Solution of the Problem P = L

The problems associated with the construction of polynomial complexity computer programs require new techniques and approaches from mathematicians. One of such approaches is representing some class of polynomial algorithms as a certain class of special logical programs. Goncharov and Sviridenko described a logical programming language L0, where programs inductively are obtained from the set of Δ0-formulas using special terms. In their work, a new idea has been proposed to look at the term as a program. The computational complexity of such programs is polynomial. In the same years, a number of other logical languages with similar properties were created. However, the following question remained: can all polynomial algorithms be described in these languages? It is a long-standing problem, and the method of describing some polynomial algorithm in a not Turing complete logical programming language was not previously clear. In this paper, special types of terms and formulas have been found and added to solve this problem. One of the main contributions is the construction of p-iterative terms that simulate the work of the Turing machine. Using p-iterative terms, the work showed that class P is equal to class L, which extends the programming language L0 with p-iterative terms. Thus, it is shown that L is quite expressive and has no halting problem, which occurs in high-level programming languages. For these reasons, the logical language L can be used to create fast and reliable programs. The main limitation of the language L is that the implementation of algorithms of complexity is not higher than polynomial.

NP-Difficult Tasks: Automatic Proof of Theorems and Turings Machine

It is offered to use for solving NP-complete (difficult) tasks a modification of methods for satisfying the constraint (CS) by including automatic proof of theorems (APT), and programming in constraints — generation of Turing's machine (TM). Currently, CS uses AP in a truncated form (logical programming), and it is suggested using the method of invariant transformations (MIT), which is a full-fledged APT. In addition, it is offered to use CS methods to generate TM solving NP-difficult tasks recorded on the TM tape, which is an extension of programming capabilities in constraints.

Implementation of a Graphic Interface Development Tool for Prolog

The work examines the current problems of the spread of use of logical programming in the development of commercial multi-platform software applications, tools for convenient development of a modern graphical interface to the logical programs. Libraries with similar concepts of use have been analyzed and described. The purpose of the proposed concept, which is implemented as an open source library, is described, and the advantages of the proposed tools over similar existing tools are indicated. The main feature and advantage of the proposed concept is the implementation of Prolog business logic and interface by means of JavaScript usage of child processes. The proposed concept of interface to Prolog takes full advantage of the possibilities provided by async await. A framework library has been created for the use of Logic Programming in graphical interface development without losses in the application performance. The paper describes the proposed concept and the developed framework (library). The ways to further improve the possibilities for expanding the purpose of the implemented library were identified. The directions of further simplification for programmers of integration of the graphic interface to logical programs have been defined. A significant advantage of the proposed tool is the easy-to-use functions to wrap and control the correctness of requests to the Prolog. The main goal of the library is to create an environment for the Prolog developers where they can create any type of software, which is meant to be user friendly, fast, and cross platform using modern and flexible. This concept also tries to solve disadvantages and architectural problems that were found in other libraries. The safety of library functionality has been analyzed. The concept of potential horizontal application scalability is described. Conclusions and future of libraries were introduced, in which the usage of TypeScript for type-safety and avoidance of run-time errors is mentioned. Overall, the library extends the use of Prolog beyond logical programming and takes a leap forward in its progress.

A Relevant SNC Application for Data Computation using Python Programming

Multiple applications of cloud servicing can be seen in the field of logical programming as well as IT industries. Complex computations over local machines may demand for plenty of system resources thereby delaying the data processing operations. In order to achieve speed in processing one must opt for cloud computing techniques. Extensive maneuver of cloud services is desirable for scientific computation of user data and application. This will require a platform designed in a way to meet the specific requirements of individual users, providing an ease for moving their data and applications over different devices. Symbolic-Numeric Computation using cloud service platform is presented in the paper. In this approach user tasks are presented in the form of symbolic expressions using languages like Java, C/C++, APIs etc. Proposed work employs Python programming for carrying out compilation process.

Theoretical foundations of the organization of branches and repetitions in programs in the logic programming language Prolog

Introduction. The organization of branches and repetitions in the context of logical programming is considered by an example of the Prolog language. The fundamental feature of the program in a logical programming language is the fact that a computer must solve a problem by reasoning like a human. Such a program contains a description of objects and relations between them in the language of mathematical logic. At the same time, the software implementation of branching and repetition remains a challenge in the absence of special operators for the indicated constructions in the logical language. The objectives of the study are to identify the most effective ways to solve problems using branching and repetition by means of the logic programming language Prolog, as well as to demonstrate the results obtained by examples of computational problems. Materials and Methods. An analysis of the literature on the subject of the study was carried out. Methods of generalization and systematization of knowledge, of the program testing, and analysis of the program execution were used. Results. Constructions of branching and repetition organization in a Prolog program are proposed. To organize repetitions, various options for completing a recursive cycle when solving problems are given. Discussion and Conclusions. The methods of organizing branches and repetitions in the logic programming language Prolog are considered. All these methods are illustrated by examples of solving computational problems. The results obtained can be used in the further development of the recursive predicates in logical programming languages, as well as in the educational process when studying logical programming in the Prolog language. The examples of programs given in the paper provide using them as a technological basis for programming branches and repetitions in the logic programming language Prolog.

A New Modern Object-Oriented Programming Languages

Industries evolve. Our thinking changes as well. Programming languages need evolvement too. “The thing is that ideas for new features with its ways of thinking will be flourished, and so perfectly designed those languages won’t be perfect anymore.” Where did logical programming go? “Notice that you can use this paradigm and just provide a set of constraints for a website and expect the website to develop automatically based on them.” It is possible to implement that. Likewise, new paradigms will sooner or later be born. It can’t be that we’ve explored everything. “Technologies are born likewise the old way of thinking, which represents by the previous programming languages might not be adequate. This project is an open-source modern object-oriented programming language that aims to bridge the gap between modern expressive programming paradigms like python and strictly typed rigid languages like Java and C#. Our goal is to provide the usefulness of an object-oriented programming language while holding the simplicity of an expressive programming language without having to sacrifice performance.

Verification of Knowledge Obtained in the Study of Business Process Models

The paper focuses on the method of formal verification of knowledge obtained in the study of business process models. As a formal language for the presentation and verification of business processes, a certain version of π-calculus was chosen, and linear temporal modal logic was chosen as a language for formulating test assignments, i.e., questions, to be checked. The paper gives the rationale for such choice, and considers the principles of developing the test assignments in the language of modal logic and their usage for knowledge verification. The study proposes to automate knowledge testing with logic programs obtained as a result of the transition from a description of business processes to a verification program in the logical programming language Visual Prolog. The formal knowledge verification technique is illustrated by examples of knowledge verification. Findings of research show how the transition from the description of business processes to the procedures of formal verification of knowledge is carried out. The prospects for the development of the proposed method are discussed

LEARNING IN SCHOOL OF LOGIC AND LOGICAL PROGRAMMING FOR PRESENTATION AND PROCESSING OF KNOWLEDGE

New trends in the development of society in the digital age determine the growing role of artificial intelligence (AI). This determines the need for its formal and informal study in different levels and in different volumes in both classroom and extracurricular activities of bulgarian schools. On the basis of a curriculum approved by the Ministry of Education and Science, the development of appropriate teaching resources and aids began. In this report, the authors will present an approach to presenting knowledge with general meaning in artificial intelligence by applying logical inferences, rules and dependencies. The main topics of the curriculum and the way of their structuring will be presented. The main idea is, following the requirements of classical artificial intelligence, to consider different methods and approaches for presenting this theory in the context of high school education.