Work

Signed $$p$$-Adic Residual Encodings of Finite-Domain All-Different Systems with a Sudoku Case Study

Year: 2026

Type: article

Abstract: We study signed, weighted affine $$p$$ -adic residual objectives as native encodings of finite-domain constraints. For primes that separate the finite alphabet, sufficiently weighted positive unary rows pin each coefficient to its allowed set, while negative rows reward unequal endpoints or clause satisfaction. A coordinatewise domination theorem places every global minimiser in the finite domain; there the loss is, up to an additive constant, the all-different conflict count or the negative number of satisfied CNF clauses. Standard Sudoku provides an $$81$$ -coefficient case study without a one-hot lift. A client-side implementation exposes the generated dataframes, arithmetic, diagnostics, and searches.

Source: P-Adic Numbers Ultrametric Analysis and Applications

DOI: 10.1134/s2070046626040060

Author: Greg Baker

Institution: Australian National University

Language: English

Topic: Constraint Satisfaction and Optimization

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Australian Government

OpenAlex ID: W7213402218

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