Related papers: Satisfiability Modulo Transcendental Functions via…
Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic…
We derive two types of representation results for increasing convex functionals in terms of countably additive measures. The first is a max-representation of functionals defined on spaces of real-valued continuous functions and the second a…
The aim of this paper is to exhibit a method for proving that certain analytic functions are not solutions of algebraic differential equations. The method is based on model-theoretic properties of differential fields and properties of…
We give a new proof of Fatou's theorem: {\em if an algebraic function has a power series expansion with bounded integer coefficients, then it must be a rational function.} This result is applied to show that for any non--trivial completely…
In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…
Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure $\lambda$-calculus, the process representations yield (at best) non-extensional $\lambda $-theories (i.e., $\beta$…
The pursuit of interpretable artificial intelligence has led to significant advancements in the development of methods that aim to explain the decision-making processes of complex models, such as deep learning systems. Among these methods,…
In the last decade we have witnessed an impressive progress in the expressiveness and efficiency of Satisfiability Modulo Theories (SMT) solving techniques. This has brought previously-intractable problems at the reach of state-of-the-art…
Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…
We prove a realization theorem for rational functions of several complex variables which extends the main theorem of M. Bessmertnyi, "On realizations of rational matrix functions of several complex variables," in Vol. 134 of Oper. Theory…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
The functional interpretation is a systematic, syntactic method for transforming certain non-constructive proofs into constructive proofs with explicit bounds. We illustrate the interpretation by working through a concrete, fairly simple…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
We present a bounded modified realisability and a bounded functional interpretation of intuitionistic nonstandard arithmetic with nonstandard principles. The functional interpretation is the intuitionistic counterpart of Ferreira and…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…
Intensional computation derives concrete outputs from abstract function definitions; extensional computation defines functions through explicit input-output pairs. In formal semantics: intensional computation interprets expressions as…
This paper introduces function alignment, a novel theory of mind and intelligence that is both intuitively compelling and structurally grounded. It explicitly models how meaning, interpretation, and analogy emerge from interactions among…
We introduce and discuss a new class of (multivalued analytic) transcendental functions which still share with algebraic functions the property that the number of their isolated zeros can be explicitly counted. On the other hand, this class…