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My motivation in defining BLC was to have the simplest measure of the complexity of things. That includes binary strings, natural numbers, tuples, lists, sets,

by tromp 3y ago

My motivation in defining BLC was to have the simplest measure of the complexity of things. That includes binary strings, natural numbers, tuples, lists, sets, and functions of those, as well as languages (according to their interpreter) and formal systems (according to their theorem enumerator) [1]. [1] https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d861 https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d8...

spencerflem 3y ago
Oh, is BLC yours? I saw the link posted earlier in the thread, its beautiful. Still trying to understand it but yeah, there's definitely a mathematical purity to it that some random ASM language doesn't have.
Vecr 3y ago
How does it compare to BrainPhoque, the language used in Learning Universal Predictors (Hutter 2024) to approximate normalized Solomonoff induction?
- tromp 3y ago
  BP is like a slightly messier BrainFuck. Its alphabet size of 17 is rather odd. Its spec (Section E.2 of [1]) says > programs containing unbalanced parentheses are made valid, in particular by skipping any additional ]. But that still leaves programs invalid programs like "[[[[". From a theoretical viewpoint, its biggest flaw is the lack of an input tape, which makes it a non-optimal description method in the sense of [2]. In particular, while BLC programs are at most a constant larger than BP ones, the reverse is not true. The version of BF that I interpret in [3] is still optimally universal, because its program delimiting fist unbalanced ] is followed by its binary input. [1] https://arxiv.org/html/2401.14953v1 https://arxiv.org/html/2401.14953v1 [2] https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d861#universality https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d8... [3] https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d861#brainfuck https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d8...

by tromp 3y ago

spencerflem 3y ago

Oh, is BLC yours? I saw the link posted earlier in the thread, its beautiful. Still trying to understand it but yeah, there's definitely a mathematical purity to it that some random ASM language doesn't have.

Vecr 3y ago

How does it compare to BrainPhoque, the language used in Learning Universal Predictors (Hutter 2024) to approximate normalized Solomonoff induction?

tromp 3y ago
BP is like a slightly messier BrainFuck. Its alphabet size of 17 is rather odd. Its spec (Section E.2 of [1]) says > programs containing unbalanced parentheses are made valid, in particular by skipping any additional ]. But that still leaves programs invalid programs like "[[[[". From a theoretical viewpoint, its biggest flaw is the lack of an input tape, which makes it a non-optimal description method in the sense of [2]. In particular, while BLC programs are at most a constant larger than BP ones, the reverse is not true. The version of BF that I interpret in [3] is still optimally universal, because its program delimiting fist unbalanced ] is followed by its binary input. [1] https://arxiv.org/html/2401.14953v1 https://arxiv.org/html/2401.14953v1 [2] https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d861#universality https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d8... [3] https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d861#brainfuck https://gist.github.com/tromp/86b3184f852f65bfb814e3ab0987d8...