Proof Engines & Convergence

Section goal

How formal proof engines behave in practice, why properties fail to converge, and the tactical workflow for closing proofs with sound abstractions and targeted constraints.

How to study this section

1. Start with each topic hub and restate the requirement intent in your own words.

2. Use reports and debug pages to classify first divergence accurately.

3. Practice worked examples and interview drills with fixed run metadata.

4. Close with checklist and residual-risk framing before signoff claims.

Topics

1. model-checking-basics/ - Model Checking Foundations in Real Flows

2. bounded-vs-unbounded-proofs/ - BMC vs Unbounded Proof Strategies

3. proof-convergence-tactics/ - Convergence Tactics for Hard Properties

4. state-space-reduction/ - State-Space Reduction and Safe Abstraction

Related topics

• Formal Verification course hub

Formal deep dive

Convergence requires engine strategy, invariant quality, and model realism to move together with measurable progress.

Concept diagram

CONVERGENCE DECISION FLOW

property bucket -> engine strategy -> helper invariants -> convergence audit -> closure

Metric graph

CONVERGENCE BURNDOWN

open hard properties    ███████
inconclusive aging      █████
closed with audit       ████████

Metrics and artifacts to collect

• engine effectiveness by property class

• induction and helper-lemma success ratio

• stalled-property aging dashboard

• runtime vs closure-quality movement

Mini case study

A stalled set closed only after case-splitting by mode and auditing fairness assumptions for realism.

Debug branches

• Bucket properties by structure and intent before tuning.

• Inspect proof core stability, not runtime alone.

• Reject speed gains that reduce legal reachability.

Senior review question

Ask: which requirement intent is proven, under which assumptions, and what residual risk remains?