{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T10:24:45Z","timestamp":1780050285774,"version":"3.53.1"},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642223204","type":"print"},{"value":"9783642223211","type":"electronic"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-22321-1_28","type":"book-chapter","created":{"date-parts":[[2011,7,14]],"date-time":"2011-07-14T23:58:48Z","timestamp":1310687928000},"page":"324-336","source":"Crossref","is-referenced-by-count":18,"title":["Describing Periodicity in Two-Way Deterministic Finite Automata Using Transformation Semigroups"],"prefix":"10.1007","author":[{"given":"Michal","family":"Kunc","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Okhotin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"28_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/3-540-10003-2_62","volume-title":"Automata, Languages and Programming","author":"P. Berman","year":"1980","unstructured":"Berman, P.: A note on sweeping automata. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol.\u00a085, pp. 91\u201397. Springer, Heidelberg (1980)"},{"key":"28_CR2","unstructured":"Berman, P., Lingas, A.: On complexity of regular languages in terms of finite automata. Report 304, Institute of Computer Science, Polish Academy of Sciences, Warsaw (1977)"},{"issue":"2","key":"28_CR3","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/0304-3975(89)90075-3","volume":"63","author":"J.-C. Birget","year":"1989","unstructured":"Birget, J.-C.: Concatenation of inputs in a two-way automaton. Theoretical Computer Science\u00a063(2), 141\u2013156 (1989)","journal-title":"Theoretical Computer Science"},{"key":"#cr-split#-28_CR4.1","doi-asserted-by":"crossref","unstructured":"Chrobak, M.: Finite automata and unary languages. Theoretical Computer Science 47, 149\u2013158 (1986);","DOI":"10.1016\/0304-3975(86)90142-8"},{"key":"#cr-split#-28_CR4.2","doi-asserted-by":"crossref","unstructured":"Errata 302, 497\u2013498 (2003)","DOI":"10.1016\/S0304-3975(03)00136-1"},{"key":"28_CR5","doi-asserted-by":"crossref","unstructured":"Geffert, V., Mereghetti, C., Pighizzini, G.: Converting two-way nondeterministic unary automata into simpler automata. Theoretical Computer Science 295(1-3), 189\u2013203 (2003)","DOI":"10.1016\/S0304-3975(02)00403-6"},{"key":"28_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1007\/978-3-642-00982-2_3","volume-title":"Language and Automata Theory and Applications","author":"M. Holzer","year":"2009","unstructured":"Holzer, M., Kutrib, M.: Descriptional and computational complexity of finite automata. In: Dediu, A.H., Ionescu, A.M., Mart\u00edn-Vide, C. (eds.) LATA 2009. LNCS, vol.\u00a05457, pp. 23\u201342. Springer, Heidelberg (2009)"},{"key":"28_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1007\/978-3-540-85780-8_35","volume-title":"Developments in Language Theory","author":"G. Jir\u00e1skov\u00e1","year":"2008","unstructured":"Jir\u00e1skov\u00e1, G., Okhotin, A.: On the state complexity of operations on two-way finite automata. In: Ito, M., Toyama, M. (eds.) DLT 2008. LNCS, vol.\u00a05257, pp. 443\u2013454. Springer, Heidelberg (2008)"},{"key":"28_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1007\/11549345_47","volume-title":"Mathematical Foundations of Computer Science 2005","author":"C.A. Kapoutsis","year":"2005","unstructured":"Kapoutsis, C.A.: Removing bidirectionality from nondeterministic finite automata. In: Jedrzejowicz, J., Szepietowski, A. (eds.) MFCS 2005. LNCS, vol.\u00a03618, pp. 544\u2013555. Springer, Heidelberg (2005)"},{"key":"28_CR9","unstructured":"Landau, E.: Uber die Maximalordnung der Permutationen gegebenen Grades (On the maximal order of permutations of a given degree). Archiv der Mathematik und Physik, Ser. 3\u00a05, 92\u2013103 (1903)"},{"key":"28_CR10","doi-asserted-by":"crossref","unstructured":"Mereghetti, C., Pighizzini, G.: Optimal simulations between unary automata. SIAM Journal on Computing\u00a030(6), 1976\u20131992 (2001)","DOI":"10.1137\/S009753979935431X"},{"key":"28_CR11","unstructured":"Mereghetti, C., Pighizzini, G.: Two-way automata simulations and unary languages. Journal of Automata, Languages and Combinatorics\u00a05(3), 287\u2013300 (2000)"},{"key":"28_CR12","doi-asserted-by":"crossref","unstructured":"Micali, S.: Two-way deterministic finite automata are exponentially more succinct than sweeping automata. Information Processing Letters\u00a012(2), 103\u2013105 (1981)","DOI":"10.1016\/0020-0190(81)90012-0"},{"key":"28_CR13","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.1109\/T-C.1971.223108","volume":"20","author":"F.R. Moore","year":"1971","unstructured":"Moore, F.R.: On the bounds for state-set size in the proofs of equivalence between deterministic, nondeterministic, and two-way finite automata. IEEE Transactions on Computers\u00a020, 1211\u20131214 (1971)","journal-title":"IEEE Transactions on Computers"},{"key":"28_CR14","first-page":"1","volume-title":"Handbook of Theoretical Computer Science vol. B","author":"D. Perrin","year":"1990","unstructured":"Perrin, D.: Finite Automata. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science vol. B, pp. 1\u201357. MIT Press, Cambridge (1990)"},{"key":"28_CR15","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1147\/rd.32.0114","volume":"3","author":"M.O. Rabin","year":"1959","unstructured":"Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM Journal of Research and Development\u00a03, 114\u2013125 (1959)","journal-title":"IBM Journal of Research and Development"},{"key":"28_CR16","doi-asserted-by":"crossref","unstructured":"Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two way finite automata. In: STOC 1978, pp. 275\u2013286 (1978)","DOI":"10.1145\/800133.804357"},{"key":"28_CR17","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1147\/rd.32.0198","volume":"3","author":"J.C. Shepherdson","year":"1959","unstructured":"Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM Journal of Research and Development\u00a03, 198\u2013200 (1959)","journal-title":"IBM Journal of Research and Development"},{"key":"28_CR18","doi-asserted-by":"crossref","unstructured":"Sipser, M.: Lower bounds on the size of sweeping automata. In: STOC 1979, pp. 360\u2013364 (1979)","DOI":"10.1145\/800135.804429"},{"issue":"5","key":"28_CR19","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1016\/0020-0190(89)90205-6","volume":"30","author":"M. Vardi","year":"1989","unstructured":"Vardi, M.: A note on the reduction of two-way automata to one-way automata. Information Processing Letters\u00a030(5), 261\u2013264 (1989)","journal-title":"Information Processing Letters"}],"container-title":["Lecture Notes in Computer Science","Developments in Language Theory"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-22321-1_28","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,12]],"date-time":"2019-06-12T20:27:34Z","timestamp":1560371254000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-22321-1_28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642223204","9783642223211"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-22321-1_28","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}