Theory 066/Information & Computation /Formal methods
Verification Cost Tracks Diameter
Verification is budgeted by state count. The expensive quantity may be how far apart states can be.
The cost of formally verifying a system scales with the diameter of its state space rather than with the number of states, so a system with more states but a smaller diameter can be cheaper to verify.
01The evidence
Model checking performance varies enormously between systems with similar state counts, and the variation tracks the depth of the search rather than its breadth.
02The tension
Complexity estimates use state-space size, which is easy to estimate and badly predicts verification time. Projects are planned on the wrong metric.
03The mechanism
A model checker explores until it reaches a fixed point. The work is bounded by the longest shortest path between states, which is the diameter, times the cost per state.
That makes diameter the scaling variable, and predicts verification time should track it across designs with different state counts.
04What this is not
Count-based estimates predict time from size. This predicts it from diameter, which explains the variance.
05Predictions
- P1Verification time should scale with diameter.
- P2Larger systems with small diameter should verify faster.
- P3Diameter reduction should give predictable speedups.
06Refutation
Time tracking state count at controlled diameter would restore the size estimate.
07What it changes
It would change how verification projects are scoped.