An inconclusive proof is not one problem. It may be limited by temporal depth, state width, arithmetic complexity, memories, symmetry, or a property that asks the engine to rediscover the same invariant repeatedly. Convergence work begins by identifying which kind of difficulty is present.
Read the obligation before tuning the engine
Reduce the property to its essential cone of influence. Remove unrelated outputs and testbench logic from the model, but do not cut state that carries the behavior being proven. Check that the clock, reset, and assumptions create the intended reachable state space.
A bounded result that advances steadily with depth suggests a different problem from a proof that stalls immediately. Deep pipelines and long response windows create temporal depth. Wide counters, memories, and independent clients create state. Multipliers and variable indexing can create difficult combinational reasoning.
Apply structure, not arbitrary limits
- Decompose the target: split independent obligations and design modes.
- Add helper invariants: state facts that are true and repeatedly needed by the main proof.
- Abstract irrelevant data: preserve control relationships while reducing value width or memory content.
- Cut at contracts: assume a reviewed interface guarantee and prove that guarantee separately.
- Exploit symmetry: avoid proving equivalent clients as unrelated state when a sound reduction exists.
Every abstraction needs an argument. A smaller counter may be unsound if wraparound matters. A nondeterministic memory model may be too permissive if address consistency matters. Document what was removed, what behavior remains, and which separate check justifies the replacement.
Use lemmas as design knowledge
Helper assertions are not merely tool hints. They capture invariants such as one-hot state, occupancy bounds, ownership, ordering, and conservation. Prove them independently, give them meaningful names, and keep them with the design contract. An unreviewed web of circular assumptions is not a proof decomposition.
Case splitting can help when a design has natural modes: empty versus non-empty, privileged versus unprivileged, reset versus operational, or one arbitration winner at a time. Split on stable architectural distinctions rather than arbitrary internal bits.
Make proofs reproducible
Pin source, constraints, tool version, engine strategy, and resource limits in regression configuration. Run from a clean state. Record whether a result is bounded or unbounded and preserve counterexamples. Tool heuristics can change; the engineering argument should not depend on an undocumented interactive session.
Convergence is achieved when the model, property, and decomposition expose the design's real invariants.
Stop when the cost of further proof exceeds the risk reduction. An honest bounded result with documented depth and complementary simulation may be more useful than an over-constrained unbounded result. The sign-off decision belongs to the verification plan, not to the solver alone.
Primary references
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