The word “spatial” fundamentally relates to human existence, evolution and activity in terrestrial and now even celestial spaces. After reviewing the spatial features of many areas, the paper describes basics of high level model and technology called Spatial Grasp for dealing with large distributed systems, which can provide spatial vision, awareness, management, control, and even consciousness. The technology description includes its key Spatial Grasp Language (SGL), self-evolution of recursive SGL scenarios, and implementation of SGL interpreter converting distributed networked systems into powerful spatial engines. Examples of typical spatial scenarios in SGL include finding shortest path tree and shortest path between network nodes, collecting proper information throughout the whole world, and elimination of multiple targets by intelligent teams of chasers. The paper also describes the new technology applications in such areas as energy-saving, water supply, national security, military, autonomous robots, decisionmaking, automatic control, as well as withstanding cyber attacks in distributed networked systems. It also compares Spatial Grasp model with traditional algorithms, confirming universality of the former for any spatial systems, while the latter just being tools for concrete applications. The technology can be effectively implemented on any platform, which was already investigated and prototyped for its previous versions in different countries.
The humankind exists, operates, and develops in large distributed spaces, where “spatial” may be considered as the basic and dominant feature philosophically, conceptually, and practically. To prosper in this spatial continuum, adequate high level methodologies, organizations and tools must be developed and used.
The aim of this paper is to describe a universal high-level model and technology for dealing with spatial systems of different natures and review its new applications (including cebersecurity) for solving concrete and often very complex problems. The rest of the paper is organized as follows.
Section 2 reviews “spatial” as the basic feature of human activity including spatial temporal analysis, space-time continuum, spatial analysis, spatial vision, spatial feeling, spatial understanding, spatial awareness, spatial consciousness, spatial ability, spatial intelligence, spatial knowledge, spatial danger, spatial warfare, spatial management, spatial planning, spatial belief, spatial faith, spatial hate, spatial crime, spatial diversity, spatial hope, and spatial virus. Section 3 describes basics of the universal model and technology oriented from the very beginning on seeing, staying, moving and making operations in spaces of any complexity, integrity, and coverage. It explains the main technology ideas, its basic Spatial Grasp Language (SGL), how SGL scenarios self-evolve in physical, virtual or imaginable spaces, and main details of the networked technology implementation allowing the whole world to be converted into a powerful spatial engine. Section 4 describes examples of typical solutions in SGL for distributed dynamic systems which include: Finding shortest path tree (SPT) from a node to all other nodes, also shortest path between two nodes, finding and collecting information on certain individuals worldwide indentified by specific features, and how the team of chasers is fighting multiple targets under dynamically supported global awareness in the team. Section 5 reviews the investigation of extended Spatial Grasp technology applications for the current works at the Institute of Mathematical Machines and Systems which cover energy-saving tools, water supply control, equipment control, situational control, national security, decision-making support and concept, multi-agent pursuit, control and automation systems, autonomous robots, automatic control, optimization and automation. A review of existing cybersecurity publications and practical scenario examples in SGL for withstanding of cyber attacks are provided too. Section 6 compares the Spatial Grasp model with traditional algorithms usually considered as a sequence of instructions, procedure for solving a problem, set of rules to be followed, step-by-step procedure, etc. it also mentions some existing algorithmic extensions such as distributed algorithms, mobile agents, and spatial analysis algorithms. Section 7 concludes the paper. References contain numerous sources on which the paper is based, and APPENDIX provides the Spatial Grasp Language summary.
We are starting here with spatial temporal analysis describing the ontological status of something
that exists in both space and time [
Within Spatial Grasp Technology (SGT) (see the related patent [25], published books [26–35], early history [36–39]), a high-level operational scenario in recursive Spatial Grasp Language (SGL), starting in any world points, propagates, covers and matches the distributed environment in parallel wavelike mode, as symbolically shown in Figure 1. Such propagation can result in returning and analyzing the reached states and data as well as in further waves from the initial and new nodes, which may be arbitrarily remote and in any numbers.
