Towards Automatic Deductive Verification of C Programs with Sisal Loops Using the C-lightVer System

The C-lightVer system is developed in IIS SB RAS for C-program deductive verification. C-kernel is an intermediate verification language in this system. Cloud parallel programming system (CPPS) is also developed in IIS SB RAS. Cloud Sisal is an input language of CPPS. The main feature of CPPS is implicit parallel execution based on automatic parallelization of Cloud Sisal loops. Cloud-Sisal-kernel is an intermediate verification language in the CPPS system. Our goal is automatic parallelization of such a superset of C that allows implementing automatic verification. Our solution is such a superset of C-kernel as C-Sisal-kernel. The first result presented in this paper is an extension of C-kernel by Cloud-Sisal-kernel loops. We have obtained the C-Sisal-kernel language. The second result is an extension of C-kernel axiomatic semantics by inference rule for Cloud-Sisal-kernel loops. The paper also presents our approach to the problem of deductive verification automation in the case of finite iterations over data structures. This kind of loops is referred to as definite iterations. Our solution is a composition of symbolic method of verification of definite iterations, verification condition metageneration and mixed axiomatic semantics method. Symbolic method of verification of definite iterations allows defining inference rules for these loops without invariants. Symbolic replacement of definite iterations by recursive functions is the base of this method. Obtained verification conditions with applications of recursive functions correspond to logical base of ACL2 prover. We use ACL2 system based on computable recursive functions. Verification condition metageneration allows simplifying implementation of new inference rules in a verification system. The use of mixed axiomatic semantics results to simpler verification conditions in some cases.

RESEARCH OF THE FUNCTIONING SYSTEM OF THE LIGHTING MODE

The article presents the results of a study carried out within the framework of a systematic approach using the "Wu Xing pentagram" symbolic method. The object of the research is the category of "lighting mode". The indicated category as a certain system are used. A diagram showing the life cycle of the "lighting mode" category is proposed. Five main components of the system have been identified based on the sequence of the formation of needs in the creation of a lighting regime in the room: investment, quantitative characteristics, quality characteristics, energy characteristics, maintenance and operating features. The characteristics of lighting installations and space-planning solutions in the main premises of preschool educational organizations are analyzed. The priority components for these premises are energy characteristics. Compliance with quantitative indicators depends on the efficiency of maintenance. The needs of aesthetic and emotional satisfaction are secondary, significant costs are not provided. Thus, it can be judged that in the premises presented, the development of the category of "lighting mode" follows the path of pathological restrictions As a result, a conclusion is made about the mechanism of functioning of the "lighting mode" category in accordance with the relations arising between its elements, namely, the relations of support or restriction. The research results can be used in the future when examining the quality of the light environment and monitoring the lighting conditions in the premises.

A refinement of Dyck paths: A combinatorial approach

Local maxima and minima of a Dyck path are called peaks and valleys, respectively. A Dyck path is called restricted[Formula: see text]-Dyck if the difference between any two consecutive valleys is at least [Formula: see text] (right-hand side minus left-hand side) or if it has at most one valley. In this paper, we use several techniques to enumerate some statistics over this new family of lattice paths. For instance, we use the symbolic method, the Chomsky–Schűtzenberger methodology, Zeilberger’s creative telescoping method, recurrence relations, and bijective relations. We count, for example, the number of paths of length [Formula: see text], the number of peaks, the number of valleys, the number of peaks of a fixed height, and the area under the paths. We also give a bijection between the restricted [Formula: see text]-Dyck paths and a family of binary words.

