Properties and Assertions: Safety, Liveness, and Sound Modeling: Comparison Matrix

Comparison matrix

Early formal choices trade closure speed against model realism. Fast proofs are only useful when legal behavior stays reachable.

+------------------+----------------+----------------+----------------+
| Approach         | Strength       | Weakness       | Best when      |
+------------------+----------------+----------------+----------------+
| Strict model     | high trust     | longer runtime | signoff-critical logic |
| Balanced model   | faster closure | needs reviews  | daily regressions |
| Heavy abstraction | runtime gain   | confidence risk | exploratory triage |
| Property refactor | debug clarity  | rewrite effort | stalled proof sets |
+------------------+----------------+----------------+----------------+

When to choose each approach

• Choose strategy by requirement criticality and residual-risk tolerance, not by runtime alone.

Interview traps

• Applying one setup strategy to all property classes without intent review.

• Accepting waivers before replaying first divergence with owners.

Formal deep dive

FPV foundations are reliable only when assumptions, reset semantics, and requirement intent are explicitly modeled and audited.

Concept diagram

FPV FOUNDATION LOOP

requirements -> property set -> assumptions and reset model -> prove/fail traces -> closure audit

Metric graph

FOUNDATION HEALTH

vacuous passes         ████
reachable proofs       ███████
inconclusive backlog   █████
reopened properties    ███

Metrics and artifacts to collect

• assumption traceability matrix

• vacuity and reachability status

• proof core relevance summary

• counterexample classification trend

Mini case study

A green-looking run was invalidated after legal-mode covers failed, exposing assumptions that removed realistic traffic.

Debug branches

• Validate requirement-to-property mapping before tuning runtime.

• Check legal scenario reachability after every assumption change.

• Classify first divergence as model issue or RTL bug.

Senior review question

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

Key takeaways

• Tie each proof claim to assumption boundaries and reachability evidence.

• Prefer minimal reversible fixes and preserve legal behavior visibility.

Common pitfalls

• Treating runtime reduction as proof-quality improvement without audits.

• Declaring closure while critical covers remain unreachable.

• Using broad waivers instead of first-divergence root-cause ownership.

Principal formal review addendum

Properties and Assertions: Safety, Liveness, and Sound Modeling should be reviewed as a requirement-evidence workflow, not a single status report.

Use non-vacuous closure rate, counterexample turnaround time, and requirement-level residual risk trend as the monitoring lens and formal closure packet: assumptions audit, proof status matrix, counterexample classification, and requirement traceability as closure proof.

Formal foundations are strongest when assumptions, reset semantics, and requirement intent are all explicit and reviewable. Strong teams preserve legal reachability while improving convergence.