Invariant and geometric aspects of algebraic complexity theory. I. (English) Zbl 0735.68033
The author investigates the following problem: What is the minimum number, denoted by \(L_ +(v_ 1,v_ 2,\dots,v_ t\mid x_ 1,x_ 2,\dots,x_ n)\), of those additive steps required to compute a given set \(v=(v_ 1,\dots,v_ t)\) of \(t\) linear forms of variables \(x_ 1,x_ 2,\dots,x_ n\).
He establishes a natural connection of this question with some problems of graph theory, projective geometry, algebraic geometry and recent results in application of combinatorics to classical invariant theory [cf. P. Doubilet, G. C. Rota and J. Stein, Stud. Appl. Math. 53, 185-216 (1974; Zbl 0426.05009)]. There are elementary motive examples in the paper. In the following paper the author intends to consider some interesting questions arisen in his investigations in this field.
He establishes a natural connection of this question with some problems of graph theory, projective geometry, algebraic geometry and recent results in application of combinatorics to classical invariant theory [cf. P. Doubilet, G. C. Rota and J. Stein, Stud. Appl. Math. 53, 185-216 (1974; Zbl 0426.05009)]. There are elementary motive examples in the paper. In the following paper the author intends to consider some interesting questions arisen in his investigations in this field.
Reviewer: N.Osetinski
MSC:
68Q15 | Complexity classes (hierarchies, relations among complexity classes, etc.) |
15A75 | Exterior algebra, Grassmann algebras |
14L24 | Geometric invariant theory |
68W30 | Symbolic computation and algebraic computation |
05C85 | Graph algorithms (graph-theoretic aspects) |
51A20 | Configuration theorems in linear incidence geometry |
Citations:
Zbl 0426.05009References:
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