04 / Work in progress
What must survive
when work is split?
From the no-three-in-line problem toward a research programme on task decomposition and agent cooperation.
From configurations to cooperation
The no-three-in-line problem asks for grid points with no collinear triple. It also offers small, exact settings in which to study what a participant can observe, which actions are possible and what a team needs to coordinate.
The foundations are established: distributed constraint optimization, sufficient statistics and communication complexity. Our proposed contribution is a checked implementation and measurements of when focused contexts preserve verified performance, including the total cost of preparing, combining and checking the work. This programme remains experimental.
Split the task. Preserve the dependencies.
We want to divide a task among research agents and recombine their work while preserving the required answer and its checkable justification. “Without loss” is relative to a declared task; it does not promise every future use of the original context.
Separate optimum answers can omit the dependencies needed for a joint optimum. A proposed interface keeps conditional answers over shared decisions, together with witnesses or retrievable evidence. Exact mathematical sufficiency and agents’ ability to use that interface are separate questions.
Context, for whom and for what?
The useful “meaning” of a piece of context depends on the recipient’s current function and the decision it must support. A detail irrelevant to one question can be necessary for another.
The next empirical question is whether contexts chosen by function preserve verified performance, and whether any saving survives the work of preparing, merging, retrieving and checking them. No efficiency gain is established here.
A checked starting point
Paper 80 separates the cost of a first insertion from the temporary loss needed to reach a maximum configuration, and gives a finite classification of repair barriers. It supplies a testbed for precise questions about cooperation.
Transferring these results to moving robots, physical observers or AI teamwork needs its own model and verification. The programme is a proposal for further work.