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The Complexity of Solving Linear Equations over a Finite Ring
[chapter]

2005
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Lecture Notes in Computer Science
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In this paper we first examine the computational complexity of the problem LCON defined as follows: given a matrix A and a column vector b over Z, determine if Ax = b is a feasible system of linear equations over Zq. Here q is also given as part of the input by its prime factorization q = p e 1 1 p e 2 2 . . . p e k k , such that each p e i i is tiny (i.e. given in unary). In [MC87] an NC 3 algorithm is given for this problem. We show that in fact the problem can be solved in randomized NC 2 .

doi:10.1007/978-3-540-31856-9_39
fatcat:iqesp3pmsbhltk22sdouahgqyq