Abstract. The features of polynomial codes application in the synthesis of built-in control circuits for combinational digital devices using Boolean complement method are described. The possibilities of accounting for the characteristics of error detection in information vectors by types (monotonic, symmetric and asymmetric) and multiplicities are considered. The main classes of polynomial codes focused on the detection of errors of a specific type and a certain multiplicity are presented. The conditions for the use of polynomial codes in the organization of built-in control circuits according to controllable groups of outputs of the original device are formulated. Examples of the implementation of built-in control circuits with the allocation of groups of device outputs that allow only one- and two-fold errors (Н2-groups of outputs) are given. A generalized algorithm for synthesizing built-in control circuits by Н2-groups of outputs is formulated.

Keywords: combinational digital devices, built-in control circuit, Boolean complement method, polynomial code, self-checking device

References:

1. Sogomonyan E.S., Slabakov E.V. Samoproveryaemye ustroystva i otkazoustoychivye sistemy (The Self-Checked Devices and Failure-Safe Systems), Moscow, 1989, 208 р. (in Russ.)
2. Drozd A.V., Kharchenko V.S., Antoshchuk S.G., Drozd Yu.V., Drozd M.A., Sulima Yu.Yu. Rabocheye diagnostirovaniye bezopasnykh informatsionno-upravlyayushchikh sistem (Working Diagnostics of Safe Information and Control Systems), Khar’kov, 2012, 614 р. (in Russ.)
3. Sapozhnikov Vl.V. Sintez sistem upravleniya dvizheniyem poyezdov na zheleznodorozhnykh stantsiyakh s isklyucheniyem opasnykh otkazov (Synthesis of Control Systems for the Movement of Trains at Railway Stations with the Exclusion of Dangerous Failures), Moscow, 2021, 229 р.
4. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Kody Khemminga v sistemakh funktsional'nogo kontrolya logicheskikh ustroystv (Hamming Codes in Functional Control Systems of Logical Devices), St. Petersburg, 2018, 151 р. (in Russ.)
5. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Kody s summirovaniyem dlya sistem tekhnicheskogo diagnostirovaniya. T. 1. Klassicheskiye kody Bergera i ikh modifikatsii (Summed Codes for Technical Diagnostic Systems. Vol. 1. Classical Berger Codes and Their Modifications), Moscow, 2020, 383 р. (in Russ.)
6. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Kody s summirovaniyem dlya sistem tekhnicheskogo diagnostirovaniya. T. 2. Vzveshennyye kody s summirovaniyem (Summed Codes for Technical Diagnostic Systems. Vol. 2. Weighted Codes with Summation), Moscow, 2021, 455 р. (in Russ.)
7. Berezyuk N.T., Andrushchenko A.G., Moshchitskiy S.S., Glushkov V.I., Benesha M.M., Gavrilov V.A. Kodirovaniye informatsii (dvoichnyye kody) (Information Coding (Binary Codes)), Khar'kov, 1978, 252 р. (in Russ.)
8. Sapozhnikov V.V., Sapozhnikov Vl.V. Samoproveryaemye diskretnye ustroystva (The Self-Checked Discrete Devices), St. Petersburg, 1992, 224 p. (in Russ.)
9. Piestrak S.J. Design of Self-Testing Checkers for Unidirectional Error Detecting Codes, Wrocław, Oficyna Wydawnicza Politechniki Wrocłavskiej, 1995, 111 p.
10. Göessel M., Ocheretny V., Sogomonyan E., Marienfeld D. New Methods of Concurrent Checking, Edition 1, Dordrecht, Springer Science+Business Media B.V., 2008, 184 p.
11. Gavrilov S.V., Gurov S.I., Zhukova T.D., Ryzhova D.I. Information Technologies, 2016, no. 12(22), pp. 931–937. (in Russ.)
12. Tshagharyan G., Harutyunyan G., Shoukourian S., Zorian Y. Proceedings of 15th IEEE East-West Design & Test Symposium (EWDTS’2017), Novi Sad, Serbia, September 29–October 2, 2017, pp. 25–28, DOI: 10.1109/EWDTS.2017.8110065.
13. Stempkovskii A.L., Tel’pukhov D.V., Zhukova T.D., Demeneva A.I., Nadolenko V.V., Gurov S.I. Russian Microelectronics, 2019, no. 4(48), pp. 240–249.
14. Drozd O., Antoniuk V., Nikul V., Drozd M. Proceedings of the 14th International Conference TCSET’2018, Lviv-Slavsko, Ukraine, 2018, pp. 805–809, DOI: 10.1109/TCSET.2018.8336320.
