# Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers

@article{Dose2016ComplexityOC, title={Complexity of Constraint Satisfaction Problems over Finite Subsets of Natural Numbers}, author={Titus Dose}, journal={Electron. Colloquium Comput. Complex.}, year={2016}, volume={23}, pages={31} }

We study the computational complexity of constraint satisfaction problems that are based on integer expressions and algebraic circuits. On input of a finite set of variables and a finite set of constraints the question is whether the variables can be mapped onto finite subsets of N (resp., finite intervals over N) such that all constraints are satisfied. According to the operations allowed in the constraints, the complexity varies over a wide range of complexity classes such as L, P, NP, PSPACE…

## 3 Citations

Balance Problems for Integer Circuits

- Mathematics, Computer ScienceElectron. Colloquium Comput. Complex.
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The work shows that the balance problem for { ∖, ⋅ } -circuits is undecidable which is the first natural problem for integer circuits or related constraint satisfaction problems that admits only one arithmetic operation and is proven to be Undecidable.

Emptiness Problems for Integer Circuits

- MathematicsMFCS
- 2017

It turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a major open problem in algebraic computing complexity.

Circuit satisfiability and constraint satisfaction around Skolem Arithmetic

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 2017

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