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- W2034774429 abstract "The accessibility problem for linear sequential machines [12] is the problem of deciding whether there is an input x such that on x the machine starting in a given state q 1 goes to a given state q 2 . Harrison shows that this problem is reducible to the following simply stated linear algebra problem, which we call the orbit problem: Given ( n, A, x, y ), where n is a natural number and A, x, and y are n x n , n x 1, and n x 1 matrices of rationals, respectively, decide whether there is a natural number I such that A i x = y . He conjectured that the orbit problem is decidable. No progress was made on the conjecture for ten years until Shank [22] showed that if n is fixed at 2, then the problem is decidable. This paper shows that the orbit problem for general n is decidable and indeed decidable in polynomial time. The orbit problem arises in several contexts; two of these, linear recurrences and the discrete logarithm problem for polynomials, are discussed, and we apply our algorithm for the orbit problem in these contexts." @default.
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- W2034774429 date "1986-08-10" @default.
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- W2034774429 title "Polynomial-time algorithm for the orbit problem" @default.
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- W2034774429 doi "https://doi.org/10.1145/6490.6496" @default.
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