This concept is based on quite different philosophy and practice of traditional dealing with large distributed and parallel systems. Instead of representing systems and solutions in them in the form of communicating parts or agents the developed Spatial Grasp paradigm is organizing everything by integral, holistic, and parallel substance self-propagating thru and covering-matching distributed worlds of different natures. The latter may include: physical world, virtual world, executive world, also their combinations.
The recursive language top level organization can be expressed just in a single string-formula mode: grasp
à constant | variable | rule ({ grasp, }) which can be further extended as follows: constant variable rule information | matter | special global | heritable | frontal | nodal | environmental movement | creation | advancement | branching | cycling | echoing | verification | assignment | transference | exchange | timing | qualifying | type | usage Some details on its components, as follows.
Constant can be self-identifiable by the way written or defined by special rules embracing them with arbitrary textual representations, being of information, matter, and special.
Variable types can be defined by how their names are written, but in general, variables may have any names if their types are declared by special rules, being of global, heritable, frontal, nodal, and environmental.
Rule may be further detailed as follows. Movement may result in virtual hopping to the existing nodes (the ones having virtual or/and executive dimensions) or in real movement to new physical locations, subsequently starting the remaining scenario in the nodes reached. Creation creates or removes nodes and/or links leading to them during distributed world navigation; after termination, the resultant values correspond to the names of reached nodes, and the next scenario steps may start from all these nodes. Advancement can organize forward advancement in space and time of the embraced scenarios; they can evolve within their sequence in synchronous or asynchronous manner. Branching rules allow the embraced set of scenario operands to develop “in breadth”, each from the same starting position, with the resultant set of positions and order of their appearance depending on the logic of a concrete branching rule. Cycling repeatedly invokes the embraced scenario; the resultant set of positions on the rule will be integration of all positions from successful scenario invocations from the same point, or those obtained on its last invocation in a sequence. Echoing oriented on various aspects of data and knowledge processing containing rules which may use local or remote values for different operations be processed in the starting points. Verification rules verify the result of concrete procedure while remaining after their completion in the same world positions where they started. Assignment rules assign the result of the right scenario operand, which may be arbitrarily remote, to the variable or set of variables named or reached by the left scenario operand, which may be remote too. Transference rules organize transference of control in distributed scenarios to the code treated either as SGL procedure or an external system; they can also trigger broadcasting of the data obtained to different destinations. Exchange rules provide input of external information or physical matter by the initiative of SGL scenario, also output of the resultant value obtained by the embraced scenario outside or to other nodes. Timing rules are dealing with conditions related to a time allowed for the scenarios they embrace, or provide the needed time delays between different scenario parts. Qualifying rules are providing or supporting certain qualities or abilities, also setting constraints or restrictions to the scenarios they embrace. Type rules explicitly assign types to different constructs, using their existing repertoire. Usage rules explain how to use the information units they embrace.
For more SGL details please see the APPENDIX.
The following are some hints on how SGL scenarios self-evolve in distributed environments. They are developing in steps, potentially parallel, with new steps produced on the results of previous steps. Any step is associated with a certain point or points of the world. Each step provides a resultant value (single or multiple) and resultant control state. Different scenario parts may evolve from the same points in ordered, unordered, or parallel manner, as independent or interdependent branches. Different scenario parts can spatially succeed each other, with new parts evolving from positions reached by the previous parts. This potentially parallel and distributed scenario can proceed in synchronous or asynchronous modes, also any combinations. SGL operations and decisions can use control states and values returned from subsequent scenario parts, effectively combining controlled forward and backward scenario evolution. Different steps from the same or different scenarios may happen to be temporarily associated with the same world points, while sharing persistent or provisional information in them. Staying with different world points, the scenarios can analyze and impact the navigated worlds via these locations. Scenarios navigating distributed spaces can form active distributed infrastructures in them, which can be shared with other scenarios. Overall organization of the world creation, coverage, modification, analysis and processing provided by SGL rules can be arbitrarily nested. The evolving SGL scenarios can abandon utilized parts if not needed any more, also self-modify and self-replicate during space navigation. The special control states (including thru, done, fail, fatal) appear after completion of different scenario steps, indicating their progress or failure. They can be used for effective control of multiple distributed processes with proper decisions at different levels.
