A Simple Constructive Bound on Circuit Size Change Under Truth Table Perturbation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917328249159680 |
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| author | Krinkin, Kirill |
| author_facet | Krinkin, Kirill |
| contents | The observation that optimum circuit size changes by at most $O(n)$ under a one-point truth table perturbation is implicit in prior work on the Minimum Circuit Size Problem. This note states the bound explicitly for arbitrary fixed finite complete bases with unit-cost gates, extends it to general Hamming distance via a telescoping argument, and verifies it exhaustively at $n = 4$ in the AIG basis using SAT-derived exact circuit sizes for 220 of 222 NPN equivalence classes. Among 987 mutation edges, the maximum observed difference is $4 = n$, confirming the bound is tight at $n = 4$ for AIG. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_09379 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Simple Constructive Bound on Circuit Size Change Under Truth Table Perturbation Krinkin, Kirill Computational Complexity Logic in Computer Science The observation that optimum circuit size changes by at most $O(n)$ under a one-point truth table perturbation is implicit in prior work on the Minimum Circuit Size Problem. This note states the bound explicitly for arbitrary fixed finite complete bases with unit-cost gates, extends it to general Hamming distance via a telescoping argument, and verifies it exhaustively at $n = 4$ in the AIG basis using SAT-derived exact circuit sizes for 220 of 222 NPN equivalence classes. Among 987 mutation edges, the maximum observed difference is $4 = n$, confirming the bound is tight at $n = 4$ for AIG. |
| title | A Simple Constructive Bound on Circuit Size Change Under Truth Table Perturbation |
| topic | Computational Complexity Logic in Computer Science |
| url | https://arxiv.org/abs/2603.09379 |