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  • Galicia (Spain)
  • 18:17 (UTC +01:00)

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Achievement: Pull Sharkx3Achievement: Pair Extraordinairex3Achievement: YOLOAchievement: QuickdrawAchievement: Arctic Code Vault Contributor

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Achievement: Pull Sharkx3Achievement: Pair Extraordinairex3Achievement: YOLOAchievement: QuickdrawAchievement: Arctic Code Vault Contributor

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toniferr/README.md

Hi, I'm Toni 👋

Cheat

1 · Logic. One gate is enough for every Boolean function $f:\lbrace 0,1\rbrace^n\to\lbrace 0,1\rbrace$:

$$\mathrm{NAND}(x,y)=1-xy,\qquad \neg x=\mathrm{NAND}(x,x),\qquad x\wedge y=\neg\,\mathrm{NAND}(x,y)$$

2 · Automata. Finite memory makes a finite automaton, $M=(Q,\Sigma,\delta,q_0,F)$ with $\delta:Q\times\Sigma\to Q$. It recognises exactly the regular languages, and it cannot count: $\lbrace a^nb^n\rbrace$ is out of reach. Climbing Chomsky's hierarchy adds power:

$$\mathsf{REG}\subsetneq\mathsf{CFL}\subsetneq\mathsf{CSL}\subsetneq\mathsf{RE}$$

3 · Computation. An unbounded tape gives Turing's machine, $\delta:Q\times\Gamma\to Q\times\Gamma\times\lbrace L,R\rbrace$, and the first impossible problem: no program decides, for every program, whether it halts.

$$\nexists\,H\ \ \forall\,M,w:\quad H(\langle M\rangle,w)=\mathbf{1}[\,M \text{ halts on } w\,]$$

4 · Information. Learning is compression: every LLM minimizes the cross-entropy between the data and its model.

$$H(p,q)=H(p)+D_{\mathrm{KL}}(p\,\|\,q)\ \ge\ H(p)=-\sum_x p(x)\log_2 p(x)$$

5 · Quantum. Swap the 1-norm of probabilities for the 2-norm of complex amplitudes, and a bit becomes a qubit:

$$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle,\qquad |\alpha|^2+|\beta|^2=1$$

🔭 Currently

  • Expanding the GitOps course module by module (Kustomize, Helm, multi-environment, secrets…).
  • Writing more chapters and demos for the math sites.
  • Exploring AI agents for software engineering, with Claude Code as a daily companion.

Built with plain Markdown. Say hi on LinkedIn or visit my site, in Spanish, English and Galician.

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