Each SGL interpreter copy can handle and process multiple active scenario code propagating in space and time. Communicating interpreters can be of arbitrary number of copies (up to thousands and millions if needed) effectively integrated with other existing systems and communications, altogether representing powerful spatial engines operating without central resources or control. Hardware or software SGL interpreters, shown in Figure 2 as universal control and processing units (working with complex spatial graph and network data) can be installed, runtime created too, in proper physical or virtual world positions.
The SGL interpreter main components and its general organization are shown in Figure 3.
The interpreter consists of a number of specialized functional processors (shown by rectangles) working with and sharing specific data structures.These include: Communication Processor (CP), Control Processor (COP), Navigation Processor (NP), Parser (P), different Operation Processors (OP), and special (external & internal) World Access Unit (WAU) directly manageable from SGL. Main data structures (also referred to as stores) with which these processors operate (shown by ovals) comprise: Grasps Queue (GQ), Suspended Grasps (SG), Track Forest (TF), Activated Rules (AR), Knowledge Network (NN), Grasps Identities (GI), Heritable Variables (HV), Fontal Variables (FV), Nodal Variables (NV), Environmental Variables (EV), Global Variables (GV), Incoming Queue (IQ), and Outgoing Queue (OQ).
As both backbone and nerve system of the distributed interpreter, its self-optimizing Spatial Track System provides hierarchical command and control as well as remote data and code access. It also supports spatial variables and merges distributed control states for decisions at higher organizational levels. The track infrastructure is automatically distributed between active components (humans, robots, computers, smart-phones, satellites, etc.) during scenario selfspreading in distributed environments. It integrates the following operational stages: forward grasping, echoing, and further forward development.
Imagine we have a distributed physical or virtual network, as of Figure 4 (which can be effectively built in SGL).
To create on this network a tree structure starting from some node d and providing shorted paths from it to all other nodes (as in Figure 4 too) we may write in SGL the following scenario (the found SPT will be embedded into the network structure with variables Up in all nodes): nodal(Dist, Up); hop_node(d); Distance = 0; frontal(Far);
This scenario is based on virus-like parallel propagation of the self-modified SGL code starting in certain node like d and then self-covering-conquering the whole network structure. After its completion, we may start in any node, say c, and follow contents of nodal variables Up leading to the above nodes of the obtained tree, finally receiving the shortest path to this node from the starting node d as follows: hop_node(c); frontal(Spath) = NAME; repeat(hop(Up); append(NAME, Spath); output(Spath) The output result will be(d,b,c).
Imagine we have to find detailed information about individuals belonging to some Group indentified by specific features, and originating in START position represented by physical or virtual address. Staying in it, the group members can be found by their features in local_databases. This may fail to find records on some or all individuals sought, but their traces may exist in local_security systems. If such traces exist and lead to known Other world locations, we may search both data and security records at other points too, and so on, with the checking potentially spreading and covering the whole world. The found match from different points can be collected and returned (with whereabouts of individuals) to the START point with final output there. This scenario can be expressed in SGL as follows (with its possible spatial coverage shown in Figure 5 where universal SGT interpreters U are supposed existing in all nodes).
hopfirst(START); nodal(Other); frontal(Group) = features; output(‘Records found worldwide:’ && repeat(free(match(Group, local_databases)), Other = traces(Group, local_security); hopfirst(Other)))
This scenario first employs forward parallel virus-like world propagation as in previous example, and then in a feedback propagation brings to the starting node all distributed results, using for this the spatial track system feature of the networked SGT interpreter.
