Solvability of orbit-finite systems of linear equations
ACM/IEEE Symposium on Logic in Computer Science (LICS)(2022)
摘要
We study orbit-finite systems of linear equations, in the setting of sets
with atoms. Our principal contribution is a decision procedure for solvability
of such systems. The procedure works for every field (and even commutative
ring) under mild effectiveness assumptions, and reduces a given orbit-finite
system to a number of finite ones: exponentially many in general, but
polynomially many when atom dimension of input systems is fixed. Towards
obtaining the procedure we push further the theory of vector spaces generated
by orbit-finite sets, and show that each such vector space admits an
orbit-finite basis. This fundamental property is a key tool in our development,
but should be also of wider interest.
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关键词
linear equations,orbit-finite
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