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07 / Records & prediction
Keep the distinctions
that the future needs.
Inspect the supplied examples, then enter your own finite deterministic update and find the coarsest partition that predicts every future displayed output.
Exact finite-state calculation; one supplied autonomous updateA present record can hide a future distinction
Refine the record partition until every class has one well-defined successor class. Stable agreement concerns all future outputs of the supplied update.
Inspect the hidden distinction
Begin with classes that retain only the present binary output. Each refinement separates states whose successors fall into different current classes. Stop when every class has one well-defined successor class.
The default example below is complete. Interactive controls become available when the script loads.
Current partition
{A, B} | {C, D}
Round 0: two present-record classes. A and B both display 0, but their next outputs are 1 and 0. The stable partition is {A} | {B} | {C, D}: three predictive states, requiring two fixed-length bits in total.
| State | Output R(x) | Successor F(x) | Next output | Class now | Stable class |
|---|---|---|---|---|---|
| A | 0 | C | 1 | 1 | 1 |
| B | 0 | A | 0 | 1 | 2 |
| C | 1 | C | 1 | 2 | 3 |
| D | 1 | D | 1 | 2 | 3 |
| Initial state | t=0 | t=1 | t=2 | t=3 | t=4 | t=5 | t=6 | t=7 |
|---|---|---|---|---|---|---|---|---|
| A | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| B | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
| C | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| D | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Complete refinement history
| Round | Classes | Number of classes |
|---|---|---|
| 0 | {A, B} | {C, D} | 2 |
| 1 | {A} | {B} | {C, D} | 3 |
Exports are calculated examples, not experimental data. No information is uploaded.
Test your own finite model
Start with the partition defined by the displayed output R. Split each class according to the pair (current class, successor class) until it stops changing.
Analyze a supplied transition table
Use 2–64 uniquely named states. Every successor must appear in the state column. Output labels may be any short letters or numbers; names can also contain underscores or hyphens. The calculation stays in this browser.
Run the table to inspect its predictive classes.
What the result establishes
At stability, R*∘F=T∘R* defines an autonomous update on predictive classes. States with identical future output sequences remain in the same class.
The displayed bit count is ⌈log₂(number of classes)⌉ for a fixed-length label. It is not a thermodynamic entropy, energy requirement or average code length. Stochastic updates and external interventions require a different equivalence test and are outside this tool.