Synchronization of finite automata
- 作者: Volkov M.V.1
-
隶属关系:
- Ural State University
- 期: 卷 77, 编号 5 (2022)
- 页面: 53-130
- 栏目: Articles
- URL: https://journals.rcsi.science/0042-1316/article/view/133711
- DOI: https://doi.org/10.4213/rm10005
- ID: 133711
如何引用文章
详细
作者简介
Mikhail Volkov
Ural State University
Email: Mikhail.Volkov@usu.ru
Doctor of physico-mathematical sciences, Professor
参考
- R. L. Adler, L. W. Goodwyn, B. Weiss, “Equivalence of topological Markov shifts”, Israel J. Math., 27:1 (1977), 49–63
- P. Ageev, “Implementation of the algorithm for testing an automaton for synchronization in linear expected time”, J. Autom. Lang. Comb., 24:2-4 (2019), 139–152
- J. Almeida, S. Margolis, B. Steinberg, M. Volkov, “Representation theory of finite semigroups, semigroup radicals and formal language theory”, Trans. Amer. Math. Soc., 361:3 (2009), 1429–1461
- J. Almeida, E. Rodaro, “Semisimple synchronizing automata and the Wedderburn–Artin theory”, Internat. J. Found. Comput. Sci., 27:2 (2016), 127–145
- J. Almeida, B. Steinberg, “Matrix mortality and the Černy–Pin conjecture”, Developments in language theory, Lecture Notes in Comput. Sci., 5583, Springer, Berlin, 2009, 67–80
- J. Almeida, M. V. Volkov, “Profinite identities for finite semigroups whose subgroups belong to a given pseudovariety”, J. Algebra Appl., 2:2 (2003), 137–163
- Д. С. Ананичев, “Порог аннуляции для частично монотонных автоматов”, Изв. вузов. Матем, 2010, № 1, 3–13
- D. S. Ananichev, V. V. Gusev, “Approximation of reset thresholds with greedy algorithms”, Fund. Inform., 145:3 (2016), 221–227
- D. S. Ananichev, I. V. Petrov, M. V. Volkov, “Collapsing words: a progress report”, Internat. J. Found. Comput. Sci., 17:3 (2006), 507–518
- D. S. Ananichev, M. V. Volkov, “Some results on Černy type problems for transformation semigroups”, Semigroups and languages, World Sci. Publ., River Edge, NJ, 2004, 23–42
- D. S. Ananichev, M. V. Volkov, “Synchronizing monotonic automata”, Theoret. Comput. Sci., 327:3 (2004), 225–239
- D. S. Ananichev, M. V. Volkov, “Synchronizing generalized monotonic automata”, Theoret. Comput. Sci., 330:1 (2005), 3–13
- Д. С. Ананичев, М. В. Волков, В. В. Гусев, “Примитивные орграфы с большими экспонентами и медленно синхронизируемые автоматы”, Комбинаторика и теория графов. IV, Первый Российско-финский симпозиум по дискретной математике (специальный выпуск), Зап. науч. сем. ПОМИ, 402, ПОМИ, СПб., 2012, 9–39
- D. Ananichev, V. Vorel, “A new lower bound for reset threshold of binary synchronizing automata with sink”, J. Autom. Lang. Comb., 24:2-4 (2019), 153–164
- J. Araujo, P. Cameron, B. Steinberg, “Between primitive and 2-transitive: synchronization and its friends”, EMS Surv. Math. Sci., 4:2 (2017), 101–184
- F. Arnold, B. Steinberg, “Synchronizing groups and automata”, Theoret. Comput. Sci., 359:1-3 (2006), 101–110
- У. Р. Эшби, Введение в кибернетику, ИЛ, М., 1959, 432 с.
