{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T11:20:48Z","timestamp":1778498448372,"version":"3.51.4"},"publisher-location":"Cham","reference-count":42,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783031661587","type":"print"},{"value":"9783031661594","type":"electronic"}],"license":[{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,1]],"date-time":"2024-01-01T00:00:00Z","timestamp":1704067200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024]]},"DOI":"10.1007\/978-3-031-66159-4_5","type":"book-chapter","created":{"date-parts":[[2024,7,26]],"date-time":"2024-07-26T09:01:34Z","timestamp":1721984494000},"page":"51-67","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Logic and\u00a0Languages of\u00a0Higher-Dimensional Automata"],"prefix":"10.1007","author":[{"given":"Amazigh","family":"Amrane","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hugo","family":"Bazille","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Uli","family":"Fahrenberg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marie","family":"Fortin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,27]]},"reference":[{"key":"5_CR1","doi-asserted-by":"crossref","unstructured":"Amrane, A., Bazille, H., Clement, E., Fahrenberg, U.: Languages of higher-dimensional timed automata. In: PETRI NETS, 2024 (2024). Accepted. https:\/\/arxiv.org\/abs\/2401.17444","DOI":"10.1007\/978-3-031-61433-0_10"},{"key":"5_CR2","doi-asserted-by":"publisher","unstructured":"Amrane, A., Bazille, H., Fahrenberg, U., Ziemia\u0144ski, K.: Closure and decision properties for higher-dimensional automata. In: \u00c1brah\u00e1m, E., Dubslaff, C., Tarifa, S.L.T. (eds.) Theoretical Aspects of Computing \u2013 ICTAC 2023. ICTAC 2023. LNCS, vol. 14446, pp. 295\u2013312. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-47963-2_18","DOI":"10.1007\/978-3-031-47963-2_18"},{"key":"5_CR3","doi-asserted-by":"crossref","unstructured":"Bedon, N.: Logic and branching automata. Log. Methods Comput. Sci. 11(4) (2015)","DOI":"10.2168\/LMCS-11(4:2)2015"},{"key":"5_CR4","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1016\/0022-4049(81)90018-9","volume":"21","author":"R Brown","year":"1981","unstructured":"Brown, R., Higgins, P.J.: On the algebra of cubes. J. Pure Appl. Alg. 21, 233\u2013260 (1981)","journal-title":"J. Pure Appl. Alg."},{"key":"5_CR5","doi-asserted-by":"crossref","unstructured":"Richard B\u00fcchi, J.: Weak second order arithmetic and finite automata. Zeitschrift f\u00fcr Mathematische Logik und Grundlagen der Mathematik 6, 66\u201392 (1960)","DOI":"10.1002\/malq.19600060105"},{"key":"5_CR6","unstructured":"Richard B\u00fcchi, J.: On a decision method in restricted second order arithmetic. In: Nagel, E., Suppes, P., Tarski, A. (eds.), LMPS\u201960, pp. 1\u201311. Stanford University Press (1962)"},{"key":"5_CR7","doi-asserted-by":"crossref","unstructured":"Courcelle, B.: The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Inf. Comput. 85(1), 12\u201375 (1990)","DOI":"10.1016\/0890-5401(90)90043-H"},{"issue":"5","key":"5_CR8","doi-asserted-by":"publisher","first-page":"406","DOI":"10.1016\/S0022-0000(70)80041-1","volume":"4","author":"J Doner","year":"1970","unstructured":"Doner, J.: Tree acceptors and some of their applications. J. Comput. Syst. Sci. 4(5), 406\u2013451 (1970)","journal-title":"J. Comput. Syst. Sci."