HISTORICAL SYMBOL BETWEEN THE CONTROVERSY OF HISTORY AND REALITY :THE NOVEL OF LOVE, WHO CROSSES THE BORDER, AS A MODEL

This approach is based on observing images, events, and symbolic characters, then encompassing them in all their aspects, then showing the symbolic method that the novelist adopted to draw and present them in the narration of the novel. (A Lover Who Crosses the Borders) We find the mythical and symbolic tendency in building the narrative, as the novelist exploits the mythical environment that opens up to the past to record the conditions of the main character, and the nature of adaptation to the external environment, in addition to how to face life and its circumstances in different ways, most of the symbolic characters symbolized the pain of reality and the fragmentation of life, so the narrator built (his long story) or (his short novel) in a way that mixes the imagined and the reality. Most of the events and characters are realistic that embodied an imaginary narrative that confronted the Iraqi reality for psychological, social and political purposes. When the stage expanded with multiple crises, success was an ally of those who archive of Iraqi pain, and who embodied the interaction and communication between its past and present, as the novelist wrote in a modernist way that drew its visions from the imagination of Iraqi pain, and the stage recognized the creative exceptions that promote the literary face, and the task of expression is an occasional product of culture.

Figuratively Semantic Analysis of Works of Art

Topicality of the study is related to the in-depth study of the art of works of Van Gogh, Velázquez and Repin by relating art to the biography of these authors. The aim of the study is to explore the symbolism and the biography of the painters using the examples of analysis from the works of Van Gogh, Velasquez, and Repin and also to determine the conditions that contribute to the awareness of the process of perception and understanding of paintings. The methodology of this study is figuratively symbolic method used with the purpose to compare the plots of the art and to relate them to the life experience of their creators. Results obtained and the most important conclusions: This is important for the author of a painting to convey his/her thoughts and feelings to the viewer. Still, there remains a problem. The author uses the language of the image and symbol, which the viewer needs to reveal. Psychology of art offers two main options for solving this problem. The essence of the first option which is the ability of the painter to direct the viewer's sight. It is called the Dutch approach. The second approach to the analyses of art is called the Italian approach. In this case this is important to understand the symbolism and knowledge gained historically by relating one’s art works to the biography of the painter. The authors of this article focus on the second approach by illustrating it with examples of analysis from the works of Van Gogh, Velázquez, and Repin. The results of this study might be of interest for those who are interested in arts and psychology.

Simulation of the Propagation of Electromagnetic Oscillations by the Method of the Modified Equation of the Telegraph Line

The article considers the physical processes associated with the propagation of electromagnetic oscillations in a long line, the size of which is the same or slightly greater than the length of the electromagnetic wave (not more than ten times). As a research method, the differential-symbolic method is used, which is applied to the modified equation of the telegraph line. The boundary conditions for the two-point problem as well as additional parameters that are coefficients for the first derivatives in terms of coordinate and time in comparison with the classical equation of the telegraph line are considered as parameters for controlling the process of propagation of electromagnetic oscillations. Based on the differential-symbolic method, the boundary conditions of the two-point problem are found, under which the most characteristic oscillatory processes are realized in a long line. Based on the research, it is possible to draw conclusions about the effectiveness of analytical methods for the analysis of specific technical objects and control of the processes that take place in them.

Theory Exploration Powered by Deductive Synthesis

This paper presents a symbolic method for automatic theorem generation based on deductive inference. Many software verification and reasoning tasks require proving complex logical properties; coping with this complexity is generally done by declaring and proving relevant sub-properties. This gives rise to the challenge of discovering useful sub-properties that can assist the automated proof process. This is known as the theory exploration problem, and so far, predominant solutions that emerged rely on evaluation using concrete values. This limits the applicability of these theory exploration techniques to complex programs and properties.In this work, we introduce a new symbolic technique for theory exploration, capable of (offline) generation of a library of lemmas from a base set of inductive data types and recursive definitions. Our approach introduces a new method for using abstraction to overcome the above limitations, combining it with deductive synthesis to reason about abstract values. Our implementation has shown to find more lemmas than prior art, avoiding redundant lemmas (in terms of provability), while being faster in most cases. This new abstraction-based theory exploration method is a step toward applying theory exploration to software verification and synthesis.