Combinational LEC: Key-Point Matching and Structural Normalization

What this topic teaches

Combinational LEC: Key-Point Matching and Structural Normalization converts formal concepts into release-ready verification decisions. Combinational LEC proves that two designs produce identical outputs for identical inputs in the same cycle, making it ideal for pure combinational logic transformations and synthesis-preserved cone rewrites.

Senior-engineer framing question

When non-vacuous closure rate, counterexample turnaround, and residual-risk trend by requirement class regresses, can you isolate the first failing assumption/property boundary, prove causality, assign owner, and close with auditable risk?

FORMAL EXECUTION FLOW - Combinational LEC: Key-Point Matching and Structural Normalization

requirement intent and risk class
      |
      v
property and assumption modeling
      |
      v
proof engine exploration and trace extraction
      |
      v
counterexample classification and fix hypothesis
      |
      v
re-proof, coverage audit, and signoff decision

Evidence to collect

• Primary metric: non-vacuous closure rate, counterexample turnaround, and residual-risk trend by requirement class.

• Primary artifact: closure packet for Combinational LEC: Key-Point Matching and Structural Normalization: assumptions audit, proof status matrix, and replay-ready divergence trace.

• Owners to include: formal verification owner, rtl owner, Equivalence Checking (LEC/SEC) owner.

• One reproducible failing trace and one stable comparator run.

• One fixed metadata run with assumptions and tool settings locked.

Ownership layers

OWNERSHIP LAYERS - Combinational LEC: Key-Point Matching and Structural Normalization

+----------------------+--------------------------------+--------------------------------+
| Team                 | Primary responsibility         | Closure artifact               |
+----------------------+--------------------------------+--------------------------------+
| formal verification owner | property and model integrity      | assumptions and proof packet   |
| rtl owner | implementation root-cause closure | RTL fix and replay evidence    |
| Equivalence Checking (LEC/SEC) owner | signoff governance and rollout    | risk memo + acceptance gates   |
+----------------------+--------------------------------+--------------------------------+

Decision matrix

EVIDENCE MATRIX - Combinational LEC: Key-Point Matching and Structural Normalization

+-----------------------------+--------------------------------+--------------------------------+---------------------------+
| Evidence                    | Tells you                      | Does not prove                 | Next action               |
+-----------------------------+--------------------------------+--------------------------------+---------------------------+
| property status by class    | closure shape by requirement   | model realism                  | pair with cover reachability |
| vacuity and trigger checks  | assertion meaningfulness       | full legal-path exploration    | inspect assumptions       |
| counterexample traces       | concrete divergence path       | complete bug-space closure     | classify and replay       |
| assumption audit trail      | model boundary confidence      | implementation correctness     | review spec traceability  |
| before/after trend packet   | mitigation movement quality    | long-window stability          | run broader matrix        |
+-----------------------------+--------------------------------+--------------------------------+---------------------------+

Key takeaways

• Start with first-divergence classification before broad model edits.

• Tie each claim to one proving artifact and one owner action.

• Close with residual-risk statement and rollback-safe criteria.

Common pitfalls

• Treating green status as correctness without vacuity and reachability audits.

• Changing assumptions and RTL together, destroying causality.

• Declaring closure without replaying representative legal scenarios.

Formal deep dive

Equivalence confidence comes from transformation-aware setup and rapid first-divergence diagnosis.

Concept diagram

EQUIVALENCE WORKFLOW

golden and revised design -> mapping and alignment -> mismatch triage -> closure evidence

Metric graph

LEC/SEC DEBUG SIGNALS

setup mismatches        █████
real behavioral deltas  ███
resolved divergences    ███████

Metrics and artifacts to collect

• compare-point match quality

• SEC latency-alignment success

• RTL-to-gate variant coverage

• ECO mismatch root-cause aging

Mini case study

A late ECO mismatch was traced to clock-gating setup, then closed with repeatable SEC alignment rules.

Debug branches

• Classify mismatch source before editing waiver sets.

• Use SEC when latency movement is intentional.

• Replay first divergence in simulation for cross-validation.

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.