Open Problem Garden

One-way functions exist ★★★★

Author(s):

Conjecture One-way functions exist.

Keywords: one way function

Posted by porton
updated October 12th, 2014

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Topology

Funcoid corresponding to reloid through lattice Gamma ★★

Author(s): Porton

Conjecture For every reloid $f$ and $\mathcal{X} \in \mathfrak{F} (\operatorname{Src} f)$ , $\mathcal{Y} \in \mathfrak{F} (\operatorname{Dst} f)$ :

$\mathcal{X} \mathrel{[(\mathsf{FCD}) f]} \mathcal{Y} \Leftrightarrow \forall F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f : \mathcal{X} \mathrel{[F]} \mathcal{Y}$

$\langle (\mathsf{FCD}) f \rangle \mathcal{X} = \bigcap_{F \in \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f} \langle F \rangle \mathcal{X}$

It's proved by me in this online article.

Keywords: funcoid corresponding to reloid

Posted by porton
updated September 26th, 2014

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funcoid corresponding to reloid

Topology

Restricting a reloid to lattice Gamma before converting it into a funcoid ★★

Author(s): Porton

Conjecture $(\mathsf{FCD}) f = \bigcap^{\mathsf{FCD}} (\Gamma (A ; B) \cap \operatorname{GR} f)$ for every reloid $f \in \mathsf{RLD} (A ; B)$ .

Keywords: funcoid corresponding to reloid; funcoids; reloids

Posted by porton
updated September 25th, 2014

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Inner reloid through the lattice Gamma ★★

Author(s): Porton

Conjecture $(\mathsf{RLD})_{\operatorname{in}} f = \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f$ for every funcoid $f$ .

Counter-example: $(\mathsf{RLD})_{\operatorname{in}} f \sqsubset \bigcap^{\mathsf{RLD}} \operatorname{up}^{\Gamma (\operatorname{Src} f ; \operatorname{Dst} f)} f$ for the funcoid $f = (=)|_\mathbb{R}$ is proved in this online article.