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Decidability of membership problems for flat rational subsets of GL(2, Q) and singular matrices

2020
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Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation
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This work relates numerical problems on matrices over the rationals to symbolic algorithms on words and finite automata. Using exact algebraic algorithms and symbolic computation, we prove new decidability results for 2 × 2 matrices over Q. Namely, we introduce a notion of flat rational sets: if is a monoid and ≤ is its submonoid, then flat rational sets of relative to are finite unions of the form 0 1 1 · · · where all s are rational subsets of and ∈ . We give quite general sufficient

doi:10.1145/3373207.3404038
dblp:conf/issac/DiekertPS20
fatcat:65rgw7q4rjdmrmjbvawecvsczq