@inproceedings{10.1145/2038642.2038659,
    Abstract = {In this paper, we consider an extended concept of invariant for polynomial dynamical systems (PDSs) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic invariants (SAIs) for such PDSs. The main idea is encoding relevant dynamical properties as conditions on the high order Lie derivatives of polynomials occurring in the SAI. A direct consequence of this criterion is a relatively complete method of SAI generation based on template assumption and semi-algebraic constraint solving. Relative completeness means if there is an SAI in the form of a predefined template, then our method can indeed find one.},
    Address = {New York, NY, USA},
    Author = {Liu, Jiang and Zhan, Naijun and Zhao, Hengjun},
    BookTitle = {Proceedings of the Ninth ACM International Conference on Embedded Software},
    File = {Computing Semi-Algebraic Invariants for Polynomial Dynamical Systems - liu2011 - a.pdf},
    ISBN = {9781450307147},
    Keywords = {invariant, semi-algebraic set, polynomial dynamical system},
    Location = {Taipei, Taiwan},
    Pages = {97--106},
    Publisher = {Association for Computing Machinery},
    Series = {EMSOFT '11},
    Title = {Computing Semi-Algebraic Invariants for Polynomial Dynamical Systems},
    URL = {https://doi.org/10.1145/2038642.2038659},
    Year = {2011},
    bdsk-url-1 = {https://doi.org/10.1145/2038642.2038659},
    date-added = {2023-04-18 07:30:40 +0200},
    date-modified = {2023-04-18 07:30:40 +0200},
    numpages = {10},
    doi = {10.1145/2038642.2038659}
}

@inproceedings{10.1145/2038642.2038659, Abstract = {In this paper, we consider an extended concept of invariant for polynomial dynamical systems (PDSs) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic invariants (SAIs) for such PDSs. The main idea is encoding relevant dynamical properties as conditions on the high order Lie derivatives of polynomials occurring in the SAI. A direct consequence of this criterion is a relatively complete method of SAI generation based on template assumption and semi-algebraic constraint solving. Relative completeness means if there is an SAI in the form of a predefined template, then our method can indeed find one.}, Address = {New York, NY, USA}, Author = {Liu, Jiang and Zhan, Naijun and Zhao, Hengjun}, BookTitle = {Proceedings of the Ninth ACM International Conference on Embedded Software}, File = {Computing Semi-Algebraic Invariants for Polynomial Dynamical Systems - liu2011 - a.pdf}, ISBN = {9781450307147}, Keywords = {invariant, semi-algebraic set, polynomial dynamical system}, Location = {Taipei, Taiwan}, Pages = {97--106}, Publisher = {Association for Computing Machinery}, Series = {EMSOFT '11}, Title = {Computing Semi-Algebraic Invariants for Polynomial Dynamical Systems}, URL = {https://doi.org/10.1145/2038642.2038659}, Year = {2011}, bdsk-url-1 = {https://doi.org/10.1145/2038642.2038659}, date-added = {2023-04-18 07:30:40 +0200}, date-modified = {2023-04-18 07:30:40 +0200}, numpages = {10}, doi = {10.1145/2038642.2038659} }