Related papers: Bounded time computation on metric spaces and Bana…
In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…
By the Riesz representation theorem using the Riemann-Stieltjes integral, linear continuous functionals on the set of continuous functions from the unit interval into the reals can either be characterized by functions of bounded variation…
Motivated by recent results of Kapron and Steinberg (LICS 2018) we introduce new forms of iteration on length in the setting of applied lambda-calculi for higher-type poly-time computability. In particular, in a type-two setting, we…
We start by an introduction to the basic concepts of computability theory and the introduction of the concept of Turing machine and computation universality. Then se turn to the exploration of trade-offs between different measures of…
One of the elegant achievements in the history of proof theory is the characterization of the provably total recursive functions of an arithmetical theory by its proof-theoretic ordinal as a way to measure the time complexity of the…
We develop a systematic algorithmic framework that unites global and local classification problems using index sets. We prove that the classification problem for continuous (binary) regular functions among almost everywhere linear,…
In 1994, S.G. Matthews introduced the notion of partial metric space in order to obtain a suitable mathematical tool for program verification [Ann. New York Acad. Sci. 728 (1994), 183-197]. He gave an application of this new structure to…
Intuitively, if we can prove that a program terminates, we expect some conclusion regarding its complexity. But the passage from termination proofs to complexity bounds is not always clear. In this work we consider Monotonicity Constraint…
It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present…
The properties of the stable distance over stable spacetimes are used as a reference to propose a simplified, abstract notion of spacetime. The discussion shows that spacetime, with its topology, causal order and (upper semi-continuous)…
In this paper we study a representation problem first considered in a simpler version by Bank and El Karoui [2004]. A key ingredient to this problem is a random measure $\mu$ on the time axis which in the present paper is allowed to have…
For any quantum algorithm given by a path in the space of unitary operators we define the computational complexity as the typical computational time associated with the path. This time is defined using a quantum time estimator associated…
Warped time-frequency systems have recently been introduced as a class of structured continuous frames for functions on the real line. Herein, we generalize this framework to the setting of functions of arbitrary dimensionality. After…
In this paper, we study functions of bounded variation on a complete and connected metric space with finite one-dimensional Hausdorff measure. The definition of BV functions on a compact interval based on pointwise variation is extended to…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…
Let X be a separable metric space and let \beta be the strict topology on the space of bounded continuous functions on X, which has the space of \tau-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonne\'{e} type…
The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been…
Concrete computing machines, either sequential or concurrent, rely on an intimate relation between computation and time. We recall the general characteristic properties of physical time and of present realizations of computing systems. We…
General quantum computation consists of unitary operations and also measurements. It is well known that intermediate quantum measurements can be deferred to the end of the computation, resulting in an equivalent purely unitary computation.…