Mathematical models and schemes of conveyor processing of unitary codes in homogeneous computing systems

Purpose of the work is to create models and pipeline schemes for high-performance processing of unitary codes in homogeneous computing systems.

The research methods are based on the theory of designing homogeneous computing systems, methods of synthesis of iterative networks and artificial intelligence systems. Unitary codes are a signal-information base for analyzing and planning parallel processes in homogeneous computing systems. Known one-dimensional and two-dimensional iterative networks are the basis for creating homogeneous pipeline schemes and recurrent computations in them.

Methods. Nevertheless, iterative networks consisting of homogeneous computing cells with regular connections, by default implement a single computing process and, as a rule, one search and computing function. To increase the specific performance of pipeline schemes, the principles of multi-functionality and multi-pipelining have been developed, allowing the implementation of several cells implementing more than one operation at each cycle of the pipeline.

Results. Practically significant pipeline schemes with the organization of several local computing processes with their own starting points have been created, which is necessary for the efficient operation of homogeneous computing systems - reconfigurable computing structures, database and knowledge machines, associative processors, etc.

Comparative assessments of pipeline schemes have been carried out for generally significant operations of processing unitary codes: arbitration, formation of the right, left series of logical "1". It is shown that the application of the principles of multi-functionality and multi-pipelining provides a proportional decrease in the time per operation.

Conclusion. The synthesis of parallel-pipeline schemes for processing unitary codes based on iterative networks is based on the unification and development of the principles of cell clocking, multi-functionality of cells, multi-pipelining, which allows for efficient processing of unitary code flows with dual interpretation of elements (digit/symbol).

1. Korneev V. V. Computing systems. Moscow: Gelios ARV; 2004. 510 p. (In Russ.).

2. Khoroshevsky V. G. Architecture of computing systems. 2nd ed. Moscow: Moskovskii gosudarstvennyi tekhnicheskii universitet im. N.E. Baumana; 2008. 520 p. (In Russ.).

3. Burtsev V. S. Parallelism of computing processes and development of supercomputer architecture. Collection of articles. Moscow: TORUS PRESS; 2006. 414 p. (In Russ.).

4. Guzik V. F., Kalyaev I. A., Levin I. I. Reconfigurable computing systems Rostov-on-Don: Yuzhnyi federal'nyi universitety; 2016. 472 p. (In Russ.).

5. Kalyaev I. A., Levin I. I. Reconfigurable computing systems based on FPGAs. Rostov-on-Don:Yuzhnyi federal'nyi universitet; 2022. 475 p. (In Russ.).

6. Ognev I. V., Borisov V. V., Sutula N. A. Associative memory, environments, systems Moscow: Goryachaya Liniya – Telecom; 2016. 420 p. (In Russ.).

7. Gary M., Johnson D. Computing machines and difficult-to-solve problems. Moscow: Mir; 1982. 416 p. (In Russ.).

8. Lothaire M. Applied Combinatorics on Words. In: Encyclopedia of Mathematics and its Applications. Cambridge: Cambridge University Press; 2005.

9. Rybina G. V. Fundamentals of Building Intelligent Systems. Moscow: Finansy i statistika; INFRA-M; 2010. 432 p. (In Russ.).

10. Kravets O. Ya., Podvalny E. S., Titov V. S., Yastrebov A. S. Architecture of Computing Systems with Elements of Conveyor Processing. Voronezh, Kursk, Sankt-Peteburg: Politekhnika; 2009. 151 p. (In Russ.).

11. Voevodin V. V. Mathematical Models and Methods in Parallel Processes. Moscow: Nauka; 1986. 296 p. (In Russ.).

12. Voevodin V. V., Voevodin Vl. V. Parallel Computing. St. Petersburg: BHV-Peterburg Publ.; 2002. 608 p. (In Russ.).

13. Bandman O.L., Mirenkov N.N., Sedukhin S.G. Specialized processors for high-performance data processing. Moscow: Radio i svyaz; 1988. 208 p. (In Russ.).

14. Fet Ya. I. Parallel processors for control systems. Moscow: Energoizdat; 1981. 160 p. (In Russ.).

15. Khanis A. L., Bespalko S. V., Titenko E. A., et al. Review of cyber insurance research. In: Intellektual'nye informatsionnye sistemy: tendentsii, problemy, perspektivy: materialy dokladov VII vserossiiskoi ochnoi nauchno-prakticheskoi konferentsii «IIS-2019» = Intelligent information systems: trends, problems, prospects. Materials of reports of the VII All-Russian face-to-face scientific and practical conference "IIS-2019". Kursk: Southwest State University; 2019. P. 108-118. (In Russ.).

16. Pavlov P. A. Mathematical models and methods for organizing computations in multiprocessor systems. Komp'yuternye issledovaniya i modelirovanie = Computer research and modeling. 2025; 17(3): 423-436. (In Russ.).

17. Kobailo A. S. Application of hybrid methods for designing real-time computing systems. Trudy BGTU. Seriya 3: Fiziko-matematicheskie nauki i informatika = Proceedings of BSTU. Series 3: Physical and mathematical sciences and computer science. 2018; (1): 120-124. (In Russ.).

18. Vatutin E. I., Zotov I. V., Titov V. S. Use of circuit shapers and binary sequence converters in the construction of combinatorial logic accelerators. Izvestiya Kurskogo gosudarstvennogo tekhnicheskogo universiteta = Proceedings of Kursk State Technical University. 2008; (4): 32-39. (In Russ.).

19. Zel'din E.A. Digital integrated circuits in information-measuring equipment. Leningrad: Energoatomizdat; 1986. 280 p. (In Russ.).

20. Titenko E. A., Vatutin E. I., Titenko M. A., et al. Hardware-oriented method for accelerated search for sample occurrences based on structural-procedural calculations. Izvestiya YuFU. Tekhnicheskie nauki = Bulletin of the Southern Federal University. Technical sciences. 2024; (5): 68-78. (In Russ.).

21. Titenko E. A., Skornyakov K.S., Busygin K.N. Methods and adders with parallel group processes. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta. Seriya: Upravlenie, vychislitel'naya tekhnika, informatika. Meditsinskoe priborostroenie = Proceedings of the Southwest State University. Series: Control, Computing Engineering, Information Science. Medical Instruments Engineering. 2013; (1): 161-166. (In Russ.).

22. Titenko E. A, Semenikhin E. A., Petrik E. A. Structural and functional organization of the arbitrator of parallel query processing. Informatsionno-izmeritel'nye i upravlyayushchie sistemy = Information, measuring and control systems. 2010; 8(11): 30-34. (In Russ.).

23. Titenko E. A., Tipikin A. P., Lapin D. V. Some ways of constructing promising computing systems for parallel processing of data arrays and images on FPGA. Elektromagnitnye volny i elektronnye sistemy = Electromagnetic waves and electronic systems. 2016; 21(10): 56-59. (In Russ.).