Related papers: Partial Functions and Recursion in Univalent Type …

We exhibit a sound and complete implicit-complexity formalism for functions feasibly computable by structural recursions over inductively defined data structures. Feasibly computable here means that the structural-recursive definition runs…

In this article, we will show that uncomputability is a relative property not only of oracle Turing machines, but also of subrecursive classes. We will define the concept of a Turing submachine, and a recursive relative version for the Busy…

For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist such a…

The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…

We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…

We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…

In reinforcement learning, conducting task composition by forming cohesive, executable sequences from multiple tasks remains challenging. However, the ability to (de)compose tasks is a linchpin in developing robotic systems capable of…

The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…

We provide an explicit characterization of the properties of primitive recursive functions that are decidable or semi-decidable, given a primitive recursive index for the function. The result is much more general as it applies to any c.e.…

This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding…

We develop domain theory in constructive and predicative univalent foundations (also known as homotopy type theory). That we work predicatively means that we do not assume Voevodsky's propositional resizing axioms. Our work is constructive…

Despite ample evidence that our concepts, our cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational…

Reverse mathematics studies which subsystems of second order arithmetic are equivalent to key theorems of ordinary, non-set-theoretic mathematics. The main philosophical application of reverse mathematics proposed thus far is foundational…

In [arXiv 0811.3913] the authors introduced the notion of quasi-polynomial function as being a mapping f: X^n -> X defined and valued on a bounded chain X and which can be factorized as f(x_1,...,x_n)=p(phi(x_1),...,phi(x_n)), where p is a…

We construct quantum mechanical observables and unitary operators which, if implemented in physical systems as measurements and dynamical evolutions, would contradict the Church-Turing thesis which lies at the foundation of computer…

Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…

We study closed choice principles for different spaces. Given information about what does not constitute a solution, closed choice determines a solution. We show that with closed choice one can characterize several models of…

Partition functions, also known as homomorphism functions, form a rich family of graph invariants that contain combinatorial invariants such as the number of k-colourings or the number of independent sets of a graph and also the partition…

We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…

This paper continues a systematic and comprehensive study on the structural properties of CFL functions, which are in general multi-valued partial functions computed by one-way one-head nondeterministic pushdown automata equipped with…