By regularly enriching the distributed swarm of chasers with a sort of global awareness over the operational area we may essentially improve its performance. This awareness can be effectively embedded into communicating chasers where the targets seen by individual chasers can be regularly exchanged with their neighbors, as in Figure 6.
This makes all chasers gradually aware of all targets in the region despite not all directly visible individually (D1 as vision threshold), always organizing their movement to be closer to the targets, and then select,_move, and destroy them. An example of such SGL solution may be as follows: hop_chasers(all); nodal(D1 = distance, Targets); frontal(Exchange); stay(Exchange = Targets; hop(neighbors); merge(Targets, Exchange)); sleep(Delay))
More details and explanations on these and many other applications of the SGT and programming in SGL can be found in many existing technology related publications, [26–35] including.
These references are reflecting the potential and practical applicability of the described Spatial Grasp technology in the ongoing engineering works. 5.1. Currently Investigated Applications of SGT Energy-saving tools in industry, transport, and construction. Water supply control systems for modern buildings. Equipment control systems in buildings and facilities. Future of situational control technologies. Innovative technologies of national security. Decision-making support systems. Multi-agent pursuit problem in three-dimensional space. Interaction of a human operator with a control system. Decision-making technologies in military systems . Automation systems of technological processes. Development of intelligent autonomous robots. Automatic control for hot rolling mills. Creation of a defense resource management system. Optimization of rolling modes in a mill. Decision-making concept and definition.Automation for thick-plate mills.
The following combined solutions summarized from the cited above papers are currently considered for their practical support by the SGT.
It is necessary to use a decision support system (DSS) to plan a military battle. The system analyzes in real time information received from all sources (drones, reconnaissance, radars) about the location of troops, meteorological conditions, logistical capabilities, data about the enemy (reconnaissance, action forecasts) and suggests routes for attacks, defense or retreat. With the help of forecasting models, the consequences of various scenarios (attack, defense, maneuvers) and the probability of success of the operation are assessed. A practical example for these decision support systems may look like the one in Figure 7 and the following SGL scenario [40–42].
a) Providing battlefield reconnaissance by drones with the returned collection of discovered targets: hop(Start); Targets = repeat(hopfirst(drone(nearby)), free(targets_seen))
The scenario propagates through the dynamic network of drones using their capabilities to communicate with each other on a certain distance, while forming spatial tree from them and collecting and returning via this tree the full list of targets seen on the ground.
b) Finding optimal routes on the battlefield from Start to the discovered targets: hop(Start); Distance = 0; frontal(Far); sequence( repeat(hop_links(all); Far += 1; or(Distance == nil, Distance > Far); Distance = Far; Up = BACK), (hop(Targets); repeat(hop(Up); Right = 1)))
The scenario forms shortest path tree (SPT) in the battlefield road network starting from Start position, and then starting from the targets positions discovered in the previous step a) marks shortest routes from them to the Start.
c) Physical movement of military force to the discovered targets by their coordinates and eliminating them: move(Start); Force = weapons; repeat(Next = (hopfirst(links_all); nonempty(Right); COORDINATE)); move(Next); if(belong(NAME, Targets), kill(Force, current)))
The scenario, originating in Start with sufficient military equipment and power, physically propagates through the military road network to the targets identified in a) via the shortest routes to them discovered in b) with eliminating them all.