- M.-P. Beal, M. V. Berlinkov, D. Perrin, “A quadratic upper bound on the size of a synchronizing word in one-cluster automata”, Internat. J. Found. Comput. Sci., 22:2 (2011), 277–288
- M.-P. Beal, D. Perrin, “A quadratic upper bound on the size of a synchronizing word in one-cluster automata”, Developments in language theory, Lecture Notes in Comput. Sci., 5583, Springer, Berlin, 2009, 81–90
- Y. Benenson, R. Adar, T. Paz-Elizur, Z. Livneh, E. Shapiro, “DNA molecule provides a computing machine with both data and fuel”, Proc. Natl. Acad. Sci. USA, 100:5 (2003), 2191–2196
- Y. Benenson, T. Paz-Elizur, R. Adar, E. Keinan, Z. Livneh, E. Shapiro, “Programmable and autonomous computing machine made of biomolecules”, Nature, 414:6862 (2001), 430–434
- M. V. Berlinkov, “On a conjecture by Carpi and D'Alessandro”, Internat. J. Found. Comput. Sci., 22:7 (2011), 1565–1576
- M. V. Berlinkov, “Synchronizing quasi-Eulerian and quasi-one-cluster automata”, Internat. J. Found. Comput. Sci., 24:6 (2013), 729–745
- M. V. Berlinkov, “Approximating the minimum length of synchronizing words is hard”, Theory Comput. Syst., 54:2 (2014), 211–223
- M. V. Berlinkov, “On two algorithmic problems about synchronizing automata”, Developments in language theory, Lecture Notes in Comput. Sci., 8633, Springer, Cham, 2014, 61–67
- M. V. Berlinkov, “On the probability of being synchronizable”, Algorithms and discrete applied mathematics, Lecture Notes in Comput. Sci., 9602, Springer, Cham, 2016, 73–84
- M. V. Berlinkov, R. Ferens, M. Szykula, “Preimage problems for deterministic finite automata”, J. Comput. System Sci., 115 (2021), 214–234
- M. V. Berlinkov, M. Szykula, “Algebraic synchronization criterion and computing reset words”, Inform. Sci., 369 (2016), 718–730
- J. Berstel, D. Perrin, C. Reutenauer, Codes and automata, Encyclopedia Math. Appl., 129, Cambridge Univ. Press, Cambridge, 2010, xiv+619 pp.
- M. T. Biskup, Error resilience in compressed data – selected topics, Ph.D. thesis, Inst. of Informatics, Univ. of Warsaw, 2008, 136 pp., par
- M. T. Biskup, “Guaranteed synchronization of Huffman codes”, Data compression conference (DCC 2008) (Snowbird, UT, 2008), IEEE, 2008, 462–471
- M. T. Biskup, W. Plandowski, “Guaranteed synchronization of Huffman codes with known position of decoder”, Data compression conference (DCC 2009) (Snowbird, UT, 2009), IEEE, 2009, 33–42
- M. T. Biskup, W. Plandowski, “Shortest synchronizing strings for {H}uffman codes”, Theoret. Comput. Sci., 410:38-40 (2009), 3925–3941
- S. Bogdanovic, B. Imreh, M. Ciric, T. Petkovic, “Directable automata and their generalizations: a survey”, Novi Sad J. Math., 29:2 (1999), 29–69
- P. Bonizzoni, N. Jonoska, “Existence of constants in regular splicing languages”, Inform. and Comput., 242 (2015), 340–353
- V. Boppana, S. P. Rajan, K. Takayama, M. Fujita, “Model checking based on sequential ATPG”, Computer aided verification, Lecture Notes in Comput. Sci., 1633, Springer-Verlag, Berlin, 1999, 418–430
- R. A. Brualdi, H. J. Ryser, Combinatorial matrix theory, Encyclopedia Math. Appl., 39, Cambridge Univ. Press, Cambridge, 1991, x+367 pp.
- P. J. Cameron, “Dixon's theorem and random synchronization”, Discrete Math., 313:11 (2013), 1233–1236
- R. M. Capocelli, L. Gargano, U. Vaccaro, “On the characterization of statistically synchronizable variable-length codes”, IEEE Trans. Inform. Theory, 34:4 (1988), 817–825
- A. Carpi, F. D'Alessandro, “Strongly transitive automata and the Černy conjecture”, Acta Inform., 46:8 (2009), 591–607
- A. Carpi, F. D'Alessandro, “The synchronization problem for locally strongly transitive automata”, Mathematical foundations of computer science 2009, Lecture Notes in Comput. Sci., 5734, Springer, Berlin, 2009, 211–222
- A. Carpi, F. D'Alessandro, “Independent sets of words and the synchronization problem”, Adv. in Appl. Math., 50:3 (2013), 339–355
- A. Carpi, F. D'Alessandro, “Locally strongly transitive automata in the Černy conjecture and related problems”, J. Autom. Lang. Comb., 24:2-4 (2019), 165–184
- J. Černy, “Poznamka k homogennym eksperimentom s konečnymi automatami”, Mat.-Fyz. Časopis Sloven. Akad. Vied., 14:3 (1964), 208–216
- J. Černy, A. Piricka, B. Rosenauerova, “On directable automata”, Kybernetika (Prague), 7:4 (1971), 289–298
- Yui-Bin Chen, D. J. Ierardi, “The complexity of oblivious plans for orienting and distinguishing polygonal parts”, Algorithmica, 14:5 (1995), 367–397
- A. Cherubini, “Synchronizing and collapsing words”, Milan J. Math., 75:1 (2007), 305–321
- A. Cherubini, A. Frigeri, Zuhua Liu, “Composing short 3-compressing words on a 2-letter alphabet”, Discrete Math. Theor. Comput. Sci., 19:1 (2017), 17, 35 pp.
