CounterScript: Difference between revisions
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m →BBCS: spacing |
Added more lower bounds. |
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|- | |- | ||
|16 | |16 | ||
|≥ | |≥ 1,554 | ||
|<code><nowiki>A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++;} while C {C--; B++; B++;}}</nowiki></code> | |<code><nowiki>A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++;}}</nowiki></code> | ||
|- | |||
|17 | |||
|≥ 9,330 | |||
|<code><nowiki>A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++;}}</nowiki></code> | |||
|- | |||
|18 | |||
|≥ 66,429 | |||
|<code><nowiki>A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++; B++;}}</nowiki></code> | |||
|- | |||
|19 | |||
|≥ 597,870 | |||
|<code><nowiki>A++; A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++; B++;}}</nowiki></code> | |||
|- | |||
|20 | |||
|≥ 4^1365 | |||
|<code><nowiki>A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}</nowiki></code> | |||
|- | |||
|21 | |||
|≥ 4^4^1365 | |||
|<code><nowiki>A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}</nowiki></code> | |||
|- | |||
|22 | |||
|≥ 4^4^4^1365 | |||
|<code><nowiki>A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}</nowiki></code> | |||
|- | |||
|23 | |||
|≥ 4^4^4^4^1365 | |||
|<code><nowiki>A++; A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}</nowiki></code> | |||
|- | |||
|24 | |||
|≥ 4^4^4^4^4^1365 | |||
|<code><nowiki>A++; A++; A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}</nowiki></code> | |||
|- | |||
|25 | |||
|≥ 2^^2^15 | |||
|<code><nowiki>A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; while D {D--; E++; E++;} while E {E--; D++;}} while D {D--; C++;}} while C {C--; B++;}}</nowiki></code> | |||
|- | |||
|26 | |||
|≥ 2^^2^^2^15 | |||
|<code><nowiki>A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; while D {D--; E++; E++;} while E {E--; D++;}} while D {D--; C++;}} while C {C--; B++;}}</nowiki></code> | |||
|- | |||
|65 | |||
|> Graham's number | |||
| | |||
|} | |} | ||
Revision as of 11:21, 27 May 2026
CounterScript is a minimal counter-based programming language designed for Busy Beaver–style program enumeration and analysis.
It features a very small instruction set operating over an unbounded set of nonnegative integer variables (counters).
BBCS(n) is the Busy Beaver function for CounterScript programs.
Definition
A CounterScript program consists of a finite sequence of instructions drawn from three primitives:
- Increment a counter
- Conditional decrement
- While loop
All counters are initialized to 0 and can grow without bound.
The model is closely related to Minsky register machines, Fractran and Brainfuck, and is therefore Turing-complete.
Instructions
Instructions are executed one by one from left to right.
| Name | Command | Definition |
|---|---|---|
| Increment | A++
|
Increment counter A by 1 |
| Decrement | A--
|
Decrement counter A by 1 if A > 0 |
| While loop | while A {...}
|
Executes the loop body while x > 0
|
BBCS
The Busy Beaver function for CounterScript, denoted BBCS(n), returns the largest score a CounterScript program of length n can have when halting.
The score of a program is the maximum value of its counters.
The length of a CounterScript program is defined as the total number of instructions.
By example, A++; B++; while A {A--; C++; C++;} has length 6 and its score is 2.
| n | BBCS(n) | Champion |
|---|---|---|
| 1 | 1 | A++;
|
| 2 | 2 | A++; A++;
|
| 3 | 3 | A++; A++; A++;
|
| 4 | 4 | A++; A++; A++; A++;
|
| 5 | 5 | A++; A++; A++; A++; A++;
|
| 6 | 6 | A++; A++; A++; A++; A++; A++;
|
| 7 | 7 | A++; A++; A++; A++; A++; A++; A++;
|
| 8 | 9 | A++; A++; A++; while A {A--; B++; B++; B++;}
|
| 9 | 12 | A++; A++; A++; A++; while A {A--; B++; B++; B++;}
|
| 10 | 16 | A++; A++; A++; A++; while A {A--; B++; B++; B++; B++;}
|
| 11 | ≥ 20 | A++; A++; A++; A++; A++; while A {A--; B++; B++; B++; B++;}
|
| 12 | ≥ 25 | A++; A++; A++; A++; A++; while A {A--; B++; B++; B++; B++; B++;}
|
| 13 | ≥ 30 | A++; A++; A++; A++; A++; A++; while A {A--; B++; B++; B++; B++; B++;}
|
| 14 | ≥ 84 | A++; A++; A++; while A {A--; B++; while B {B--; C++; C++;} while C {C--; B++; B++;}}
|
| 15 | ≥ 340 | A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++;} while C {C--; B++; B++;}}
|
| 16 | ≥ 1,554 | A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++;}}
|
| 17 | ≥ 9,330 | A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++;}}
|
| 18 | ≥ 66,429 | A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++; B++;}}
|
| 19 | ≥ 597,870 | A++; A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; C++; C++;} while C {C--; B++; B++; B++;}}
|
| 20 | ≥ 4^1365 | A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}
|
| 21 | ≥ 4^4^1365 | A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}
|
| 22 | ≥ 4^4^4^1365 | A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}
|
| 23 | ≥ 4^4^4^4^1365 | A++; A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}
|
| 24 | ≥ 4^4^4^4^4^1365 | A++; A++; A++; A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; D++;} while D {D--; C++; C++;}} while C {C--; B++;}}
|
| 25 | ≥ 2^^2^15 | A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; while D {D--; E++; E++;} while E {E--; D++;}} while D {D--; C++;}} while C {C--; B++;}}
|
| 26 | ≥ 2^^2^^2^15 | A++; A++; A++; A++; while A {A--; B++; while B {B--; C++; while C {C--; D++; while D {D--; E++; E++;} while E {E--; D++;}} while D {D--; C++;}} while C {C--; B++;}}
|
| 65 | > Graham's number |
Cryptids
TODO