CounterScript

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++;}