- A. Cherubini, A. Kisielewicz, “Collapsing words, permutation conditions and coherent colorings of trees”, Theoret. Comput. Sci., 410:21-23 (2009), 2135–2147
- A. Cherubini, A. Kisielewicz, “Recognizing 3-collapsing words over a binary alphabet”, Theoret. Comput. Sci., 629 (2016), 64–79
- A. Cherubini, A. Kisielewicz, B. Piochi, “On the length of shortest 2-collapsing words”, Discrete Math. Theor. Comput. Sci., 11:1 (2009), 33–44
- K. Chmiel, A. Roman, “COMPAS – a computing package for synchronization”, Implementation and application of automata, Lecture Notes in Comput. Sci., 6482, Springer, Berlin, 2011, 79–86
- Hyunwoo Cho, Seh-Woong Jeong, F. Somenzi, C. Pixley, “Multiple observation time single reference test generation using synchronizing sequences”, 1993 European conference on design automation with the European event in ASIC design (Paris, 1993), IEEE, 1993, 494–498
- Hyunwoo Cho, Seh-Woong Jeong, F. Somenzi, C. Pixley, “Synchronizing sequences and symbolic traversal techniques in test generation”, J. Electronic Testing, 4 (1993), 19–31
- Т. Кормен, Ч. Лейзерсон, Р. Ривест, К. Штайн, Алгоритмы: построение и анализ, 3-е изд., Вильямс, М., 2011, 1324 с.
- Zhen He Cui, Yong He, Shi Yuan Sun, “Synchronizing bounded partially ordered automata”, (Chinese), Chinese J. Comput., 42:3 (2019), 610–623
- M. de Bondt, A short proof of a theorem of J.-E. Pin, 2018, 12 pp.
- M. de Bondt, H. Don, H. Zantema, “DFAs and PFAs with long shortest synchronizing word length”, Developments in language theory, Lecture Notes in Comput. Sci., 10396, Springer, Cham, 2017, 122–133
- F. M. Dekking, “The spectrum of dynamical systems arising from substitutions of constant length”, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 41:3 (1978), 221–239
- H. Don, H. Zantema, “Finding DFAs with maximal shortest synchronizing word length”, Language and automata theory and applications, Lecture Notes in Comput. Sci., 10168, Springer, Cham, 2017, 249–260
- H. Don, H. Zantema, “Counting symbol switches in synchronizing automata”, J. Autom. Lang. Comb., 24:2-4 (2019), 253–286
- L. Dubuc, “Sur les automates circulaires et la conjecture de Černy”, RAIRO Inform. Theor. Appl., 32:1-3 (1998), 21–34
- M. Dżyga, R. Ferens, V. V. Gusev, M. Szykula, “Attainable values of reset thresholds”, 42nd international symposium on mathematical foundations of computer science, LIPIcs. Leibniz Int. Proc. Inform., 83, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2017, 40, 14 pp.
- D. Eppstein, “Reset sequences for monotonic automata”, SIAM J. Comput., 19:3 (1990), 500–510
- D. Eppstein, J.-C. Falmagne, “Algorithms for media”, Discrete Appl. Math., 156:8 (2008), 1308–1320
- H. Fernau, V. V. Gusev, S. Hoffmann, M. Holzer, M. V. Volkov, P. Wolf, “Computational complexity of synchronization under regular constraints”, 44th international symposium on mathematical foundations of computer science, LIPIcs. Leibniz Int. Proc. Inform., 138, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2019, 63, 14 pp.
- H. Fernau, P. Heggernes, Y. Villanger, “A multi-parameter analysis of hard problems on deterministic finite automata”, J. Comput. System Sci., 81:4 (2015), 747–765
- H. Fernau, A. Krebs, “Problems on finite automata and the exponential time hypothesis”, Algorithms (Basel), 10:1 (2017), 24, 25 pp.
