Second-Order Logic over Strings: Regular and Non-regular Fragments

@inproceedings{Eiter2001SecondOrderLO,
  title={Second-Order Logic over Strings: Regular and Non-regular Fragments},
  author={Thomas Eiter and Georg Gottlob and Thomas Schwentick},
  booktitle={Developments in Language Theory},
  year={2001}
}
By a well-known result due to Buchi and Trakhtenbrot, all monadic second-order sentences over words describe regular languages. In this paper, we investigate prefix classes of general second-order logic. Such a prefix class is called regular, if each of its sentences describes a regular language, and nonregular otherwise. Recently, the regular and nonregular prefix classes of existential secondorder logic ?11 were exhaustively determined. We briefly recall these results and continue this line… 
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