Children's images in the works of Pyotr Dik

Pyotr Dik's graphics are well known in the professional community and are kept in the collections of leading Russian museums, but it is difficult to consider Dik's works fully studied. Compositions containing figurative images that can be interpreted as children's images are common among the artist works of the mature period. However, no separate works have been found on the theme of childhood in the master's work. The purpose of this article is to study children's images from a formal and meaningful point of view. This work uses elements of formal stylistic, iconological, and cultural-historical analyses as methods of studying the topic. The specificity of Dick's artistic method was that the artist did not set itself the task of a detailed study of nature and the reflection of its unique properties on the sheet, but used visual impressions to build his own plastic system, characterized by a recognizable language of conditional geometrized figures. Pyotr Dik addressed children's images in the framework of single-figure, two-figure and group compositions. Single-figure compositions have a meaningful connection with the problem of childhood loneliness, although in some cases they can be a visual metaphor for childhood as a special spiritual state. One of the characteristic motifs of two-figure compositions is the motif of interaction between a child and an adult (especially interesting in this type of composition with images of elderly people). Group compositions containing children's images, in some cases, are associated with the theme of teaching in the broad sense of the word. The artist may have tried to operate with complex categories of a philosophical order, as well as to explore the problem of kinship and alienation through his own system of figurative motives. Графика Петра Дика хорошо известна в профессиональной среде и хранится в собраниях ведущих российских музеев, однако трудно считать наследие Дика полностью изученным. Среди работ художника зрелого периода распространены композиции, содержащие фигуративные изображения, которые можно интерпретировать как детские образы. Однако к настоящему моменту не было обнаружено отдельных работ, посвященных теме детства в творчестве мастера. Целью этой статьи является изучение детских образов с формальной и содержательной точек зрения. В качестве методов изучения темы в данной работе применяются элементы формально-стилистического, иконологического и культурно-исторического анализов. Специфика художественного метода Дика заключалась в том, что график не ставил перед собой задачи детального исследования натуры и отражения ее уникальных свойств на листе, а использовал визуальные впечатления для построения собственной пластической системы, отличающейся узнаваемым языком условных геометризированных фигур. Петр Дик обращался к детским образам в рамках однофигурных, двухфигурных и групповых композиций. Однофигурные композиции содержательно соприкасаются с проблемой детского одиночества, хотя в отдельных случаях могут быть визуальной метафорой детства как особенного духовного состояния. Одним из характерных мотивов двухфигурных композиций стал мотив взаимодействия ребенка и взрослого (особенно интересны в рамках данного типа композиции с образами пожилых людей). Групповые композиции, содержащие детские образы, в некоторых случаях связаны с темой учительства в широком смысле слова. Через собственную систему фигуративных мотивов художник, возможно, пытался оперировать сложными категориями философского порядка, а также исследовать проблему родства и отчуждения.

Weak Separation Problem for Tree Languages

Forest algebras are defined for investigating languages of forests [ordered sequences] of unranked trees, where a node may have more than two [ordered] successors. They consist of two monoids, the horizontal and the vertical, with an action of the vertical monoid on the horizontal monoid, and a complementary axiom of faithfulness. A pseudovariety is a class of finite algebras of a given signature, closed under the taking of homomorphic images, subalgebras and finitary direct products. By looking at the syntactic congruence for monoids and as the natural extension in the case of forest algebras, we could define a version of syntactic congruence of a subset of the free forest algebra, not just a forest language. Let [Formula: see text] be a finite alphabet and [Formula: see text] be a pseudovariety of finite forest algebras. A language [Formula: see text] is [Formula: see text]-recognizable if its syntactic forest algebra belongs to [Formula: see text]. Separation is a classical problem in mathematics and computer science. It asks whether, given two sets belonging to some class, it is possible to separate them by another set of a smaller class. Suppose that a forest language [Formula: see text] and a forest [Formula: see text] are given. We want to find if there exists any proof for that [Formula: see text] does not belong to [Formula: see text] just by using [Formula: see text]-recognizable languages, i.e. given such [Formula: see text] and [Formula: see text], if there exists a [Formula: see text]-recognizable language [Formula: see text] which contains [Formula: see text] and does not contain [Formula: see text]. In this paper, we present how one can use profinite forest algebra to separate a forest language and a forest term and also to separate two forest languages.

THE CHOMSKY-SCHÜTZENBERGER THEOREM FOR QUANTITATIVE CONTEXT-FREE LANGUAGES

Weighted automata model quantitative aspects of systems like the consumption of resources during executions. Traditionally, the weights are assumed to form the algebraic structure of a semiring, but recently also other weight computations like average have been considered. Here, we investigate quantitative context-free languages over very general weight structures incorporating all semirings, average computations, lattices. In our main result, we derive the Chomsky-Schützenberger Theorem for such quantitative context-free languages, showing that each arises as the image of the intersection of a Dyck language and a recognizable language under a suitable morphism. Moreover, we show that quantitative context-free languages are expressively equivalent to a model of weighted pushdown automata. This generalizes results previously known only for semirings. We also investigate under which conditions quantitative context-free languages assume only finitely many values.

CLASS COUNTING AUTOMATA ON DATAWORDS

In the theory of automata over infinite alphabets, a central difficulty is that of finding a suitable compromise between expressiveness and algorithmic complexity. We propose an automaton model where we count the multiplicity of data values on an input word. This is particularly useful when such languages represent behaviour of systems with unboundedly many processes, where system states carry such counts as summaries. A typical recognizable language is: "every process does at most k actions labelled a". We show that emptiness is elementarily decidable, by reduction to the covering problem on Petri nets.

ON RECOGNIZABLE LANGUAGES OF INFINITE PICTURES

In a recent paper, Altenbernd, Thomas and Wöhrle have considered acceptance of languages of infinite two-dimensional words (infinite pictures) by finite tiling systems, with the usual acceptance conditions, such as the Büchi and Muller ones, firstly used for infinite words. The authors asked for comparing the tiling system acceptance with an acceptance of pictures row by row using an automaton model over ordinal words of length ω2. We give in this paper a solution to this problem, showing that all languages of infinite pictures which are accepted row by row by Büchi or Choueka automata reading words of length ω2 are Büchi recognized by a finite tiling system, but the converse is not true. We give also the answer to two other questions which were raised by Altenbernd, Thomas and Wöhrle, showing that it is undecidable whether a Büchi recognizable language of infinite pictures is E-recognizable (respectively, A-recognizable).