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Title:  Parikh's Theorem in Commutative Kleene Algebra 
Authors:  Hopkins, Mark Kozen, Dexter 
Keywords:  computer science technical report 
Issue Date:  Jan1999 
Publisher:  Cornell University 
Citation:  http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR991724 
Abstract:  Parikh's Theorem says that the commutative image of every context free language is the commutative image of some regular set. Pilling has shown that this theorem is essentially a statement about least solutions of polynomial inequalities. We prove the following general theorem of commutative Kleene algebra, of which Parikh's and Pilling's theorems are special cases: Every system of polynomial inequalities $f_i(x_1,\ldots,x_n) \leq x_i$, $1\leq i\leq n$, over a commutative Kleene algebra $K$ has a unique least solution in $K^n$; moreover, the components of the solution are given by polynomials in the coefficients of the $f_i$. We also give a closedform solution in terms of the Jacobian matrix. 
URI:  http://hdl.handle.net/1813/7378 
Appears in Collections:  Computer Science Technical Reports

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