Related papers: Functional boxes, communication complexity and inf…
Marginalization -- summing a function over all assignments to a subset of its inputs -- is a fundamental computational problem with applications from probabilistic inference to formal verification. Despite its computational hardness in…
With the advent of larger and more complex deep learning models, such as in Natural Language Processing (NLP), model qualities like explainability and interpretability, albeit highly desirable, are becoming harder challenges to tackle and…
Uncertainties in the real world mean that is impossible for system designers to anticipate and explicitly design for all scenarios that a robot might encounter. Thus, robots designed like this are fragile and fail outside of…
We introduce and explore the notion of "spaces of input histories", a broad family of combinatorial objects which can be used to model input-dependent, dynamical causal order. We motivate our definition with reference to traditional partial…
In this article we extend the framework of execution of concurrent functions on different abstract levels from previous work with communication between the concurrent functions. We classify the communications and identify problems that can…
We develop and investigate a general theory of representations of second-order functionals, based on a notion of a right comodule for a monad on the category of containers. We show how the notion of comodule representability naturally…
Causality among events is widely recognized as a most fundamental structure of spacetime, and causal sets have been proposed as discrete models of the latter in the context of quantum gravity theories, notably in the Causal Set Programme.…
Causal modelling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing frameworks for quantum causality tend to focus on acyclic causal…
Operations that are trivial in the classical world, like accessing information without introducing any change or disturbance, or like copying information, become non-trivial in the quantum world. In this note we discuss several limitations…
Challenging the standard notion of totality in computable functions, one has that, given any sufficiently expressive formal axiomatic system, there are total functions that, although computable and "intuitively" understood as being total,…
We investigate the space efficiency of a Propositional Knowledge Representation (PKR) formalism. Intuitively, the space efficiency of a formalism F in representing a certain piece of knowledge A, is the size of the shortest formula of F…
Process matrices are a framework to model causal relations in the absence of a well-defined acyclic causal order. The framework is very general and does not even assume the existence of a background spacetime. As a result, it is an open…
We consider the problem of communicating over a channel for which no mathematical model is specified, and the achievable rates are determined as a function of the channel input and output sequences known a-posteriori, without assuming any…
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
We develop an extension of the process matrix (PM) framework for correlations between quantum operations with no causal order that allows multiple rounds of information exchange for each party compatibly with the assumption of well-defined…
Quantum theory describes multipartite objects of various types: quantum states, nonlocal boxes, steering assemblages, teleportages, distributed measurements, channels, and so on. Such objects describe, for example, the resources shared in…
Within a global physical theory, a notion of locality allows us to find and justify information-processing primitives, like non-signalling between distant agents. Here we propose exploring the opposite direction: to take agents as the basic…
An open problem in communication complexity proposed by several authors is to prove that for every Boolean function f, the task of computing f(x AND y) has polynomially related classical and quantum bounded-error complexities. We solve a…
In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of…