Geometrical images of finite state machines

V. A. Tverdokhlebov

Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 5 (2005) no. 1, pp. 141-153.

Résumé

ln this work а пеw way of defining finite state machines (FSM) is being suggested. The discrete word geometry is built for that purpose, in which machine image is expressed as а set of lines. The methods of synthesis and analysis of geometrical images of FSMs and their features are researched. The new way of defining the FSMs allows analyzing the machine's behavior, excluding the exhausting recursive procedure of defining the initial fragments of machine functioning.

Bibliographie

[1] “Matematika”, Bolshoi entsiklopedicheskii slovar, M., 1999

[2] McCulloch W. S., Pitts W. N., “A logical calculis of the ideas immanent in nervous activity”, Bull. Math. Biophys., 5 (1943), 115–133 | DOI | MR | Zbl

[3] Tverdokhlebov V. A., “Tekhnicheskoe diagnostirovanie v geometricheskoi interpretatsii zadach, modelei i metodov”, Avtomatizatsiya proektirovaniya diskretnykh sistem, Materialy Mezhdunar. konf. (Minsk, 1995), v. 1, 97

[4] Tverdokhlebov V. A., “Raspoznavanie avtomatov na osnove geometricheskoi interpretatsii”, Problemy teoreticheskoi kibernetiki, Tez. dokl. XI Mezhdunar. konf., M., 1996, 191

[5] Rezchikov A. F., Tverdokhlebov V. A., Upravlenie idiagnostirovanie v slozhnykh sistemakh, Saratov, 1997

[6] Tverdokhlebov V. A., “Tekhnicheskoe diagnostirovanie v geometricheskoi interpretatsii”, Problemy i perspektivy pretsizionnoi mekhaniki i upravleniya v mashinostroenii, Materialy Mezhdunar. konf. (Saratov, 1997), 137–140

[7] Tverdokhlebov V. A., “Diskretnye slovarnye geometrii dlya analiza i sinteza matematicheskikh avtomatov”, Voprosy preobrazovatelnoi tekhniki, chastotnogo elektroprivoda i upravleniya, Mezhvuz. nauch. sb. (Saratov, 1998), 71–79

[8] Tverdokhlebov V. A., “Diskretnye slovarnye geometrii dlya analiza i sinteza matematicheskikh avtomatov”, Dokl. Akademii voennykh nauk. Saratov, 1999, no. 1, 100–113 | MR

[9] Tverdokhlebov V. A., “Sintez i analiz geometricheskikh obrazov konechnykh avtomatov”, Problemy teoreticheskoi kibernetiki, Tez. dokl. XII Mezhdunar. konf., v. II, M., 1999, 225

[10] Tverdokhlebov V. A., “Tekhnicheskoe diagnostirovanie na osnove raspoznavaniya svoistv perekhodov i vykhodov avtomatov”, Informatsionno-upravlyayuschie sistemy na zheleznodorozhnom transporte, 2000, no. 4, 45–47

[11] Smirnov A. K., Tverdokhlebov V. A., Upravlenie zhiznennymi tsiklami slozhnykh sistem, Saratov, 2000

[12] Tverdokhlebov V. A., “Diskretnoe upravlenie v tolerantnykh i implikativnykh prostranstvakh”, Problemy i perspektivy pretsizionnoi mekhaniki i upravleniya v mashinostroenii, Materialy Mezhdunar. konf. (Saratov, 2002), 211–215

[13] Tverdokhlebov V. A., “Discrete space for trajectories of diagnostic symptoms”, Radioelektronika i informatika, 2003, no. 23, 121

[14] Tverdokhlebov V. A., “Diskretnoe prostranstvo dlya obrazov povedeniya konechnykh avtomatov”, Teoreticheskie problemy informatiki i ee prilozhenii, 5, Saratov, 2003, 163–174

[15] Tverdokhlebov V. A., “Diskretnye prostranstva v zadachakh upravleniya i diagnostirovaniya”, Dokl. AVN. Povolzh. otd-nie, 2003, no. 9, 102–108

[16] Tverdokhlebov V. A., “Postroenie i analiz geometricheskikh obrazov konechnykh avtomatov”, Problemy tochnoi mekhaniki i upravleniya, Sb. nauch. tr., IPTMU RAN, Saratov, 2004, 94–100

[17] Tverdokhlebov V. A., “Rekurrentnost geometricheskikh obrazov”, Informatsionno-upravlyayuschie sistemy na zheleznodorozhnom transporte, 2004, no. 4–5, 88–90

[18] Tverdokhlebov V. A., “The general features of geometrical images of finite state machines”, Proc. of East-West Design Test Workshop, EWDTW'2004 (Alushta, 2004), 243–247

[19] Tverdokhlebov V. A., “Osnovnye svoistva geometricheskikh obrazov avtomatov”, Problemy tochnoi mekhaniki i upravleniya, Sb. nauch. tr., IPTMU RAN, Saratov, 2004, 187–192 | MR

[20] Tverdokhlebov V. A., Eremenko R. N., Putyatinskii S. E., “Analiz predstavleniya irratsionalnykh posledovatelnostei funktsiyami $k$-znachnoi logiki”, Problemy tochnoi mekhaniki i upravleniya, Sb. nauch. tr., IPTMU RAN, Saratov, 2004, 170–175

[21] Tverdokhlebov V. A., “Diskretnye sistemy i geometricheskie obrazy ikh funktsionirovaniya”, Avtomatizatsiya proektirovaniya diskretnykh sistem, Materialy 5-i Mezhdunar. konf. (Minsk, 2004), v. 1, 217–226 | MR

[22] Tverdokhlebov V. A., “Diskretnye prostranstva v zadachakh upravleniya i diagnostirovaniya”, Avtomatizatsiya proektirovaniya diskretnykh sistem, Materialy 5-i Mezhdunar. konf. (Minsk, 2004), v. 2, 104–113

[23] Mur E., “Umozritelnye eksperimenty s posledovatelnymi mashinami”, Avtomaty, Sb. st., eds. K. Shennon, D. Makkarti, M., 1956, 179–213

[24] Gill A., Vvedenie v teoriyu konechnykh avtomatov, M., 1966

[25] Glushkov V. M., Sintez tsifrovykh avtomatov, M., 1962

[26] Brauer V., Vvedenie v teoriyu konechnykh avtomatov, M., 1987

[27] Arbib M., “Automata theory and control theory: a rapprochement”, Automatica, 3 (1966), 161–189 | DOI | Zbl

[28] Arbib M., “Tolerance automata”, Kybernetic, 3 (1967), 223–233 | MR | Zbl

[29] Kallman R., Falb P., Arbib M., Ocherki po matematicheskoi teorii sistem, M., 1971