15. Drozd O., Perebeinos I., Martynyuk O., Zashcholkin K., Ivanova O., Drozd M. Proceedings of the IEEE International Conference on Advanced Trends in Radioelectronics, Telecommunications and Computer Engineering (TCSET), 25–29 February 2020, Lviv-Slavsko, Ukraine, paper 142, DOI: 10.1109/TCSET49122.2020.235591.
16. Gessel M., Morozov A.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2003, no. 1, pp. 153–161.
17. Saposhnikov Vl.V., Dmitriev A., Goessel M., Saposhnikov V.V. Proceedings of 14th IEEE VLSI Test Symposium, USA, Princeton, 1996, pp. 162–168.
18. Aksyonova G.P. Automation and Remote Control, 1973, no. 2(34), pp. 267–273.
19. Efanov D.V. Journal of Instrument Engineering, 2019, no. 7(62), pp. 621–631, DOI: 10.17586/0021-3454-2019-62-7-621-631. (in Russ.)
20. Efanov D.V. Electronic modeling, 2019, no. 6(41), pp. 49–64, DOI: 10.15407/emodel.41.06.049. (in Russ.)
21. Saposhnikov V.V., Saposhnikov Vl.V., Morozov A., Goessel M., Osadchy G. Proceedings of 2nd IEEE East-West Design & Test Symposium (EWDTS’2004), Crimea, Ukraine, September 15–17, 2004, pp. 83-87.
22. Goessel M., Morozov A.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2005, no. 8, pp. 1336–1346.
23. Das D.K., Roy S.S., Dmitiriev A., Morozov A., Gössel M. Proceedings of the 10th International Workshops on Boolean Problems, Freiberg, Germany, September, 2012, pp. 33–40.
24. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Electronic modeling, 2016, no. 6(38), pp. 25–43.
25. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Control Sciences, 2017, no. 1, pp. 57–64. (in Russ.)
26. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V., Pivovarov D.V. Electronic modeling, 2017, no. 2(39), pp. 15–34.
27. Morozov M., Saposhnikov V.V., Saposhnikov Vl.V., Goessel M. Proceedings of 6th IEEE International On-Line Testing Workshop, Palma de Mallorca, Spain, July 3–5, 2000, pp. 171–176.
28. Nikolos D. Chapter 7 in On-Line Testing for VLSI, 1998, pp. 69–79, DOI 10.1007/978-1-4757-60-69-9_7.
29. Efanov D.V. Vestnik Tashkentskogo instituta inzhenerov zheleznodorozhnogo transporta, 2019, no. 2, pp. 109–124.
30. Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Electronic Modeling, 2021, no. 1(43), pp. 28–45, DOI: 10.15407/emodel.43.01.028.
31. Efanov D., Osadchy G., Zueva M. Proceedings of 19th IEEE East-West Design & Test Symposium (EWDTS’2021), Batumi, Georgia, September 10-13, 2021, рр. 59—69. DOI: 10.1109/EWDTS52692.2021.9581036.
32. Efanov D., Osadchy G., Zueva M. Proceedings of 11th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS’2021), Cracow, Poland, September 22–25, 2021, рр. 424—431. DOI: 10.1109/IDAACS53288.2021.9660837.
33. Sagalovich Yu.L. Vvedeniye v algebraicheskiye kody (Introduction to Algebraic Codes) Moscow, 2010, 302 р. (in Russ.)
34. Efanov D., Plotnikov D., Sapozhnikov V., Sapozhnikov Vl., Abdullaev R. Proceedings of 16th IEEE East-West Design & Test Symposium (EWDTS’2018), Kazan, Russia, September 14–17, 2018, pp. 184–190, DOI: 10.1109/EWDTS.2018.8524684.
35. Abdullaev R.B., Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Proceedings of 17th IEEE East-West Design & Test Symposium (EWDTS’2019), Batumi, Georgia, September 13–16, 2019, pp. 157–161, DOI: 10.1109/EWDTS.2019.8884451.
36. Abdullaev R., Efanov D. Proceedings of 19th IEEE East-West Design & Test Symposium (EWDTS’2021), Batumi, Georgia, September 10–13, 2021, рр. 40—46. DOI: 10.1109/EWDTS52692.2021.9580992.
37. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Journal of Instrument Engineering, 2015, no. 5(58), pp. 333–343, DOI: 10.17586/0021-3454-2015-58-5-333-343. (in Russ.)
38. Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Trudy ISP RAS (ISPRAS Proceedings), 2017, no. 5(29), рр. 39–60, DOI: 10.15514/ISPRAS-2017-29(5)-3. (in Russ.)
39. Efanov D., Sapozhnikov V., Sapozhnikov Vl., Osadchy G., Pivovarov D. Proceedings of 17th IEEE East-West Design & Test Symposium (EWDTS’2019), Batumi, Georgia, September 13–16, 2019, pp. 136–143, DOI: 10.1109/EWDTS.2019.8884398.