bio | website | |
---|---|---|
location | Germany | |
age | 49 | |
visits | member for | 5 years, 1 month |
seen | 2 hours ago | |
stats | profile views | 3,382 |
My interests:
abstract structures
(e.g. graphs, groups, polytopes, spaces, ...)
^{in the course of this}category theory
model theory
presentations and representations
(e.g. of abstract structures by or inside other abstract structures)
^{next to this}philosophy
(esp. of mathematics, science, and mind)
^{especially concerned with}atomism
(i.e. reductionistic or other theories referring to some kind of "atoms")- ancient atomism
- set theories (with and without urelements)
- logical atomism
- particle physics
- neuroscience
^{and}
their refutations
Jan 17 |
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Contexts and notations for composing asymmetric simplices
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Jan 17 |
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Contexts and notations for composing asymmetric simplices
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Contexts and notations for composing asymmetric simplices
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Jan 17 |
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Contexts and notations for composing asymmetric simplices
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Jan 17 |
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Contexts and notations for composing asymmetric simplices
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Contexts and notations for composing asymmetric simplices
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Contexts and notations for composing asymmetric simplices
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Contexts and notations for composing asymmetric simplices
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Contexts and notations for composing asymmetric simplices
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Jan 15 |
asked | Contexts and notations for composing asymmetric simplices |
Dec 22 |
awarded | Nice Answer |
Dec 18 |
awarded | Yearling |
Oct 14 |
awarded | Self-Learner |
Oct 14 |
answered | Supervenience in mathematics |
Sep 29 |
comment |
Rationale behind an requirement on Turing machines
Notice further, that $b$ can not only be read but also be written. |
Sep 29 |
comment |
Rationale behind an requirement on Turing machines
Re-reading your answer I am still not satisfied: In Hopcroft/Ullman's definition of a Turing machine as a 7-tupel the blank symbol $b$ is distinguished (among the tape symbols), but there seems to be no requirement on a Turing machine involving $b$. Especially the transition function $\delta$ can be defined on the whole tape alphabet (including $b$). The same holds - by the way - for the initial state $q_0$. |
Sep 27 |
awarded | Nice Answer |
Sep 24 |
awarded | Autobiographer |
Sep 3 |
awarded | Peer Pressure |
Aug 30 |
comment |
When are two algorithms essentially the same?
I didn't want to ask for a single equivalence, sorry if it sounded like this. I am looking for any (sensible) equivalence. One came to my mind only today: $T$ is equivalent to $T'$ when they have the same symbols and blank symbol, compute the same function, have the same number of internal states and there is a bijection $f$ between the states that preserves - among other things - starting and halting, next state $S(f(x),s)$ is $f(S(x),s)$, and so on. One may find this trivial, but it is a sensible equivalence, isn't? And there may be others. |