Related papers: Space and Time Complexity for Infinite Time Turing…
Linear Temporal Logic (LTL) is the de-facto standard temporal logic for system specification, whose foundational properties have been studied for over five decades. Safety and cosafety properties define notable fragments of LTL, where a…
Performance of cryptanalytic quantum search algorithms is mainly inferred from query complexity which hides overhead induced by an implementation. To shed light on quantitative complexity analysis removing hidden factors, we provide a…
Cumulative memory -- the sum of space used per step over the duration of a computation -- is a fine-grained measure of time-space complexity that was introduced to analyze cryptographic applications like password hashing. It is a more…
In this paper we intend to study implications in their most general form, generalizing different classes of implications including the Heyting implication, sub-structural implications and weak strict implications. Following the topological…
The class $\mathcal{UP}$ of `ultimate polynomial time' problems over $\mathbb C$ is introduced; it contains the class $\mathcal P$ of polynomial time problems over $\mathbb C$. The $\tau$-Conjecture for polynomials implies that…
We provide five rearticulations of the thesis that the structure of spacetime is conventional, rather than empirically determined, based upon variation of the structures that are empirically underdetermined and modal contexts in which this…
This paper presents a new abstract method for proving lower bounds in computational complexity. Based on the notion of topological and measurable entropy for dynamical systems, it is shown to generalise three previous lower bounds results…
Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate…
We continue our analysis of volume and energy measures that are appropriate for quantifying inductive inference systems. We extend logical depth and conceptual jump size measures in AIT to stochastic problems, and physical measures that…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
Computational complexity theory contains a corpus of theorems and conjectures regarding the time a Turing machine will need to solve certain types of problems as a function of the input size. Nature {\em need not} be a Turing machine and,…
This thesis discusses the possibility of uncertainty relations for space and energy given a state of fixed entropy. In particular, it discusses the results in the paper of Dam/Nguyen. There, the authors propose a lower bound for the mixed…
The field of implicit complexity has recently produced several bounded-complexity programming languages. This kind of language allows to implement exactly the functions belonging to a certain complexity class. We here present a…
In recent times, Discrete Space Time Architectures are being considered, in the context of Quantum Gravity, Quantum Super Strings, Dark Energy and so on. We show that such a scheme is intimately tied up with a varying $G$ cosmology, which…
We initiate the computability-theoretic study of ringed spaces and schemes. In particular, we show that any Turing degree may occur as the least degree of an isomorphic copy of a structure of these kinds. We also show that these structures…
The Kolmogorov complexity of a physical state is the minimal physical resources required to reproduce that state. We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity. There are two…
Space-time singularities, viz. Big bang, Big crunch and black holes have been shown to follow from the singularity theorems of General relativity. Whether the entropy at such infinite proper-time objects can be other than zero has also been…
We develop a theory of complexity for numerical computations that takes into account the condition of the input data and allows for roundoff in the computations. We follow the lines of the theory developed by Blum, Shub, and Smale for…
Equivalence in physics is discussed on the basis of experimental data accompanied by experimental errors. It is pointed out that the introduction of the equivalence being consistent with the mathematical definition is possible only in…
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…