- M. A. Fischler, M. Tannenbaum, “Synchronizing and representation problems for sequential machines with masked outputs”, 11th annual symposium on switching and automata theory (SWAT 1970), IEEE, 1970, 97–103
- P. Frankl, “An extremal problem for two families of sets”, European J. Combin., 3:2 (1982), 125–127
- D. Frettlöh, B. Sing, “Computing modular coincidences for substitution tilings and point sets”, Discrete Comput. Geom., 37:3 (2007), 381–407
- A. Frigeri, E. Rodaro, “Missing factors of ideals and synchronizing automata”, J. Autom. Lang. Comb., 24:2-4 (2019), 309–320
- P. Gawrychowski, Complexity of shortest synchronizing word, preprint, 2008
- P. Gawrychowski, D. Straszak, “Strong inapproximability of the shortest reset word”, Mathematical foundations of computer science 2015, Part I, Lecture Notes in Comput. Sci., 9234, Springer, Heidelberg, 2015, 243–255
- M. Gerbush, B. Heeringa, “Approximating minimum reset sequences”, Implementation and application of automata, Lecture Notes in Comput. Sci., 6482, Springer, Berlin, 2011, 154–162
- A. Gill, “State-identification experiments in finite automata”, Information and Control, 4:2-3 (1961), 132–154
- С. Гинзбург, “О длине кратчайшего однородного эксперимента, устанавливающего конечные состояния машины”, Киберн. сб., 3, ИЛ, М., 1961, 167–186
- S. Ginsburg, An introduction to mathematical machine theory, Addison-Wesley Publishing Co., Inc., Reading, MA–Palo Alto, CA–London, 1962, ix+147 pp.
- K. Y. Goldberg, “Orienting polygonal parts without sensors”, Algorithmica, 10:2-4 (1993), 201–225
- F. Gonze, V. V. Gusev, R. M. Jungers, B. Gerencser, M. V. Volkov, “On the interplay between Černy and {B}abai's conjectures”, Internat. J. Found. Comput. Sci., 30:1 (2019), 93–114
- F. Gonze, R. M. Jungers, A. N. Trahtman, “A note on a recent attempt to improve the Pin–Frankl bound”, Discrete Math. Theor. Comput. Sci., 17:1 (2015), 307–308
- P. Goralčik, V. Koubek, “Rank problems for composite transformations”, Internat. J. Algebra Comput., 5:3 (1995), 309–316
- Р. Грэхем, Д. Кнут, О. Паташник, Конкретная математика. Основание информатики, 2-е изд., испр., Мир, Бином. Лаборатория знаний, М., 2006, 703 с.
- M. Grech, A. Kisielewicz, “The Černy conjecture for automata respecting intervals of a directed graph”, Discrete Math. Theor. Comput. Sci., 15:3 (2013), 61–72
- M. Grech, A. Kisielewicz, “Synchronizing sequences for road colored digraphs”, Discrete Appl. Math., 285 (2020), 128–140
- V. V. Gusev, “Lower bounds for the length of reset words in Eulerian automata”, Reachability problems, Lecture Notes in Comput. Sci., 6945, Springer, Berlin, 2011, 180–190
- V. V. Gusev, R. M. Jungers, D. Průša, “Dynamics of the independence number and automata synchronization”, Developments in language theory, Lecture Notes in Comput. Sci., 11088, Springer, Cham, 2018, 379–391
- V. V. Gusev, M. I. Maslennikova, E. V. Pribavkina, “Principal ideal languages and synchronizing automata”, Fund. Inform., 132:1 (2014), 95–108
- V. V. Gusev, E. V. Pribavkina, “On codeword lengths guaranteeing synchronization”, Combinatorics on words, Lecture Notes in Comput. Sci., 11682, Springer, Cham, 2019, 207–216
- J. Hastad, “Clique is hard to approximate within $n^{1-varepsilon}$ ”, Acta Math., 182:1 (1999), 105–142
- S. Hoffmann, “On a class of constrained synchronization problems in NP”, Proceedings of the 21st Italian conference on theoretical computer science (Ischia, 2020), CEUR Workshop Proceedings, 2756, 2020, 145–157
- S. Hoffmann, “Completely reachable automata, primitive groups and the state complexity of the set of synchronizing words”, Language and automata theory and applications, Lecture Notes in Comput. Sci., 12638, Springer, Cham, 2021, 305–317
- S. Hoffmann, “State complexity of the set of synchronizing words for circular automata and automata over binary alphabets”, Language and automata theory and applications, Lecture Notes in Comput. Sci., 12638, Springer, Cham, 2021, 318–330