Considers the process of automated control of rolling a steel sheet with a given thickness. Analyzes data from technological information sensors (temperature, speed, pressure, sheet thickness, work position), and the system calculates the optimal rolling parameters (speed, temperature, gap between rolls), calculates control effects and issues tasks to the drives of the mill mechanisms. The human-machine interface ensures interaction between operators and the system, response to emergency situations, displays the current state of the system, and adjusts operating parameters. See also Figure 8 and short SGL example of continuous distributed rolling mill management below [43, 44].
b (hop(ACRP); whirl(frontal(Ex) = ACRP_state; hop(DMS, HMI); use(Ex))), (hop(GI); whirl(frontal(Ex) = GI_state; hop(ACRP, DMS); use(Ex))), (hop(HMI); whirl(frontal(Ex) = HMI_state; hop(ACRP, DMS); use(Ex))), (hop(DMS); whirl(frontal(Ex) = DMS_state; hop(R); use(Ex))), (hop(R); whirl(anayze_execute(R_state))))
The following is some explanation of this scenario which directly reflects the management scheme of Figure 8b. It starts in parallel in all scheme nodes by their abbreviated names, activating and allowing them to continue their own operation any time and in a cyclic manner by using rule whirl. During the operation, they supposedly communicate with the external world by updating properly their own state, and also exchange it with the subordinate destination nodes (as of Figure 8b) by frontal variables Ex, with the use of them there for updating own states. All this integral cooperative activity of the whole management scheme allows us to properly coordinate both software and hardware of the rolling mill (symbolically depicted in Figure 8a).
Subsystems in a distributed smart home control system work with various functions of the house, for example, lighting, heating, water supply, security systems and household appliances. When the user returns home in the evening, a motion sensor detects a person approaching the house, the camera recognizes the user’s face and confirms his identity. Then the outdoor lighting is turned on, the floor heating is turned on, the temperature is updated to a comfortable level, the curtains are closed, and so on, see also Figure 9 and SGL code following [45]. frontal(Identity) = ...; hop(motion_sensor); hop(camera); if(negative(Identity), (stop, ALARM)); hop(outdoor_lighting); switch_on(current); hop(opening_lock); unlock(current); hop(shutters); raise(current); hop(lights); turn_on(current); hop(floor_heating); switch_on(current); wait(temperature >= threshold); hop(curtains); close(current); ...
This SGL text directly corresponds to the arrival scenario of Figure 9b, where different stages are performed sequentially, one after the other, with some checking additional conditions or even providing rejection (like after motion sensor and camera identifying the arrived person), or just waiting (like after proper heating of the floor), etc. 5.2. New cybersecurity applications of SGT
Cybersecurity [46] is the practice of protecting systems, networks, and programs from digital attacks. Implementing effective cybersecurity measures is particularly challenging today because there are more devices than people, and attackers are becoming more innovative. Common internet cyber attacks [40] may be symbolically depicted as in Figure 10.
A cyber attack usually refers to an action designed to target a computer or any element of a computerized information system to change, destroy, or steal data, as well as exploit or harm a network. Cyber attacks have been on the rise, in sync with the digitization of business that has become more and more popular in recent years. More types of cyber attacks can be found in [ 47] with their short review following.
DoS and DDoS attacks. A denial-of-service (DoS) attack is designed to overwhelm the resources of a system to the point where it is unable to reply to legitimate service requests.
MITM attacks. Man-in-the-middle (MITM) types of cyber attacks refer to breaches in cybersecurity that make it.
Phishing attacks. A phishing attack occurs when a malicious actor sends emails that seem to be coming from trusted, legitimate sources in an attempt to grab sensitive information from the target.
Whale-phishing attacks. A whale-phishing attack is so-named because it goes after the “big fish” or whales of an organization, which typically include those in the C-suite or others in charge of the organization.
Spear-phishing attacks. Spear phishing refers to a specific type of targeted phishing attack. The attacker takes the time to research their intended targets and then write messages the target is likely to find personally relevant.
Ransomware. With Ransomware, the victim’s system is held hostage until they agree to pay a ransom to the attacker.
Password attacks. Passwords are the access verification tool of choice for most people, so figuring out a target’s password is an attractive proposition for a hacker.
SQL injection attacks. Structured Query Language (SQL) injection is a common method of taking advantage of websites that depend on databases to serve their users.
URL interpretation. With URL interpretation, attackers alter and fabricate certain URL addresses and use them to gain access to the target’s personal and professional data.
