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 |
| Published: |
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 |
| Summary: | 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. |
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| ISSN: | 2251-7650 2251-7669 |