- S. Hoffmann, “Constrained synchronization and subset synchronization problems for weakly acyclic automata”, Developments in language theory, Lecture Notes in Comput. Sci., 12811, Springer, Cham, 2021, 204–216
- S. Hoffmann, “Computational complexity of synchronization under sparse regular constraints”, Fundamentals of computation theory, Lecture Notes in Comput. Sci., 12867, Springer, Cham, 2021, 272–286
- S. Hoffmann, “Ideal separation and general theorems for constrained synchronization and their application to small constraint automata”, Computing and combinatorics, Lecture Notes in Comput. Sci., 13025, Springer, Cham, 2021, 176–188
- S. Hoffmann, “Constrained synchronization and commutativity”, Theoret. Comput. Sci., 890 (2021), 147–170
- H. J{ü}rgensen, “Synchronization”, Inform. and Comput., 206:9-10 (2008), 1033–1044
- J. Kari, “A counter example to a conjecture concerning synchronizing words in finite automata”, Bull. Eur. Assoc. Theor. Comput. Sci. EATCS, 73 (2001), 146
- J. Kari, “Synchronizing finite automata on Eulerian digraphs”, Theoret. Comput. Sci., 295:1-3 (2003), 223–232
- J. Kari, M. Volkov, “Černy's conjecture and the road colouring problem”, Handbook of automata theory, Ch. 15, v. I, Theoretical foundations, EMS Press, Berlin, 2021, 525–565
- A. Kisielewicz, J. Kowalski, M. Szykula, “Computing the shortest reset words of synchronizing automata”, J. Comb. Optim., 29:1 (2015), 88–124
- A. Kisielewicz, J. Kowalski, M. Szykula, “Experiments with synchronizing automata”, Implementation and application of automata, Lecture Notes in Comput. Sci., 9705, Springer, Cham, 2016, 176–188
- A. Kisielewicz, M. Szykula, “Generating small automata and the Černy conjecture”, Implementation and application of automata, Lecture Notes in Comput. Sci., 7982, Springer, Heidelberg, 2013, 340–348
- A. Kisielewicz, M. Szykula, “Synchronizing automata with extremal properties”, Mathematical foundations of computer science 2015, Part 1, Lecture Notes in Comput. Sci., 9234, Springer, Heidelberg, 2015, 331–343
- С. К. Клини, “Представление событий в нервных сетях и конечных автоматах”, Автоматы, Сб. ст., ИЛ, М., 1956, 15–67
- А. А. Клячко, И. К. Рысцов, М. А. Спивак, “Об одной экстремальной комбинаторной задаче, связанной с оценкой длины возвратного слова в автомате”, Кибернетика, 25:2 (1987), 16–20
- Z. Kohavi, J. Winograd, “Bounds on the length of synchronizing sequences and the order of information losslessness”, Theory of machines and computations, Academic Press, New York, 1971, 197–206
- Z. Kohavi, J. Winograd, “Establishing certain bounds concerning finite automata”, J. Comput. System Sci., 7:3 (1973), 288–299
- D. Kozen, “Lower bounds for natural proof systems”, 18th annual symposium on foundations of computer science (Providence, RI, 1977), IEEE Comput. Sci., Long Beach, CA, 1977, 254–266
- M. W. Krentel, “The complexity of optimization problems”, J. Comput. System Sci., 36:3 (1988), 490–509
- A. E. Laemmel, A general class of discrete codes and certain of their properties, Res. rep. R-459-55, PIB-389, Microwave Research Inst., Polytechnic Inst., Brooklyn, NY, 1956
- A. E. Laemmel, Study on application of coding theory, Tech. rep. PIBMRI-895.5-63, Dept. Electrophysics, Microwave Research Inst., Polytechnic Inst., Brooklyn, NY, 1963
- A. E. Laemmel, B. Rudner, Study of the application of coding theory, Tech. rep. PIBEP-69-034, Dept. Electrophysics, Polytechnic Inst., Brooklyn, Farmingdale, NY, 1969
- В. И. Левенштейн, “Самонастраивающиеся автоматы для декодирования сообщений”, Докл. АН СССР, 141:6 (1961), 1320–1323
- Chung Laung Liu, “Determination of the final state of an automaton whose initial state is unknown”, IEEE Trans. Electronic Computers, EC-12:6 (1963), 918–920
- Chung Laung Liu, Some memory aspects of finite automata, Tech. rep. 411, Research Lab. Electronics, Massachusetts Inst., MIT Res. Lab. Electronics, Cambridge, MA, 1963, 71 pp.
