Formal Verification of Romanov's Triplet Logic: A Verified Filter for Sliding-window 3-CNF with Application to Structured Formulas
We present the first mechanised formalisation of Romanov's Triplet Logic (TLS) in the Rocq proof assistant. TLS is a combinatorial framework originally motivated by Boolean satisfiability, based on triplet structures and a filter that we call Simple Vertex Intersection (SVI). We formalise the core of TLS, including its translation from 3-CNF, the clearing procedure, and the SVI algorithm. For the well-formed sliding-window fragment, we prove explicit polynomial-time bounds for the filter stages and verify the translation and intersection operations. Our main contribution is a precise correctness boundary: for general formulas, SVI non-emptiness is necessary but not sufficient for satisfia...
| Authors | Dmitry V. Alexandrov |
|---|---|
| Primary category | cs.LO |
| Published | 19 August 2026 |
| Last updated at source | 25 August 2026 |
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