Timeline for An operation on binary strings
Current License: CC BY-SA 3.0
4 events
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| May 23, 2013 at 15:13 | history | edited | user6976 | CC BY-SA 3.0 |
added 285 characters in body
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| May 23, 2013 at 12:32 | comment | added | user6976 | No, this rewriting system is not interesting because it is not terminating. Your monoid seems to be isomorphic to the direct product of the free monoid of countable rank and the 2-element group. Indeed, consider the set $S_1$ of all words starting with 1. It is a submonoid. Every element either is in $S_1$ or is equal to $0\cdot u$ where $u\in S_1$. This decomposition is unique and $(0\cdot u)\cdot (0\cdot v)=u\cdot v=1\cdot (u\cdot v)$. | |
| May 23, 2013 at 11:54 | comment | added | Hans-Peter Stricker | Do you suggest to see the monoid as a string rewriting system, with two rules for every string $\sigma$: $1 \rightarrow \sigma$, $0 \rightarrow \overline{\sigma}$? Do you treat this string rewriting system explicitly in your book? | |
| May 23, 2013 at 10:26 | history | answered | user6976 | CC BY-SA 3.0 |