Calculus: Foundations and Applications
Horatiu Cirstea
Computer Science , 2000,
Abstract: This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus, which generalizes the first order term rewriting and lambda-calculus, and makes possible the representation of the non-determinism. In our approach the abstraction operator as well as the application operator are objects of calculus. The result of a reduction in the rewriting calculus is either an empty set representing the application failure, or a singleton representing a deterministic result, or a set having several elements representing a not-deterministic choice of results. In this thesis we concentrate on the properties of the rewriting calculus where a syntactic matching is used in order to bind the variables to their current values. We define evaluation strategies ensuring the confluence of the calculus and we show that these strategies become trivial for restrictions of the general rewriting calculus to simpler calculi like the lambda-calculus. The rewriting calculus is not terminating in the untyped case but the strong normalization is obtained for the simply typed calculus. In the rewriting calculus extended with an operator allowing to test the application failure we define terms representing innermost and outermost normalizations with respect to a set of rewriting rules. By using these terms, we obtain a natural and concise description of the conditional rewriting. Finally, starting from the representation of the conditional rewriting rules, we show how the rewriting calculus can be used to give a semantics to ELAN, a language based on the application of rewriting rules controlled by strategies.
IFRS, US GAAP OR ROMANIAN REGULATIONS CAN THEY BECOME ONE?
Cirstea Andreea,Cirstea Stefan,Fulop Melinda
Annals of the University of Oradea : Economic Science , 2010,
Abstract: In a period when convergence is the main driving force of IASB and FASB programmes, who needs a comparison of the two sets of standards-IFRS issued by IASB and US GAAP issued by FASB? Arent they mainly the same after 5 years of hard work of those who establish the two sets of standards? The answer lies in the fact that mostly all people who work in a multinational company has to understand the present differences between these two sets of standards. A combination of the convergence of the national standards with the IFRS and the follow-up use of IFRS standards would mean that the two accounting languages from all over the world should be reduced rapidly only to IFRS and US GAAP. Although these two sets of standards are more and more similar to each other, they are not totally identical-yet. And until they become identical it will be necessary to state clearly and explain the differences that exist between them.
Feminism and Faith: Exploring Christian Spaces in the Writing of Sara Maitland and Michèle Roberts
Arina LUNGU-CIRSTEA
E-rea : Revue électronique d’études sur le Monde Anglophone , 2011, DOI: 10.4000/erea.1563
Abstract: En 1983, les féministes britanniques Sara Maitland et Jo Garcia ont publié Walking on the Water (London : Virago), une collection d’essais, de récits, de poèmes et de photos produits par des femmes sur le thème de la spiritualité. Les contributrices ont été en particulier invitées à explorer la relation entre leur identité féministe et leurs croyances religieuses. Le ton de ces contributions varie fortement, allant de l’envie passionnée de concilier les objectifs du féminisme avec le christianisme à un rejet total de l’Eglise comme institution patriarcale suprême. Cet article met en dialogue des récits diamétralement opposés du rapport entre christianisme et féminisme en s’intéressante plus particulièrement à deux des contributrices, Sara Maitland (1950 - ) et Michèle Roberts (1949 - ). Ces deux écrivaines, qui se sont activement impliquées dans les mouvements féministes des années 1970, ont toutes deux lutté pour se réconcilier avec leur héritage chrétien. Néanmoins, alors que Maitland tente essentiellement de revisiter le christianisme en y incorporant les points essentiels d’une idéologie féministe, Roberts sent le besoin impérieux de se défaire de son identité religieuse afin de devenir indépendante ; en effet, dans son autobiographie Paper Houses (2007) elle décrit son éducation catholique comme “autoritaire et misogyne” (16). Cet article explore les fa ons dont l’identité spirituelle se construit dans le jeu complexe des interactions entre féminisme et foi. Il se propose, dans une perspective comparatiste, d’analyser d’une part le recueil de nouvelles de Sara Maitland intitulé A Book of Spells, et d’autre part, le roman acclamé de Michèle Roberts, Daughters of the House. Dans ces écrits, Maitland et Roberts ont un objectif commun qui est de renégocier la place des femmes dans l’histoire chrétienne dont elles reconnaissent – il est vrai à partir de perspectives différentes – la dimension fondatrice de l’identité occidentale contemporaine.Quel que soit le choix personnel de ces auteures, la spiritualité chrétienne se révèle être un facteur clé pour déterminer le lieu précis qu’elles - ou leurs héro nes - occupent dans le monde social. Prenant comme point de départ l’idée que “les identités du lieu sont toujours variables, attaquées et multiples” (Doreen Massey), cet article se concentre sur les efforts que déploient ces écrivaines pour affirmer l’identité spirituelle des femmes contre les frontières rigides de l’espace social. In 1983, British feminists Sara Maitland and Jo Garcia edited Walking on the Water (London: Virago), a collection of “essays,
Boundary blow-up in nonlinear elliptic equations of Bieberbach--Rademacher type
Florica Corina Cirstea,Vicentiu Radulescu
Mathematics , 2005,
Abstract: We establish the uniqueness of the positive solution for equations of the form $-\Delta u=au-b(x)f(u)$ in $\Omega$, $u|\_{\partial\Omega}=\infty$. The special feature is to consider nonlinearities $f$ whose variation at infinity is \emph{not regular} (e.g., $\exp(u)-1$, $\sinh(u)$, $\cosh(u)-1$, $\exp(u)\log(u+1)$, $u^\beta \exp(u^\gamma)$, $\beta\in {\mathbb R}$, $\gamma>0$ or $\exp(\exp(u))-e$) and functions $b\geq 0$ in $\Omega$ vanishing on $\partial\Omega$. The main innovation consists of using Karamata's theory not only in the statement/proof of the main result but also to link the non-regular variation of $f$ at infinity with the blow-up rate of the solution near $\partial\Omega$.
