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Compatibility of Systems of Linear Constraints over the Set of Natural Numbers |
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| Authors: | S. L. Kryvyi |
| Affiliation: | (1) Cybernetics Institute, National Academy of Sciences of Ukraine, Kiev, Ukraine |
| Abstract: | Criteria of compatibility of a system of linear Diophantine equations, strict inequations, and nonstrict inequations are considered. Upper bounds for components of a minimal set of solutions and algorithms of construction of minimal generating sets of solutions for all types of systems are given. These criteria and the corresponding algorithms for constructing a minimal supporting set of solutions can be used in solving all the considered types of systems and systems of mixed types. |
| Keywords: | system of linear Diophantine equations homogeneous linear Diophantine equations nonhomogeneous linear Diophantine equations system of linear Diophantine constraints homogeneous linear Diophantine constraints nonhomogeneous linear Diophantine constraints linear Diophantine inequations homogeneous linear Diophantine inequations criteria of compatibility truncated set of solutions |
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