Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Tverdokhlebov V. A. The Geometric Form of Automaton Mappings, Recurrent and Z-recurrent Definition of Sequences. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 2, pp. 232-241. DOI: 10.18500/1816-9791-2016-16-2-232-241, EDN: WCNQND

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
14.06.2016
Full text:
download
(downloads: 219)
Language: 
Russian
Heading: 
Computer Sciences
UDC: 
519.713.1; 519.713.4
DOI: 
10.18500/1816-9791-2016-16-2-232-241
EDN: 
WCNQND

The Geometric Form of Automaton Mappings, Recurrent and Z-recurrent Definition of Sequences

Autors: 
Tverdokhlebov Vladimir Aleksandrovich, Saratov State University
Abstract: 

For automaton mappings we present a method to construct geometric images, a method for complexity estimate by geometric forms, a method of Z-recurrent definition of sequences. A method for complexity estimate for finite sequences by recurrent and Z-recurrent numerical indicators is proposed. Numerical indicators of recurrent and Z-recurrent definitions of sequences are systematized into the spectrum of recurrent definitions with 5 levels of numerical indicators. The spectrum includes the order of a recurrent form, the numerical characteristics of various types of recurrent sequences, etc.

Key words: 
automaton mappings
geometric images
recurrent sequence
Z-recurrent sequences
sequences
complexity estimate of a sequence
References: 
  1. Tverdokhlebov V. A. Geometricheskie obrazy zakonov funktsionirovaniia avtomatov [Geometric images of machines functioning laws]. Saratov, Nauchnaia kniga, 2008, 183 p. (in Russian).
  2. Tverdokhlebov V. A. Geometricheskie obrazy konechnykh determinirovannykh avtomatov [The geometrical images of finite deterministic automata]. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2005, vol. 5, iss. 1, pp. 141–153. (in Russian).
  3. Tverdokhlebov V. A. Geometricheskie modeli i metody v tekhnicheskom diagnostirovanii [Geometric patterns and techniques in technical diagnosis]. Informatsionno-upravliaiushchie sistemy na zh.-d. transporte, 1996, no. 3/4, pp. 58 (in Russian).
  4. Tverdokhlebov V. A. Raspoznavanie avtomatov na osnove geometricheskoi interpretatsii [Recognition of machines based on the geometric interpretation.]. Problemy teoreticheskoi kibernetiki : tez. dokl. XI Mezhdunar. konf. [Problems of Theoretical Cybernetics : mes. rep. XI Intern. Conf.], Moscow, Izd-vo RGGU, 1996, pp. 85–93 (in Russian).
  5. Tverdokhlebov V. A. Diskretnye slovarnye geometrii dlia analiza i sinteza matematicheskikh avtomatov [Discrete geometry vocabulary for the analysis and synthesis of mathematical machines]. Dokl. Akad. voen. nauk. Ser. Analiticheskaia mekhanika. Analiticheskaia teoriia avtomaticheskogo upravleniia [Dokl. Acad. Mil. Sciences. Ser. Analytical Mechanics. Analytical theory of automatic control], 1999, no. 1, pp. 100–112 (in Russian).
  6. Tverdokhlebov V. A. The general features of geometrical images of finite state machines. Proc. East-West Design & Test Workshop (EWDTW’04), Kharkov, National University of Radioelectronics, 2004, pp. 243–246.
  7. Tverdokhlebov V. A. Diskretnye sistemy i geometricheskie obrazy ikh funktsionirovaniia [Discrete systems and geometric images of their functioning]. Avtomatizatsiia proektirovaniia diskretnykh sistem : materialy Piatoi mezhdunar. konf. [Computer-aided design of discrete systems : Proc. of the Fifth Intern. Conf.], Minsk, 2004, vol. 1, pp. 217–226 (in Russian).
