Fragile words and Cayley type transducers
We address the problem of finding examples of non-bireversible transducers defining free groups, we show examples of transducers with sink accessible from every state which generate free groups, and, in general, we link this problem to the non-existence of certain words with interesting combinatoria...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2018-09-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://ijgt.ui.ac.ir/article_21976_d42f2c0b8452fc83cb7f694995548600.pdf |
| _version_ | 1818308443387199488 |
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| author | Daniele D'Angeli Emanuele Rodaro |
| author_facet | Daniele D'Angeli Emanuele Rodaro |
| author_sort | Daniele D'Angeli |
| collection | DOAJ |
| description | We address the problem of finding examples of non-bireversible transducers defining free groups, we show examples of transducers with sink accessible from every state which generate free groups, and, in general, we link this problem to the non-existence of certain words with interesting combinatorial and geometrical properties that we call fragile words. By using this notion, we exhibit a series of transducers constructed from Cayley graphs of finite groups whose defined semigroups are free, and thus having exponential growth. |
| first_indexed | 2024-12-13T07:14:21Z |
| format | Article |
| id | doaj.art-5c90be21f1f643f3ab6544d3bc972120 |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-12-13T07:14:21Z |
| publishDate | 2018-09-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-5c90be21f1f643f3ab6544d3bc9721202022-12-21T23:55:35ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692018-09-01739510910.22108/ijgt.2017.100358.139821976Fragile words and Cayley type transducersDaniele D'Angeli0Emanuele Rodaro1TUGrazDipartimento di Matematica, Politecnico di Milano, Milano, ItaliaWe address the problem of finding examples of non-bireversible transducers defining free groups, we show examples of transducers with sink accessible from every state which generate free groups, and, in general, we link this problem to the non-existence of certain words with interesting combinatorial and geometrical properties that we call fragile words. By using this notion, we exhibit a series of transducers constructed from Cayley graphs of finite groups whose defined semigroups are free, and thus having exponential growth.http://ijgt.ui.ac.ir/article_21976_d42f2c0b8452fc83cb7f694995548600.pdfFragile wordsCayley type transducersautomaton groups |
| spellingShingle | Daniele D'Angeli Emanuele Rodaro Fragile words and Cayley type transducers International Journal of Group Theory Fragile words Cayley type transducers automaton groups |
| title | Fragile words and Cayley type transducers |
| title_full | Fragile words and Cayley type transducers |
| title_fullStr | Fragile words and Cayley type transducers |
| title_full_unstemmed | Fragile words and Cayley type transducers |
| title_short | Fragile words and Cayley type transducers |
| title_sort | fragile words and cayley type transducers |
| topic | Fragile words Cayley type transducers automaton groups |
| url | http://ijgt.ui.ac.ir/article_21976_d42f2c0b8452fc83cb7f694995548600.pdf |
| work_keys_str_mv | AT danieled039angeli fragilewordsandcayleytypetransducers AT emanuelerodaro fragilewordsandcayleytypetransducers |