- P. V. Martugin, “A series of slowly synchronizing automata with a zero state over a small alphabet”, Inform. and Comput., 206:9-10 (2008), 1197–1203
- M. Maslennikova, “Reset complexity of ideal languages over a binary alphabet”, Internat. J. Found. Comput. Sci., 30:6-7 (2019), 1177–1196
- M. Maslennikova, E. Rodaro, “Representation of (left) ideal regular languages by synchronizing automata”, Computer science – theory and applications, Lecture Notes in Comput. Sci., 9139, Springer, Cham, 2015, 325–338
- M. Maslennikova, E. Rodaro, “Trim strongly connected synchronizing automata and ideal languages”, Fund. Inform., 162:2-3 (2018), 183–203
- A. Mateescu, A. Salomaa, “Many-valued truth functions, Černy's conjecture, and road coloring”, Current trends in theoretical computer science. Entering the 21th century, World Sci. Publ., River Edge, NJ, 2001, 693–707
- Ю. Т. Медведев, “О классе событий, допускающих представление в конечном автомате”, Автоматы, Сб. ст., ИЛ, М., 1956, 385–401
- E. H. Moore, “On certain crinkly curves”, Trans. Amer. Math. Soc., 1:1 (1900), 72–90
- Э. Ф. Мур, “Умозрительные эксперименты с последовательностными машинами”, Автоматы, Сб. ст., ИЛ, М., 1956, 179–210
- B. K. Natarajan, “An algorithmic approach to the automated design of parts orienters”, 27th annual symposium on foundations of computer science (SFCS 1986) (Toronto, ON, 1986), IEEE, 1986, 132–142
- B. K. Natarajan, “Some paradigms for the automated design of parts feeders”, Int. J. Robot. Res., 8:6 (1989), 98–109
- C. Nicaud, “The Černy conjecture holds with high probability”, J. Autom. Lang. Comb., 24:2-4 (2019), 343–365
- J. Olschewski, M. Ummels, “The complexity of finding reset words in finite automata”, Mathematical foundations of computer science 2010, Lecture Notes in Comput. Sci., 6281, Springer, Berlin, 2010, 568–579
- C. H. Papadimitriou, Computational complexity, Addison-Wesley Publishing Co., Reading, MA, 1994, xvi+523 pp.
- C. H. Papadimitriou, M. Yannakakis, “The complexity of facets (and some facets of complexity)”, J. Comput. System Sci., 28:2 (1984), 244–259
- J.-E. Pin, Le problème de la synchronisation et la conjecture de Černy, Thèse de 3ème cycle, Univ. Paris VI, 1978
- J.-E. Pin, “Sur un cas particulier de la conjecture de Cerny”, Automata, languages and programming (Udine, 1978), Lecture Notes in Comput. Sci., 62, Springer, Berlin–New York, 1978, 345–352
- J.-E. Pin, “Utilisation de l'algèbre lineaire en theorie des automates”, Actes du 1er colloque AFCET-SMF de mathematiques appliquees (Palaiseau, 1978), AFCET, 1978, 85–92
- J. E. Pin, “On two combinatorial problems arising from automata theory”, Combinatorial mathematics (Marseille–Luminy, 1981), North-Holland Math. Stud., 75, Ann. Discrete Math., 17, North-Holland, Amsterdam, 1983, 535–548
- C. Pixley, S.-W. Jeong, G. D. Hachtel, “Exact calculation of synchronizing sequences based on binary decision diagrams”, IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., 13:8 (1994), 1024–1034
- R. Pöschel, M. V. Sapir, N. V. Sauer, M. G. Stone, M. V. Volkov, “Identities in full transformation semigroups”, Algebra Universalis, 31:4 (1994), 580–588
- Е. В. Прибавкина, “Медленно синхронизируемые автоматы с нулем и непокрывающие множества”, Матем. заметки, 90:3 (2011), 422–430
- E. V. Pribavkina, E. Rodaro, “Synchronizing automata with finitely many minimal synchronizing words”, Inform. and Comput., 209:3 (2011), 568–579
- N. Pytheas Fogg, Substitutions in dynamics, arithmetics and combinatorics, Lecture Notes in Math., 1794, eds. V. Berthe, S. Ferenczi, C. Mauduit, A. Siegel, Springer-Verlag, Berlin, 2002
- M. O. Rabin, D. Scott, “Finite automata and their decision problems”, IBM J. Res. Develop., 3:2 (1959), 114–125
- J. L. Ramirez Alfonsin, The Diophantine Frobenius problem, Oxford Lecture Ser. Math. Appl., 30, Oxford Univ. Press, Oxford, 2005, xvi+243 pp.