},{"key":"5_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/978-3-662-47666-6_14","volume-title":"Automata, Languages, and Programming","author":"J Dubut","year":"2015","unstructured":"Dubut, J., Goubault, \u00c9., Goubault-Larrecq, J.: Natural homology. In: Halld\u00f3rsson, M.M., Iwama, K., Kobayashi, N., Speckmann, B. (eds.) ICALP 2015. LNCS, vol. 9135, pp. 171\u2013183. Springer, Heidelberg (2015). https:\/\/doi.org\/10.1007\/978-3-662-47666-6_14"},{"key":"5_CR10","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1090\/S0002-9947-1961-0139530-9","volume":"98","author":"CC Elgot","year":"1961","unstructured":"Elgot, C.C.: Decision problems of finite automata design and related arithmetics. Trans. Am. Math. Soc. 98, 21\u201352 (1961)","journal-title":"Trans. Am. Math. Soc."},{"key":"5_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/978-3-540-31982-5_12","volume-title":"Foundations of Software Science and Computational Structures","author":"U Fahrenberg","year":"2005","unstructured":"Fahrenberg, U.: A category of higher-dimensional automata. In: Sassone, V. (ed.) FoSSaCS 2005. LNCS, vol. 3441, pp. 187\u2013201. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/978-3-540-31982-5_12"},{"key":"5_CR12","unstructured":"Fahrenberg, U.: Higher-dimensional timed and hybrid automata. Leibniz Trans. Embed. Syst. 8(2), 03:1\u201303:16 (2022)"},{"issue":"5","key":"5_CR13","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1017\/S0960129521000293","volume":"31","author":"U Fahrenberg","year":"2021","unstructured":"Fahrenberg, U., Johansen, C., Struth, G., Ziemia\u0144ski, K.: Languages of higher-dimensional automata. Math. Struct. Comput. Sci. 31(5), 575\u2013613 (2021)","journal-title":"Math. Struct. Comput. Sci."},{"key":"5_CR14","unstructured":"Fahrenberg, U., Johansen, C., Struth, G., Ziemia\u0144ski, K.: A Kleene theorem for higher-dimensional automata. In: Klin, B., Lasota, S., Muscholl, A. (eds.), CONCUR, volume 243 of Leibniz International Proceedings in Informatics, pp. 29:1\u201329:18. Schloss Dagstuhl - Leibniz-Zentrum f\u00fcr Informatik (2022)"},{"key":"5_CR15","doi-asserted-by":"crossref","unstructured":"Fahrenberg, U., Johansen, C., Struth, G., Ziemia\u0144ski, K.: Posets with interfaces as a model for concurrency. Inf. Comput. 285(B), 104914 (2022)","DOI":"10.1016\/j.ic.2022.104914"},{"issue":"2","key":"5_CR16","first-page":"93","volume":"2","author":"U Fahrenberg","year":"2007","unstructured":"Fahrenberg, U., Raussen, M.: Reparametrizations of continuous paths. J. Homotopy Relat. Struct. 2(2), 93\u2013117 (2007)","journal-title":"J. Homotopy Relat. Struct."},{"key":"5_CR17","doi-asserted-by":"publisher","unstructured":"Fahrenberg, U., Ziemia\u0144ski, K.: A myhill-nerode theorem for higher-dimensional automata. In: Gomes, L., Lorenz, R. (eds.) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2023. LNCS, vol. 13929, pp. 167\u2013188. Springer, Cham (2023). https:\/\/doi.org\/10.1007\/978-3-031-33620-1_9","DOI":"10.1007\/978-3-031-33620-1_9"},{"key":"5_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1007\/978-3-642-28869-2_14","volume-title":"Programming Languages and Systems","author":"L Fajstrup","year":"2012","unstructured":"Fajstrup, L., Goubault, \u00c9., Haucourt, E., Mimram, S., Raussen, M.: Trace spaces: an efficient new technique for state-space reduction. In: Seidl, H. (ed.) ESOP 2012. LNCS, vol. 7211, pp. 274\u2013294. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-28869-2_14"},{"key":"5_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-15398-8","volume-title":"Directed Algebraic Topology and Concurrency","author":"L Fajstrup","year":"2016","unstructured":"Fajstrup, L., Goubault, E., Haucourt, E., Mimram, S., Raussen, M.: Directed Algebraic Topology and Concurrency. Springer, Cham (2016). https:\/\/doi.org\/10.1007\/978-3-319-15398-8"},{"key":"5_CR20","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1023\/B:APCS.0000013812.75342.de","volume":"12","author":"L Fajstrup","year":"2004","unstructured":"Fajstrup, L., Raussen, M., Goubault, E., Haucourt, E.: Components of the fundamental category. Appl. Categ. Struct. 