Vector and scalar reachability problems in SL(2,Z)
作者：
Highlights：
• The vector reachability problem in SL(2,Z) is decidable.
• The scalar reachability problem in SL(2,Z) is decidable.
• Reachability problem by fractional linear transformations in SL(2,Z) is decidable.
• Proofs are based on translating matrix equations into problems on regular languages.
• We give a geometric interpretation and prove generalizations of these results.
摘要
•The vector reachability problem in SL(2,Z) is decidable.•The scalar reachability problem in SL(2,Z) is decidable.•Reachability problem by fractional linear transformations in SL(2,Z) is decidable.•Proofs are based on translating matrix equations into problems on regular languages.•We give a geometric interpretation and prove generalizations of these results.
论文关键词：Vector reachability problem,Scalar reachability problem,Matrix semigroup,Special linear group,Linear fractional transformation,Automata and formal languages
论文评审过程：Received 28 December 2016, Revised 12 February 2018, Accepted 11 September 2018, Available online 20 September 2018, Version of Record 19 November 2018.
论文官网地址：https://doi.org/10.1016/j.jcss.2018.09.003