- A. S. Rao, K. Y. Goldberg, “Manipulating algebraic parts in the plane”, IEEE Trans. Robotics Autom., 11:4 (1995), 598–602
- R. Reis, E. Rodaro, “Ideal regular languages and strongly connected synchronizing automata”, Theoret. Comput. Sci., 653 (2016), 97–107
- June-Kyung Rho, F. Somenzi, C. Pixley, “Minimum length synchronizing sequences of finite state machine”, 30th ACM/IEEE design automation conference (Dallas, TX, 1993), ACM, New York, NY, 1993, 463–468
- E. Rodaro, “Strongly connected synchronizing automata and the language of minimal reset words”, Adv. in Appl. Math., 99 (2018), 158–173
- E. Rodaro, “A bound for the length of the shortest reset words for semisimple synchronizing automata via the packing number”, J. Algebraic Combin., 50:3 (2019), 237–253
- A. Roman, M. Szykula, “Forward and backward synchronizing algorithms”, Expert Syst. Appl., 42:24 (2015), 9512–9527
- И. К. Рысцов, “Оценка длины ядерного слова для конечного автомата”, Автоматы, Межвуз. науч. сб., т. 2, Сарат. гос. ун-т, Саратов, 1977, 43–48
- И. К. Рысцов, “О минимизации синхронизирующих слов для конечных автоматов”, Теоретические вопросы проектирования вычислительных систем, АН УССР, Науч. совет по пробл. “Кибернетика”, Ин-т кибернетики, Киев, 1980, 75–82
- I. K. Rystsov, “Polynomial complete problems in automata theory”, Inform. Process. Lett., 16:3 (1983), 147–151
- И. К. Рысцов, “О ранге конечного автомата”, Кибернетика и системный анализ, 28:3 (1992), 3–10
- И. К. Рысцов, “Возвратные слова для разрешимых автоматов”, Кибернетика и системный анализ, 30:6 (1994), 21–26
- И. К. Рысцов, “Почти оптимальная оценка длины возвратного слова для регулярных автоматов”, Кибернетика и системный анализ, 31:5 (1995), 40–48
- I. K. Rystsov, “Quasioptimal bound for the length of reset words for regular automata”, Acta Cybernet., 12:2 (1995), 145–152
- I. Rystsov, “Exact linear bound for the length of reset words in commutative automata”, Publ. Math. Debrecen, 48:3-4, suppl. (1996), 405–409
- I. Rystsov, “Reset words for commutative and solvable automata”, Theoret. Comput. Sci., 172:1-2 (1997), 273–279
- И. К. Рысцов, “О длине возвратных слов для автоматов с простыми идемпотентами”, Кибернетика и системный анализ, 36:3 (2000), 32–39
- I. K. Рисцов, “Проблема Чернi для автоматiв iз простими iдемпотентами”, Кiбернетика та системний аналiз, 58:1 (2022), 3–10
- A. Ryzhikov, “Synchronization problems in automata without non-trivial cycles”, Theoret. Comput. Sci., 787 (2019), 77–88
- A. Ryzhikov, M. Szykula, “Finding short synchronizing words for prefix codes”, 43rd international symposium on mathematical foundations of computer science (Liverpool, UK, 2018), LIPIcs. Leibniz Int. Proc. Inform., 117, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2018, 21, 14 pp.
- A. Salomaa, “Compositions over a finite domain: from completeness to synchronizable automata”, A half-century of automata theory. Celebration and inspiration (London, ON, 2000), World Sci. Publ., River Edge, NJ, 2001, 131–143
- A. Salomaa, “Generation of constants and synchronization of finite automata”, J. UCS, 8:2 (2002), 332–347
- A. Salomaa, “Synchronization of finite automata: contributions to an old problem”, The essence of computation. Complexity, analysis, transformation, Essays dedicated to N. D. Jones [on occasion of his 60th birthday], Lecture Notes in Comput. Sci., 2566, Springer, Berlin, 2002, 37–59
- A. Salomaa, “Composition sequences for functions over a finite domain”, Theoret. Comput. Sci., 292:1 (2003), 263–281
- S. Sandberg, “Homing and synchronizing sequences”, Model-based testing of reactive systems. Advanced lectures, Lecture Notes in Comput. Sci., 3472, Springer-Verlag, Berlin, 2005, 5–33
- M. Schützenberger, “On an application of semi groups methods to some problems in coding”, IRE Trans. Inform. Theory, 2:3 (1956), 47–60
- Y. Shitov, “An improvement to a recent upper bound for synchronizing words of finite automata”, J. Autom. Lang. Comb., 24:2-4 (2019), 367–373
- E. Skvortsov, E. Tipikin, “Experimental study of the shortest reset word of random automata”, Implementation and application of automata, Lecture Notes in Comput. Sci., 6807, Springer, Heidelberg, 2011, 290–298
- P. H. Starke, “Eine Bemerkung über homogene Experimente”, Elektron. Informationsverarb. Kybernet., 2 (1966), 257–259
- P. H. Starke, Abstrakte Automaten, VEB Deutscher Verlag der Wissenschaften, Berlin, 1969, 392 pp.
