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About this paper
OpenAI
The authors give a deterministic algorithm for exactly counting satisfying assignments of Boolean formulas with fixed-width clauses. It reorganizes assignment sums into group-by-group sums using shared measurements and interpolation. For each fixed width, the worst-case running time is polynomial in the input size times 2^{O(n log log n/√log n)}, with polynomial space; the exponent improves for linearly many clauses, but this does not give subexponential algorithms for general NP problems.
Key insights
- A global counting problem can become separable when cross-group dependence is routed through a controlled set of shared measurements.
- Interpolation can recover the original count from transformed instances, while computing Taylor coefficients at evaluation points helps limit the number of evaluations required.
- The authors claim the approach extends beyond SAT counting to several other exact-counting and optimization tasks, though these consequences depend on the central proof being correct.
Summary by alphaXiv.
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