DNS spoofing. With Domain Name System (DNS) spoofing, a hacker alters DNS records to send traffic to a fake or “spoofed” website.
Session hijacking. Session hijacking is one of multiple types of MITM attacks. The attacker takes over a session between a client and the server.
Brute force attacks. A brute-force attack gets its name from the “brutish” or simple methodology employed by the attack. The attacker simply tries to guess the login credentials of someone with access to the target system.
Web attacks. Web attacks refer to threats that target vulnerabilities in web-based applications. Every time you enter information into a web application, you are initiating a command that generates a response.
Insider threats. Sometimes, the most dangerous actors come from within an organization. People within a company’s own doors pose a special danger because they typically have access to a variety of systems.
Trojan horses. A Trojan horse attack uses a malicious program that is hidden inside a seemingly legitimate one. When the user executes the presumably innocent program, the malware inside the Trojan can be used to open a backdoor into the system.
Drive-by attacks. In a drive-by attack, a hacker embeds malicious code into an insecure website. When a user visits the site, the script is automatically executed on their computer, infecting it.
XSS attacks. With XSS, or cross-site scripting, the attacker transmits malicious scripts using clickable content that gets sent to the target’s browser.
Eavesdropping attacks. Eavesdropping attacks involve the bad actor intercepting traffic as it is sent through the network.
Birthday attack. In a birthday attack, an attacker abuses a security feature: hash algorithms, which are used to verify the authenticity of messages.
Malware attack. Malware is a general term for malicious software, hence the “mal” at the start of the word. Malware infects a computer and changes how it functions, destroys data, or spies on the user or network traffic as it passes through.
a) Nodes contain records of being infected, and also from which neighbors, as in Figure 11.
The following SGL scenario starting from any infected node (like C) and tracing virus source via the infected predecessors may be as follows. This spatial cycle terminating in the virus source node having no registered infection predecessor, and its name is issued outside the network from the starting node: hop_direct(C); STATUS == infected; output(
Some explanation may be as follows. Starting from any nodes having infection time registered, the scenario first finds the neighboring nodes with earlier infection time and then moves to them. Repeating this networking search until such neighbors exist. This spatial process can potentially terminate in more than a single node, and the node with the earliest infection time is proclaimed either as virus source or be closest to it (as the latter may be self-protected from discovery): hop_direct(any reachable nodes); STATUS == infected; frontal(Time) = TIME; output_min( hop(all_links; STATUS == infected; Infection_time < Time; Time = Infection_time); NAME && Time)
Algorithm is a finite sequence of mathematically rigorous instructions typically used to solve
a class of specific problems or to perform a computation.A procedure for solving a mathematical
problem in a finite number of steps that frequently involves repetition of an operation [48]. A
procedure used for solving a problem or performing a computation which acts as an exact list of
instructions that conduct specified actions step by step in either hardware- or software-based
routines [41]. A systematic procedure that produces in a finite number of steps the answer to a
question or the solution of a problem [
Elementary algorithm structures are shown in Figure 13 a, b, where Figure 13b reflects the flowchart with three decision making nodes (1, 2, 3) for finding the greatest common divisor of two numbers.
Distributed algorithm is an algorithm designed to run on computer hardware constructed
from interconnected processors; used in application areas of distributed computing. Mobile agent
is a piece of software combined with data that is able to migrate from one computer to another
autonomously and continue its execution on the destination. Spatial analysis algorithms are
used for Geographic Information Systems (GIS) especially for manipulation of map coordinates
[
In comparison with the described SG Model and Language, the traditional as well as extended algorithms may be considered just as specific tools for solving concrete problems. Whereas the Spatial Grasp may actually, not only symbolically, represent a universal philosophy, paradigm and technology oriented on explaining, covering, and ruling the whole universe.
The described Spatial Grasp paradigm covers any spatial systems philosophically, methodologically and practically within the same spatial model and vision, whereas traditional algorithms being just specific tools for solving concrete problems.
