Generating networks of genetic processors

The Networks of Genetic Processors (NGPs) are non-conventional models of computation based on genetic operations over strings, namely mutation and crossover operations as it was established in genetic algorithms. Initially, they have been proposed as acceptor machines which are decision problem solvers. In that case, it has been shown that they are universal computing models equivalent to Turing machines. In this work, we propose NGPs as enumeration devices and we analyze their computational power. First, we define the model and we propose its definition as parallel genetic algorithms. Once the correspondence between the two formalisms has been established, we carry out a study of the generation capacity of the NGPs under the research framework of the theory of formal languages. We investigate the relationships between the number of processors of the model and its generative power. Our results show that the number of processors is important to increase the generative capability of the model up to an upper bound, and that NGPs are universal models of computation if they are formulated as generation devices. This allows us to affirm that parallel genetic algorithms working under certain restrictions can be considered equivalent to Turing machines and, therefore, they are universal models of computation.

6.1. FEATURES OF RESOURCE SUPPORT FOR INNOVATION AND INVESTMENT PROJECTS

В настоящее время существуют различные модели и источники финансирования процесса реализации инновационных проектов. При этом выделить универсальные модели, методы и инструменты финансирования инновационной деятельности, эффективные для любых инновационных проектов, невозможно. Это обусловливает необходимость дополнительного исследования особенностей ресурсного обеспечения инновационно-инвестиционных проектов и направ­лений их развития. Статья посвящена анализу современных практик финансирования инновационно-инвестиционных проектов в контексте развития цифровой экономики. Цель исследования заключается в выявлении возможностей и направлений развития отечественных практик финансирования инновационных проектов с помощью различных механизмов ресурсного обеспечения, в том числе путем крауд-финансирования. В результате исследования выявлены основные направления развития системы финансирования инновационных проектов в РФ. Currently, there are various models and sources of funding for the implementation of innovative projects. At the same time, it is impossible to single out universal models, methods and instruments for financing innovative activities that are effective for any innovative projects. This necessitates an additional study of the features of resource provision for innovation and investment projects and the directions of their development. The article is devoted to the analysis of modern practices of financing innovation and investment projects in the context of the development of the digital economy. The purpose of the study is to identify opportunities and directions for the development of domestic practices of financing innovative projects using various mechanisms of resource provision, including through crowd funding. As a result, the research identified the main directions of development of the system of financing innovative projects in the Russian Federation.

NNIL-formulas revisited: Universal models and finite model property

NNIL-formulas, introduced by Visser in 1983–1984 in a study of $\varSigma _1$-subsitutions in Heyting arithmetic, are intuitionistic propositional formulas that do not allow nesting of implication to the left. The first results about these formulas were obtained in a paper of 1995 by Visser et al. In particular, it was shown that NNIL-formulas are exactly the formulas preserved under taking submodels of Kripke models. Recently, Bezhanishvili and de Jongh observed that NNIL-formulas are also reflected by the colour-preserving monotonic maps of Kripke models. In the present paper, we first show how this observation leads to the conclusion that NNIL-formulas are preserved by arbitrary substructures not necessarily satisfying the topo-subframe condition. Then, we apply it to construct universal models for NNIL. It follows from the properties of these universal models that NNIL-formulas are also exactly the formulas that are reflected by colour-preserving monotonic maps. By using the method developed in constructing the universal models, we give a new direct proof that the logics axiomatized by NNIL-axioms have the finite model property.

On the Question of Pedagogical Digital Competence

Educational institutions develop professional training programs for teachers so they could bring technology into the classroom and take the quality of education to a new level. However, despite the measures being adopted, a number of researchers report unsatisfying results. One of the root causes of this situation seems to be the absence of clear understanding of what the notions of digital competence and pedagogical digital competence are supposed to include. This problem is tightly connected with the problem of creating a framework for the development of digital skills of an instructor. On one hand, there is a demand for universal models that would include a wide range of pedagogical digital skills. There is a demand for universal models, which would include the widest possible range of digital competences of a teacher. Among them there are such existing frameworks as DigiCompEdu, ICT CFT, TETCs, which cover numerous aspects of instructors’ work. Meanwhile, there is the lack of models that would structurize the professional practice of a teacher at the micro level of using a digital instrument. There is a necessity for the framework comprising a limited set of primary basic skills which would be universal enough to be applicable to operating any kind of technology. In the article, we propose a version of this type of a framework.

Computing Cores for Existential Rules with the Standard Chase and ASP

To reason with existential rules (a.k.a. tuple-generating dependencies), one often computes universal models. Among the many such models of different structure and cardinality, the core is arguably the “best”. Especially for finitely satisfiable theories, where the core is the unique smallest universal model, it has advantages in query answering, non-monotonic reasoning, and data exchange. Unfortunately, computing cores is difficult and not supported by most reasoners. We therefore propose ways of computing cores using practically implemented methods from rule reasoning and answer set programming. Our focus is on cases where the standard chase algorithm produces a core. We characterise this desirable situation in general terms that apply to a large class of cores, derive concrete approaches for decidable special cases, and generalise these approaches to non-monotonic extensions of existential rules.

Characterizing Boundedness in Chase Variants

Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions.

Conservative Extensions in Horn Description Logics with Inverse Roles

We investigate the decidability and computational complexity of conservative extensions and the related notions of inseparability and entailment in Horn description logics (DLs) with inverse roles. We consider both query conservative extensions, defined by requiring that the answers to all conjunctive queries are left unchanged, and deductive conservative extensions, which require that the entailed concept inclusions, role inclusions, and functionality assertions do not change. Upper bounds for query conservative extensions are particularly challenging because characterizations in terms of unbounded homomorphisms between universal models, which are the foundation of the standard approach to establishing decidability, fail in the presence of inverse roles. We resort to a characterization that carefully mixes unbounded and bounded homomorphisms and enables a decision procedure that combines tree automata and a mosaic technique. Our main results are that query conservative extensions are 2ExpTime-complete in all DLs between ELI and Horn-ALCHIF and between Horn-ALC and Horn-ALCHIF, and that deductive conservative extensions are 2ExpTime-complete in all DLs between ELI and ELHIF_bot. The same results hold for inseparability and entailment.