Decidability is shown for single-variable Presburger expansions with fixed powers via hyperelliptic Diophantine solvability and with degree-at-most-three polynomials via low-genus curves, with hardness results when restrictions are removed.
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On Variable-Bounded Non-Linear Expansions of Presburger Arithmetic
Decidability is shown for single-variable Presburger expansions with fixed powers via hyperelliptic Diophantine solvability and with degree-at-most-three polynomials via low-genus curves, with hardness results when restrictions are removed.