12, 81\u2013108 (2004)","journal-title":"Appl. Categ. Struct."},{"key":"5_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/978-3-642-02424-5_7","volume-title":"Applications and Theory of Petri Nets","author":"J Fanchon","year":"2009","unstructured":"Fanchon, J., Morin, R.: Pomset languages of finite step transition systems. In: Franceschinis, G., Wolf, K. (eds.) PETRI NETS 2009. LNCS, vol. 5606, pp. 83\u2013102. Springer, Heidelberg (2009). https:\/\/doi.org\/10.1007\/978-3-642-02424-5_7"},{"key":"5_CR22","doi-asserted-by":"crossref","unstructured":"Fishburn, P.C.: Interval Orders and Interval Graphs: A Study of Partially Ordered Sets. Wiley, Hoboken (1985)","DOI":"10.1016\/0012-365X(85)90042-1"},{"issue":"6","key":"5_CR23","doi-asserted-by":"publisher","first-page":"920","DOI":"10.1016\/j.ic.2006.01.005","volume":"204","author":"B Genest","year":"2006","unstructured":"Genest, B., Kuske, D., Muscholl, A.: A Kleene theorem and model checking algorithms for existentially bounded communicating automata. Inf. Comput. 204(6), 920\u2013956 (2006)","journal-title":"Inf. Comput."},{"issue":"2","key":"5_CR24","doi-asserted-by":"publisher","first-page":"427","DOI":"10.3233\/FI-1981-4210","volume":"4","author":"J Grabowski","year":"1981","unstructured":"Grabowski, J.: On partial languages. Fundam. Inform. 4(2), 427 (1981)","journal-title":"Fundam. Inform."},{"issue":"8","key":"5_CR25","first-page":"185","volume":"11","author":"M Grandis","year":"2003","unstructured":"Grandis, M., Mauri, L.: Cubical sets and their site. Theory Appl. Categ. 11(8), 185\u2013211 (2003)","journal-title":"Theory Appl. Categ."},{"issue":"1\u20132","key":"5_CR26","doi-asserted-by":"publisher","first-page":"31","DOI":"10.3233\/FI-2019-1838","volume":"169","author":"R Janicki","year":"2019","unstructured":"Janicki, R., Koutny, M.: Operational semantics, interval orders and sequences of antichains. Fundam. Inform. 169(1\u20132), 31\u201355 (2019)","journal-title":"Fundam. Inform."},{"key":"5_CR27","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.tcs.2016.04.018","volume":"631","author":"T Kahl","year":"2016","unstructured":"Kahl, T.: Topological abstraction of higher-dimensional automata. Theor. Comput. Sci. 631, 97\u2013117 (2016)","journal-title":"Theor. Comput. Sci."},{"key":"5_CR28","doi-asserted-by":"crossref","unstructured":"Kahl, T.: Weak equivalence of higher-dimensional automata. Discret. Math. Theor. Comput. Sci. 23(1) (2021)","DOI":"10.46298\/dmtcs.5884"},{"key":"5_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1007\/3-540-45022-X_55","volume-title":"Automata, Languages and Programming","author":"D Kuske","year":"2000","unstructured":"Kuske, D.: Infinite series-parallel posets: logic and languages. In: Montanari, U., Rolim, J.D.P., Welzl, E. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 648\u2013662. Springer, Heidelberg (2000). https:\/\/doi.org\/10.1007\/3-540-45022-X_55"},{"issue":"2","key":"5_CR30","first-page":"187","volume":"7","author":"D Kuske","year":"2002","unstructured":"Kuske, D., Morin, R.: Pomsets for local trace languages. J. Autom. Lang. Comb. 7(2), 187\u2013224 (2002)","journal-title":"J. Autom. Lang. Comb."},{"key":"5_CR31","doi-asserted-by":"crossref","unstructured":"Pratt, V.R.: Modeling concurrency with geometry. In: POPL, pp. 311\u2013322. ACM Press, New York City (1991)","DOI":"10.1145\/99583.99625"},{"key":"5_CR32","first-page":"1","volume":"141","author":"MO Rabin","year":"1969","unstructured":"Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Am. Math. Soc. 141, 1\u201335 (1969)","journal-title":"Trans. Am. Math. Soc."