On iterating linear transformations over recognizable sets of integers

@article{Boigelot2003OnIL,
  title={On iterating linear transformations over recognizable sets of integers},
  author={Bernard Boigelot},
  journal={Theor. Comput. Sci.},
  year={2003},
  volume={309},
  pages={413-468}
}
It has been known for a long time that the sets of integer vectors that are recognizable by finite-state automata are those that can be defined in an extension of Presburger arithmetic. In this paper, we address the problem of deciding whether the closure of a linear transformation preserves the recognizable nature of sets of integer vectors. We solve this problem by introducing an original extension of the concept of recognizability to sets of vectors with complex components. This… CONTINUE READING
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