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For each $a \in \mathbb{R}$, we define a Borel function $f_a : \mathbb{R} \to \mathbb{R}$ which encodes $a$ in a certain sense. We show that for each Borel $g : \mathbb{R} \to \mathbb{R}$, $f_a \cap g = \emptyset$ implies $a \in…
In this paper, by using C-class functions [4] for integral type of Suzuki-type mappings, some fixed point results are established on a metric space that gener- alize the results of Aleomraninejad and Shokouhnia [Adv. Fixed Point Theory, 5…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
An integer--valued function is an entire function which maps the nonnegative integers $\mathbb N$ to the integers. An example is $2^z$. A Hurwitz function is an entire function having all derivatives taking integer values at $0$. An example…
This paper studies fundamental questions concerning category-theoretic models of induction and recursion. We are concerned with the relationship between well-founded and recursive coalgebras for an endofunctor. For monomorphism preserving…
In a previous work, we proved that an important part of the Calculus of Inductive Constructions (CIC), the basis of the Coq proof assistant, can be seen as a Calculus of Algebraic Constructions (CAC), an extension of the Calculus of…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
This paper is a concise and painless introduction to the $\lambda$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular…
Resolution lies at the foundation of both logic programming and type class context reduction in functional languages. Terminating derivations by resolution have well-defined inductive meaning, whereas some non-terminating derivations can be…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
Consider a decision problem whose instance is a function. Its degree of undecidability, measured by the corresponding class of the arithmetic (or Kleene-Mostowski) hierarchy hierarchy, may depend on whether the instance is a partial…
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of…
We define and prove isomorphisms between three combinatorial classes involving labeled trees. We also give an alternative proof by means of generating functions.
computable functions are defined by abstract finite deterministic algorithms on many-sorted algebras. We show that there exist finite universal algebraic specifications that specify uniquely (up to isomorphism) (i) all abstract computable…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
We define recursive harmonic numbers as a generalization of harmonic numbers. The table of recursive harmonic numbers, which is like Pascal's triangle, is constructed. A formula for recursive harmonic numbers containing binomial…
In this paper Euler shows how, if we have recursive functions f,g,h and an infinite sequence A,B,C,... which satisfies fA=gB+hC, f'B=g'C+h'D, f''C=g''D+h''E, f'''D=g'''E+h'''F, etc., where the primes denote an index not a derivative, then…
The Hobby-Rice Theorem states that, given $n$ functions $f_j$ on ${\mathbb{R}}^N$, there exists a multiplier $h$ such that the integrals of $f_jh$ are all simultaneously zero. This multiplier takes values~$\pm1$ and is discontinuous. We…
Let $h \geq 2$ and let ${ \mathcal A} = (A_1,\ldots, A_h)$ be an $h$-tuple of sets of integers. For nonzero integers $c_1,\ldots, c_h$, consider the linear form $\varphi = c_1 x_1 + c_2x_2 + \cdots + c_h x_h$. The \emph{representation…