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Characterizing Algebraic Invariants by Differential Radical Invariants (CMU-CS-13-129)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ghorbal, Khalil Platzer, André |
| Copyright Year | 2014 |
| Abstract | We prove that any invariant algebraic set of a given polynomial vector field can be algebraically represented by one polynomial and a finite set of its successive Lie derivatives. This so-called differential radical characterization relies on a sound abstraction of the reachable set of solutions by the smallest variety that contains it. The characterization leads to a differential radical invariant proof rule that is sound and complete, which implies that invariance of algebraic equations over real-closed fields is decidable. Furthermore, the problem of generating invariant varieties is shown to be as hard as minimizing the rank of a symbolic matrix, and is therefore NP-hard. We investigate symbolic linear algebra tools based on Gaussian elimination to efficiently automate the generation. The approach can, e.g., generate nontrivial algebraic invariant equations capturing the airplane behavior during take-off or landing in longitudinal motion. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://repository.cmu.edu/cgi/viewcontent.cgi?article=3734&context=compsci |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