This approach also fundamentally differs from any other models and languages for description, composition, control and management of large distributed dynamic systems traditionally representing solutions by their distributed parts (or agents) communicating with each other and exchanging messages. Leaving this culture and types of operations only for the automatic implementation, the SGT scenarios describe all solutions on a much higher level, in the form of integral parallel spatial flooding, or even clever super-virus. The latter will always remain alive by being self-organized and selfconfident during freely self-propagating, self-replicating, self-matching and self-recovering in distributed spaces, even after or during any possible disruptions and damages, in the most unpredictable and hostile environments. These high level spatial scenarios in SGL independently operating “over” rather than “in” distributed systems are much clearer and enormously shorter (up to hundred times) than in traditional C or Java languages.
Investigations and trial implementations of SGT and its predecessor WAVE were made in
different countries and demonstrated via the internet [26–39]. Any new technology versions can be
carried out quickly by a small group of system programmers and on any existing platforms, also
effectively integrated with advanced communication systems. Results of the ongoing investigation
of SGT applicability in new areas of management, control, and cybersecurity [
Declaration on Generative AI While preparing this work, the authors used the AI programs Grammarly Pro to correct text grammar and Strike Plagiarism to search for possible plagiarism. After using this tool, the authors reviewed and edited the content as needed and took full responsibility for the publication’s content. [22] B. Roy, Space Horizons: An Era of Hope in the Geostationary Orbit, University of Oregon School of Law, 2020. https://scholarsbank.uoregon.edu/items/dd40b459-2a12-4396-bdd8e41348793bfe [23] P. Kumberger, F. Frey, et al., Multiscale modeling of virus replication and spread, Wiley, FEBS
Letters, 13 (2016) 1972–1986. doi:10.1002/1873-3468.12095 [24] G. A. Funk, V. A. A. Jansen, et al., Spatial models of virus-immune dynamics, J. Theor. Biology, 233(2) 21 (2005). doi:10.1016/j.jtbi.2004.10.004 [25] P. S. Sapaty, A distributed processing system, European Patent N 0389655, Publ. 10.11.93,
European Patent Office. [26] P. S. Sapaty, Ruling Distributed Dynamic Worlds. New York: John Wiley & Sons, 2005. [27] P. S. Sapaty, Managing Distributed Dynamic Systems with Spatial Grasp Technology,
Springer, 2017. [28] P. S. Sapaty, Holistic Analysis and Management of Distributed Social Systems, Springer, 2018. [29] V. Grechaninov, et al., Models and Methods for Determining Application Performance Estimates in Distributed Structures, in: Cybersecurity Providing in Information and Telecommunication Systems, vol. 3288, 2022, 134–141. [30] S. Zhebka, et al., Method for Adaptive Allocation of Cryptographic Resources in Distributed Databases, in: Cybersecurity Providing in Information and Telecommunication Systems, vol. 3991 (2025) 620–628. [31] P. S. Sapaty, Complexity in International Security: A Holistic Spatial Approach, Emerald
Publishing, 2019. [32] P. S. Sapaty, Symbiosis of Real and Simulated Worlds under Spatial Grasp Technology,
Springer, 2021. [33] P. S. Sapaty, Spatial Grasp as a Model for Space-based Control and Management Systems, CRC
Press, 2022. [34] P. S. Sapaty, Spatial Networking in the United Physical, Virtual, and Mental World, Springer, 2024. [35] P. S. Sapaty, Self-Healing and Self-Recovering Systems under the Spatial Grasp Model,
Emerald Publishing Limited, 2025. [36] A. T. Bondarenko, S. B. Mikhalevich, A. I. Nikitin, P. S. Sapaty, Software of BESM-6 computer for communication with peripheral computers via telephone channels, Computer Software, 5 (1970). [37] P. S. Sapaty, A Method of organization of an intercomputer dialogue in the radial computer systems, in The Design of Software and Hardware for Automatic Control Systems, Inst. of Cybernetics Press, Kiev, 1973. [38] S. Sapaty, A wave language for parallel processing of semantic networks. Comput. Artif. Intell.
