Development of Vector Systems Applied Theory for Robotic Technology as an Alternative for Quantum One

Introduction

Vector systems theory is a new subfield of combinatorial theory [1] that relates finding optimal solutions to problems connected from sets that have finite number of elements, where the sets of feasible solutions are discrete. Classic combinatorial optimization problems are, for example, the traveling, and the knapsack problem. In such problems, exhaustive search is not high-quality, and so directed on algorithms that quickly rule out large parts of the search space or estimate algorithms must be resorted to instead. Combinatorial optimization is related to algorithm theory, operations research, and computational complexity theory. It has significant applications in several fields, including robotics, artificial intelligence, theoretical computer science, and data mining technologies, intelligent systems, computational linguistics, and big data [2, 3, 4, 5]. A number of research works consider combinatorial configurations using optimization of integer programming together with discrete optimization of big vector data coding and data mining technologies, which are composed with multi- dimensional systems theory [6]. Applications profiting from optimum vector information technologies based on the multi-dimensional combinatorial systems theory provide for example data mining technologies and big vector data processing, data analysis and system security, signal compression and reconstruction, vector computing and telecommunications, and other branches of sciences and advanced information technologies. Development of the theory for robot design allows database downsizing by a list of attribute sets at the same time due to vector binary processing data.

Fundamentals

An n-stage ring sequence K2D= {(k11, k12), (k21, k22), ...,(ki1, ki2),….,(kn1, kn2)}, where we require all terms in each vector-sum to be 2-stage (t=2) sequences together with vectors of the sequence enumerates of coordinate set of a topologically closed two-dimensional grid m1×m2 is called a two-dimensional “Ideal Vector Basis” (2D IVB).

) 3 mod ,2 (mod (0,2) (1,0) (1,2) (0,0) (1,2) (1,1) (0,1) (1,1) (1,0)

≡ + ≡ + ≡ +

   For example, the 2D IVB {(1,0), (1,1), (1,2)} gives the next vector sums modulo m1 =2, m2=3:

So long as the vectors (1,0), (1,1), (1,2) of the 2D IVB themselves are two-dimensional (t=2) vector sums also, the modular (m1=2, m2=3) vector sums form a set of two- modular reference grid m1 x m2 = 2 x 3: (0,0) (0,1) (0,2) (1, 0) (1,1) (1,2) Schematic diagram of creating coordinate grid 2×3 generated by Ideal Vector Basis {(1,0),(1,1),(1,2)} is given below (Figure 1).

Click to enlarge

Diagram (Figure 1) consists of two three-stage (n=3) sequences of 2-stage (t=2) sub-sequences placed inside another, so that inner sequence is the 2D IVB {(1,0), (1,1), (1,2)} (yellow beads), while the outside one forms the rest 2D vectors by summing modulo 2 and 3 of 2D vectors {(0,1),(0,2),(0,0)} (blue beads). The arrows point to the summing giving locations of all modular sums in the ring diagram. We can observe that each modular sum from (0,0) to (1,2) occurs exactly once on the diagram. Table 1 demonstrates optimized two-dimensional binary code, based on the 2D IVB {(1,0), (1,1),(1,2)} with informative parameters S=7, n=3.

Table 1 defines two-dimensional (t=2) binary code system under a torus surface coordinate grid m1× m2 =(n–1)×n = 2×3 with two ring axes m1=2, and m2=3. Here is an example of code system design, using the combinatorial optimization systems theory prospected from rotational symmetry of order seven (S=7) [1]. The next example belongs design of an optimized data system processing two (t=2) sets of category attributes concurrently under a torus surface coordinate grid m1× m2 = 2×3.

Table 2 contains 2n=8 binary 2D vector 3-digit (n=3) combinations for coding 2n-2=6 distinct two-dimensional (t =2) data sets both with two (m1=2) attributes of the first, and three (m2=3)-the second category concurrently. In the general case, an optimized multidimensional data system processing based on t-dimensional IVB {(k11, k12,…,k1t), (k21, k22,...,k2t),…(kn1, kn2,...,knt)} provides vector data coding sets of category attributes concurrently under a coordinate grid m1× m2 ×…×mt. The underlying system provides vector data processing for robot design with vector- weighed binary code of nearly 2n code size.

Conclusion and Outlook

The objectives of the proposed project are a development of the theory for robotic technology providing ability to process data arrays in streaming mode by lists of attribute sets at the same time, ability to update completed tables with indexing of names, packages, procedures, etc. in the selected coordinate database, followed by processing in the database network. Data arrays can be described by multidimensional sets of attributes of arbitrary content at any level of indexing and theoretically infinitely by a large number of attribute categories. Encryption of the processed data, for example, periodic renaming of coordinate axis numbers, reinsertion of vector weights, etc. for increasing the level of protection against unauthorized access when channeling through communication channels of converting multidimensional signals for robotic design. The prospects for the development of vector information technologies are opened based on the minimization of the basic structure of multi-dimensional information flow processing systems and the functionality of vector computer systems is expanded. At last, optimum vector combinatorial systems theory discovers direct application of the underlying scientific approach for robot design for development perspective R&S research in contemporary vector information technologies, computing, systems engineering, and education. The processing of multi-dimensional data sets on the minimized basis of a t-dimensional coordinate system opens up prospects for the development of vector systems applied theory for robotic technologies as an alternative to quantum ones.