Related papers: Z-polyregular functions
In this paper, as an analogue of the integer case, we define congruence preserving functions over the residue class rings of polynomials over finite fields. We establish a counting formula for such congruence preserving functions, determine…
A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…
A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of…
The class of uniformly computable real functions with respect to a small subrecursive class of operators computes the elementary functions of calculus, restricted to compact subsets of their domains. The class of conditionally computable…
We give some connections between various functions defined on finitely presented groups (isoperimetric, isodiametric, Todd-Coxeter radius, filling length functions, etc.), and we study the relation between those functions and the…
We present polygraphic programs, a subclass of Albert Burroni's polygraphs, as a computational model, showing how these objects can be seen as first-order functional programs. We prove that the model is Turing complete. We use polygraphic…
Polynomial functions on the group of units Q_n of the ring Z_{2^n} are considered. A finite set of reduced polynomials RP_n in Z[x] that induces the polynomial functions on Q_n is determined. Each polynomial function on Q_n is induced by a…
In a recent article, the class of functions from the integers to the integers computable in polynomial time has been characterized using discrete ordinary differential equations (ODE), also known as finite differences. Doing so, we pointed…
We introduce new zeta functions related to an endomorphism $\phi$ of a discrete group $\Gamma$. They are of two types: counting numbers of fixed ($\rho\sim \rho\circ\phi^n$) irreducible representations for iterations of $\phi$ from an…
An important problem in combinatorial noncommutative algebra is to characterize the growth functions of finitely generated algebras (equivalently, semigroups, or hereditary languages). The growth function of every finitely generated,…
A syntactical proof is given that all functions definable in a certain affine linear typed lambda-calculus with iteration in all types are polynomial time computable. The proof provides explicit polynomial bounds that can easily be…
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…
To minimize or upper-bound the value of a function "robustly", we might instead minimize or upper-bound the "epsilon-robust regularization", defined as the map from a point to the maximum value of the function within an epsilon-radius. This…
J.Ritt has investigated the structure of complex polynomials with respect to superposition. In particular, he listed all the polynomials admitting different double decompositions into indecomposable polynomials. The analogues of Ritt theory…
This preliminary report addresses the expressive power of unit resolution regarding input data encoded with partial truth assignments of propositional variables. A characterization of the functions that are computable in this way, which we…
We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
Recursive analysis was introduced by A. Turing [1936], A. Grzegorczyk [1955], and D. Lacombe [1955]. It is based on a discrete mechanical framework that can be used to model computation over the real numbers. In this context the…
We prove first-order definability of the prime subring inside polynomial rings, whose coefficient rings are (commutative unital) reduced and indecomposable. This is achieved by means of a uniform formula in the language of rings with…