},{"key":"5_CR33","doi-asserted-by":"crossref","unstructured":"Serre, J.-P.: Homologie singuli\u00e8re des espaces fibr\u00e9s. PhD thesis, Ecole Normale Sup\u00e9rieure, Paris, France (1951)","DOI":"10.2307\/1969485"},{"issue":"1","key":"5_CR34","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/BF01691346","volume":"2","author":"JW Thatcher","year":"1968","unstructured":"Thatcher, J.W., Wright, J.B.: Generalized finite automata theory with an application to a decision problem of second-order logic. Math. Syst. Theory 2(1), 57\u201381 (1968)","journal-title":"Math. Syst. Theory"},{"key":"5_CR35","unstructured":"Thomas, W.: On logical definability of trace languages. In: Algebraic and Syntactic Methods in Computer Science (ASMICS), Report TUM-I9002, Technical University of Munich, pp. 172\u2013182 (1990)"},{"key":"5_CR36","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/978-3-642-59126-6_7","volume-title":"Handbook of Formal Languages","author":"W Thomas","year":"1997","unstructured":"Thomas, W.: Languages, automata, and logic. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, pp. 389\u2013455. Springer, Heidelberg (1997). https:\/\/doi.org\/10.1007\/978-3-642-59126-6_7"},{"key":"#cr-split#-5_CR37.1","unstructured":"Trakhtenbrot, B.A.: Finite automata and monadic second order logic. Sib. Math. J. 3, 103-131 (1962). In Russian"},{"key":"#cr-split#-5_CR37.2","unstructured":"English translation in Amer. Math. Soc. Transl. 59(1966), 23-55"},{"key":"5_CR38","unstructured":"van Glabbeek, R.J.: Bisimulations for higher dimensional automata. Email message, June 1991. http:\/\/theory.stanford.edu\/~rvg\/hda"},{"key":"5_CR39","first-page":"441","volume":"17","author":"N Wiener","year":"1914","unstructured":"Wiener, N.: A contribution to the theory of relative position. Proc. Camb. Philos. Soc. 17, 441\u2013449 (1914)","journal-title":"Proc. Camb. Philos. Soc."},{"issue":"2","key":"5_CR40","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1051\/ita\/1987210200991","volume":"21","author":"W Zielonka","year":"1987","unstructured":"Zielonka, W.: Notes on finite asynchronous automata. RAIRO - Informatique Th\u00e9orique et Applications 21(2), 99\u2013135 (1987)","journal-title":"RAIRO - Informatique Th\u00e9orique et Applications"},{"issue":"3","key":"5_CR41","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s10485-018-9551-1","volume":"27","author":"K Ziemia\u0144ski","year":"2019","unstructured":"Ziemia\u0144ski, K.: Stable components of directed spaces. Appl. Categ. Struct. 27(3), 217\u2013244 (2019)","journal-title":"Appl. Categ. Struct."}],"container-title":["Lecture Notes in Computer Science","Developments in Language Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-66159-4_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,19]],"date-time":"2024-10-19T08:02:43Z","timestamp":1729324963000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-66159-4_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024]]},"ISBN":["9783031661587","9783031661594"],"references-count":42,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-66159-4_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024]]},"assertion":[{"value":"27 July 2024","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"DLT","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Developments in Language Theory","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"G\u00f6ttingen","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 August 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 August 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"28","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"dlt2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}