Cyclic rational transductions and polynomials of rational functions

Iteration of rational transductions

The purpose of this paper is to show connections between iterated length preserving rational transductions and linear space computations Hence we study the smallest family of transductions containing length preserving rational transductions and closed under union composition and iteration We give several characterizations of this class using re stricted classes of length preserving rational tra...

Computer Algebra of Polynomials and Rational Functions

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Logical and Algebraic Characterizations of Rational Transductions

Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free automata, star-free expressions, aperiodic (finite) congruences, or first-order (FO) logic. In particular, their algebraic characterization by aperiodic con...

Faber Polynomials for Rational Mapping Functions

VC Dimension and Learnability of Sparse Polynomials and Rational Functions

We prove upper and lower bounds on the VC dimension of sparse univariate polynomi-als over reals, and apply these results to prove uniform learnability of sparse polynomials and rational functions. As another application we solve an open problem of Vapnik ((Vap-nik 82]) on uniform approximation of the general regression functions, a central problem of computational statistics (cf. Vapnik 82]), ...