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The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n…
In this work, we reveal a new type of impossibility discovered in our recent research which forbids comparing the closeness of multiple unknown quantum states with any non-trivial threshold in a perfect or an unambiguous way. This…
In this paper, we study quantitative properties of quantum programs. Properties of interest include (positive) almost-sure termination, expected runtime or expected cost, that is, for example, the expected number of applications of a given…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
Machine learning techniques have influenced the field of computer architecture like many other fields. This paper studies how the fundamental machine learning techniques can be applied towards computer architecture problems. We also provide…
This work summarizes part of current knowledge on High-level Cognitive process and its relation with biological hardware. Thus, it is possible to identify some paradoxes which could impact the development of future technologies and…
Through a straightforward Bayesian approach we show that under some general conditions a maximum running time, namely the number of discrete steps performed by a computer program during its execution, can be defined such that the…
We suggest analyzing neural networks through the prism of space constraints. We observe that most training algorithms applied in practice use bounded memory, which enables us to use a new notion introduced in the study of space-time…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
The architecture of neural Turing machines is differentiable end to end and is trainable with gradient descent methods. Due to their large unfolded depth Neural Turing Machines are hard to train and because of their linear access of…
Performance variability is an important measure for a reliable high performance computing (HPC) system. Performance variability is affected by complicated interactions between numerous factors, such as CPU frequency, the number of…
We introduce a neural stack architecture, including a differentiable parametrized stack operator that approximates stack push and pop operations for suitable choices of parameters that explicitly represents a stack. We prove the stability…
Universality is one of the most important ideas in computability theory. There are various criteria of simplicity for universal Turing machines. Probably the most popular one is to count the number of states/symbols. This criterion is more…
A common trait of many machine learning models is that it is often difficult to understand and explain what caused the model to produce the given output. While the explainability of neural networks has been an active field of research in…
The paper explores known results related to the problem of identifying if a given program terminates on all inputs -- this is a simple generalization of the halting problem. We will see how this problem is related and the notion of proof…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
In the last years, different types of patterns in permutations have been studied: vincular, bivincular and mesh patterns, just to name a few. Every type of permutation pattern naturally defines a corresponding computational problem: Given a…
Incorporating constraints is a major concern in probabilistic machine learning. A wide variety of problems require predictions to be integrated with reasoning about constraints, from modelling routes on maps to approving loan predictions.…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
We study weakest precondition reasoning about the (co)variance of outcomes and the variance of run-times of probabilistic programs with conditioning. For outcomes, we show that approximating (co)variances is computationally more difficult…