  8. Tverdokhlebov V. A. Rekurrentnost’ geometricheskikh obrazov [The recurrent geometric images]. Informatsiino-keruiuchi cistemi na zaliznichnomu transporti, 2004, no. 4/5 (48/49), pp. 88–90 (in Russian).
  9. Tverdokhlebov V. A. Konechnye avtomaty i analiz ikh geometricheskikh obrazov [Finite state machines and the analysis of their geometrical images]. Problemy teoreticheskoi kibernetiki : tez. dokl. XIV Mezhdunar. konf., posviashch. 80-letiiu so dnia rozhd, P. V. Yablonskogo [Problems of Theoretical Cybernetics : mes. rep. XIV Intern. conf., is dedicated 80th anniversary of birth. P. V. Yablonsky], Moscow, Moscow Univ. Press, 2005, pp. 153 (in Russian).
  10. Tverdokhlebov V. A. Geometrical images of behaviour of the discrete determined systems. Radioelectronic and computer systems, 2006, no. 5(17), pp. 161–165 (in Russian).
  11. Tverdokhlebov V. A. Technical diagnosing on the basis of geometrical structures of laws of functioning. Radioelectronic and computer systems, 2007, no. 7, pp. 158–167 (in Russian).
  12. Tverdokhlebov V. A. Spektry dlia geometricheskikh obrazov avtomatov i ikh sviaz’ s posledovatel’nostiami i figurami [Spectra for geometric images of machines and their connection with sequences and figures]. Diskretnaia matematika i ee prilozheniia : materialy IX Mezhdunar. seminara [Discrete mathematics and its applications : Materials IX Intern. workshop], Moscow, 2007, pp. 409–412 (in Russian).
  13. Tverdokhlebov V. A. Interpoliatsiia geometricheskikh obrazov avtomatov v tekhnicheskom diagnostirovanii [Interpolation geometric images in automatic technical diagnosis]. Dokl. Akad. voen. nauk [Dokl. Acad. Mil. Sciences], 2007, no. 1(25), pp. 55–62 (in Russian).
  14. Tverdokhlebov V. A. Geometricheskie obrazy zakonov funktsionirovaniia avtomatov i analiz svoistv avtomatov [Geometric images of machines functioning of laws and analysis of the properties of automata]. Diskretnye modeli v teorii upravliaiushchikh sistem : tr. vos’moi mezhdunar. konf. [Discrete models in the theory of control systems : mp. Eighth Intern. Conf.], Moscow, Moscow Univ. Press; MAKS Press, 2009, pp. 301–305 (in Russian).
  15. Tverdokhlebov V. A. Geometrical models of automatons mappings and automatons. Vestn. Kiev. nats. un-ta im. T. Shevchenko. Ser. fiz.-matem. nauki, 2011, iss. 1, pp. 202–207 (in Russian).
  16. Tverdokhlebov V. A. Geometrical approach to technical diagnosing of automatons. Proc. IEEE EastWest Design & Test Symposium (EWDTS’2011), Kharkov, National Univ. of Radioelectronics, 2011, pp. 240–243.
  17. Tverdokhlebov V. A. Geometricheskie modeli i metody raspoznavaniia avtomatov [Geometric patterns and automatic recognition techniques]. Intellektual’nye sistemy i komp’iuternye nauki : materialy Kh Mezhdunar. konf. [Intelligent Systems and Computer Science : Materials X Intern. Conf.], Moscow, Moscow Univ. Press, 2011, pp. 168–171 (in Russian).
  18. Tverdokhlebov V. A. Klassifikatsiia geometricheskikh obrazov avtomatnykh otobrazhenii [Classification of geometric images automaton mappings]. Dokl. Akad. voen. nauk [Dokl. Acad. Mil. Sciences], 2012, no. 5 (54), pp. 97–105 (in Russian).
  19. Tverdokhlebov V. A. Basic theorems for construction of geometric image of automatons mappiings. Radioelectronic and computer systems, 2013, no. 5(64), pp. 379–384 (in Russian).
  20. Tverdokhlebov V. A. Geometrical models and methods of recognition of automata. Intelligent systems, 2013, vol. 17, iss. 1–4, pp. 187–191 (in Russian).
Received: 
24.01.2016
Accepted: 
25.05.2016
Published: 
30.06.2016
  • 1152 reads