5(4) (1986) 289–314. [39] P. S. Sapaty, Distributed modeling of cooperative behavior by mobile agents, Proc. Sixth Conference on Computer Generated Forces and Behavioral Representation, IST UCF, Orlando, FL, 1996, 599-613. [40] Common internet Cyber Attacks. https://www.shutterstock.com/image-vector/vector-infographic-common-internet-attacks-606244733 [41] A. S. Gillis, What is an algorithm? https://www.techtarget.com/whatis/definition/algorithm [42] Algorithm. https://dictionary.cambridge.org/dictionary/english/algorithm [43] M. G. Ievlev, One of the methods of decomposition of the problem of optimization of rolling modes in a thick-plate mill, Math. Machines Syst. 3 (2022) 108–120. [44] A. O. Morozov, V. P. Klymenko, G. G. Grabovsky, M. G. Ievlev, S. E. Moiseenko, Concepts of human-machine automation in the ACS of thick-plate mills, Math. Machines Syst. 1 (2022) 81– 96. [45] V. P. Klymenko, V. B. Korbut, M. G. Ievlev, et al., Energy-saving automation tools and LED lighting systems in industry, transport, construction and municipal sectors, Sci. Innov. 5 (2013) 19–26. [46] What is cybersecurity? https://www.cisco.com/site/us/en/learn/topics/security/what-iscybersecurity.html [47] Types of cyber attacks. https://www.fortinet.com/uk/resources/cyberglossary/types-of-cyberattacks [48] Algorithm. https://www.merriam-webster.com/dictionary/algorithm 2023.
In the language summary below, syntactic categories are shown in italics, vertical bar separates alternatives, parts in braces indicate zero or more repetitions with a delimiter at the right, and constructs in brackets are optional. The remaining characters and words are the language symbols (including boldfaced braces): information
string | scenario | number grasp constant string scenario number matter special variable global heritable frontal nodal constant | variable | [ rule ] [({ grasp,})] information | matter | special ‘{character}’ {{character}} “{character}” [sign]{digit}[.{digit}[e[sign]{digit}]] thru | done | fail | fatal | infinite | nil | any | all | other | allother | current | passed | existing | neighbors | direct | forward | backward | synchronous | asynchronous | virtual | physical | executive | engaged | vacant | firstcome | unique global | heritable | frontal | nodal | environmental
environmental TYPE | NAME | CONTENT | ADDRESS | QUALITIES | WHERE |
movement | creation | advancement | branching | cycling | echoing | verification | assignment | transference | exchange | timing | qualifying | type | usage movement hop | hopfirst | hopforth | move | shift | follow creation create | linkup | delete | unlink advancement advance | slide | align | fringe branching branch | sequence | parallel | if | or | and | orsequence | orparallel | andsequence | andparallel | choose | quickest | | split | replicate cycling repeat | cycle | loop | sling | whirl echoing state | rake | order | unit | unique | sum | count | first | last | min | max | random | average | sortup | sortdown | reverse | element | position | fromto | add | subtract | multiply | divide | degree | separate | unite | attach | append | common | withdraw | increment | decrement | access | invert | apply | location | distance verification equal | nonequal | less | lessorequal | more | moreorequal | bigger | smaller | heavier | lighter | longer | shorter | empty | nonempty | belong | notbelong | intersect | notintersect | yes | no assignment assign | assignpeers transference run | call exchange input | output | send | receive | emit | get timing sleep | allowed qualifying contain | release | trackless | free | blind | quit | abort | stay | lift | seize | exit type global | heritable | frontal | nodal | environmental | matter | number | string | scenario | constant usage address | coordinate | content | index | time | speed | name | place | center | range | doer | node | link | unit