Vector Reachability Problem in SL(2, Z)
نویسندگان
چکیده
This paper solves two open problems about the decidability of the vector reachability problem over a finitely generated semigroup of matrices from SL(2,Z) and the point to point reachability (over rational numbers) for fractional linear transformations, where associated matrices are from SL(2,Z). The approach to solving reachability problems is based on the characterization of reachability paths between points which is followed by the translation of numerical problems on matrices into computational and combinatorial problems on words and formal languages. We will also use this technique to prove that a special case of the scalar reachability problem is decidable.
منابع مشابه
Vector Reachability Problem in $\mathrm{SL}(2,\mathbb{Z})$
This paper is showing the solution for two open problems about decidability of vector reachability problem in a finitely generated semigroup of matrices from SL(2,Z) and the point to point reachability (over rational numbers) for fractional linear transformations, where associated matrices are form SL(2,Z). The approach of solving reachability problems is based on analysis of reachability paths...
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