Nonlinear problems with boundary blow-up: a Karamata regular variation theory approach
Florica Corina Cirstea,Vicentiu Radulescu
Mathematics , 2005,
Abstract: We study the uniqueness and expansion properties of the positive solution of the logistic equation $\Delta u+au=b(x)f(u)$ in a smooth bounded domain $\Omega$, subject to the singular boundary condition $u=+\infty$ on $\partial\Omega$. The absorption term $f$ is a positive function satisfying the Keller--Osserman condition and such that the mapping $f(u)/u$ is increasing on $(0,+\infty)$. We assume that $b$ is non-negative, while the values of the real parameter $a$ are related to an appropriate semilinear eigenvalue problem. Our analysis is based on the Karamata regular variation theory.
EUROPEAN HARMONIZATION OF CONSOLIDATED FINANCIAL STATEMENTS REGULATIONS?
Baltariu Carmen-Alexandra,Cirstea Andreea
Annals of the University of Oradea : Economic Science , 2012,
Abstract: The purpose of this paper is to analyze the degree of formal accounting harmonization within the European Union with respect to the EC Regulation No. 1606/2002 adopted by the European Parliament and European Council on the 19th of July 2002, which regulates the application of IAS/IFRS regarding the financial reporting of listed European companies. The conclusions of the paper were drawn after the completion of a thorough analysis performed by using correlation and/ or association coefficients, namely: the Jaccard ¢a a ¢s Correlation Coefficients, Rogers and Tanimoto Coefficient, Lance and Williams Coefficient and Binary Euclidian Distance Coefficient. The results lead us to conclude that although our first hypothesis is verified, the degree of harmonization between the accounting systems of EU Member States could be truly quantified only through an analysis of the material accounting harmonization, more precisely by analyzing the way the companies put into practice the requirements imposed through the EC Regulation No. 1606/2002.
Representation of multivariate functions via the potential theory
Florica-Corina Cirstea,Sever Silvestru Dragomir
Mathematics , 2003,
Abstract: In this paper, by the use of Potential Theory, some representation results for multivariate functions from the Sobolev spaces in terms of the double layer potential and the fundamental solution of Laplace's equation are pointed out. Applications for multivariate inequalities of Ostrowski type are also provided.
EXPTIME Tableaux for the Coalgebraic mu-Calculus
Corina Cirstea,Clemens Kupke,Dirk Pattinson
Mathematics , 2011, DOI: 10.2168/LMCS-7(3:03)2011
Abstract: The coalgebraic approach to modal logic provides a uniform framework that captures the semantics of a large class of structurally different modal logics, including e.g. graded and probabilistic modal logics and coalition logic. In this paper, we introduce the coalgebraic mu-calculus, an extension of the general (coalgebraic) framework with fixpoint operators. Our main results are completeness of the associated tableau calculus and EXPTIME decidability for guarded formulas. Technically, this is achieved by reducing satisfiability to the existence of non-wellfounded tableaux, which is in turn equivalent to the existence of winning strategies in parity games. Our results are parametric in the underlying class of models and yield, as concrete applications, previously unknown complexity bounds for the probabilistic mu-calculus and for an extension of coalition logic with fixpoints.
Lattice-Theoretic Progress Measures and Coalgebraic Model Checking (with Appendices)
Ichiro Hasuo,Shunsuke Shimizu,Corina Cirstea
Computer Science , 2015,
Abstract: In the context of formal verification in general and model checking in particular, parity games serve as a mighty vehicle: many problems are encoded as parity games, which are then solved by the seminal algorithm by Jurdzinski. In this paper we identify the essence of this workflow to be the notion of progress measure, and formalize it in general, possibly infinitary, lattice-theoretic terms. Our view on progress measures is that they are to nested/alternating fixed points what invariants are to safety/greatest fixed points, and what ranking functions are to liveness/least fixed points. That is, progress measures are combination of the latter two notions (invariant and ranking function) that have been extensively studied in the context of (program) verification. We then apply our theory of progress measures to a general model-checking framework, where systems are categorically presented as coalgebras. The framework's theoretical robustness is witnessed by a smooth transfer from the branching-time setting to the linear-time one. Although the framework can be used to derive some decision procedures for finite settings, we also expect the proposed framework to form a basis for sound proof methods for some undecidable/infinitary problems.
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