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math.CO2026
The satisfiability threshold of random linear equations over finite commutative rings
Pu Gao, Theodore Morrison
We extend the study of random linear equations over finite fields to equations over finite commutative rings. We characterize precisely when the satisfiability threshold occurs at…
math.CO2026
The satisfiability threshold and solution space of random uniquely extendable constraint satisfaction problems
Pu Gao, Theodore Morrison
We study the satisfiability threshold and solution-space geometry of random constraint satisfaction problems defined over uniquely extendable (UE) constraints. Motivated by a conje…