- B. Steinberg, “Černy's conjecture and group representation theory”, J. Algebraic Combin., 31 (2010), 83–109
- B. Steinberg, “The averaging trick and the Černy conjecture”, Internat. J. Found. Comput. Sci., 22:7 (2011), 1697–1706
- B. Steinberg, “The Černy conjecture for one-cluster automata with prime length cycle”, Theoret. Comput. Sci., 412:39 (2011), 5487–5491
- M. Suomalainen, A. Q. Nilles, S. M. LaValle, “Virtual reality for robots”, 2020 IEEE/RSJ international conference on intelligent robots and systems (IROS) (Las Vegas, NV, 2020), IEEE, 2020, 11458–11465
- M. Szykula, Algorithms for synchronizing automata, Ph.D. thesis, Inst. of Computer Science, Univ. of Wroclaw, 2014
- M. Szykula, “Improving the upper bound on the length of the shortest reset word”, 35th symposium on theoretical aspects of computer science, LIPIcs. Leibniz Int. Proc. Inform., 96, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, 2018, 56, 13 pp.
- M. Szykula, V. Vorel, “An extremal series of {E}ulerian synchronizing automata”, Developments in language theory, Lecture Notes in Comput. Sci., 9840, Springer, Berlin, 2016, 380–392
- A. N. Trahtman, “An efficient algorithm finds noticeable trends and examples concerning the Černy conjecture”, Mathematical foundations of computer science 2006, Lecture Notes in Comput. Sci., 4162, Springer, Berlin, 2006, 789–800
- A. N. Trahtman, “The Černy conjecture for aperiodic automata”, Discrete Math. Theor. Comput. Sci., 9:2 (2007), 3–10
- A. Trahtman, “Some aspects of synchronization of DFA”, J. Comput. Sci. Tech., 23:5 (2008), 719–727
- A. N. Trahtman, “The road coloring problem”, Israel J. Math., 172:1 (2009), 51–60
- A. N. Trahtman, “Modifying the upper bound on the length of minimal synchronizing word”, Fundamentals of computation theory, Lecture Notes in Comput. Sci., 6914, Springer, Heidelberg, 2011, 173–180
- A. N. Trahtman, The Černy conjecture, 2022 (v1 – 2012), 14 pp.
- A. N. Trahtman, The length of a minimal synchronizing word and the Černy conjecture, 2021 (v1 – 2014), 14 pp.
- A. N. Trahtman, Cerny–Starke conjecture from the sixties of XX century, 2021 (v1 – 2020), 18 pp.
- M. V. Volkov, “Synchronizing automata and the Černy conjecture”, Language and automata theory and applications, Lecture Notes in Comput. Sci., 5196, Springer, Berlin, 2008, 11–27
- M. V. Volkov, “Synchronizing automata preserving a chain of partial orders”, Theoret. Comput. Sci., 410:37 (2009), 3513–3519
- M. V. Volkov, “Slowly synchronizing automata with idempotent letters of low rank”, J. Autom. Lang. Comb., 24:2-4 (2019), 375–386
- V. Vorel, Synchronization and discontinuous input processing in transition systems, Doctoral thesis, Charles Univ., Prague, 2018, 137 pp., par
- V. Vorel, A. Roman, “Parameterized complexity of synchronization and road coloring”, Discrete Math. Theor. Comput. Sci., 17:1 (2015), 283–305
- H. Wielandt, “Unzerlegbare, nicht negative Matrizen”, Math. Z., 52 (1950), 642–648
- D. Zuckerman, “Linear degree extractors and the inapproximability of max clique and chromatic number”, Theory Comput., 3 (2007), 6, 103–128
补充文件
