Related papers: Incomputability after Alan Turing
This article presents a theoretical investigation of computation beyond the Turing barrier from emergent behavior in distributed systems. In particular, we present an algorithmic network that is a mathematical model of a networked…
Notoriously, quantum computation shatters complexity theory, but is innocuous to computability theory. Yet several works have shown how quantum theory as it stands could breach the physical Church-Turing thesis. We draw a clear line as to…
This paper constructively proves the existence of an effective procedure generating a computable (total) function that is not contained in any given effectively enumerable set of such functions. The proof implies the existence of machines…
The abstraction introduced by von Neumann correctly reflected the state of the art 70 years ago. Although it omitted data transmission time between components of the computer, it served as an excellent base for classic computing for…
In 1957, Lacombe initiated a systematic study of the different possible notions of "computable topological spaces". However, he interrupted this line of research, settling for the idea that "computably open sets should be computable unions…
The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and…
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
Indifferentiability is a popular cryptographic paradigm for analyzing the security of ideal objects -- both in a classical as well as in a quantum world. It is typically stated in the form of a composable and simulation-based definition,…
Social computing encompasses the mechanisms through which people interact with computational systems: crowdsourcing systems, ranking and recommendation systems, online prediction markets, citizen science projects, and collaboratively edited…
Provided that there is no theoretical frame for complex engineered systems (CES) as yet, this paper claims that bio-inspired engineering can help provide such a frame. Within CES bio-inspired systems play a key role. The disclosure from…
Living things, computers, societies, and even books are part of a grand evolutionary struggle to survive. That struggle shapes nature, nations, religions, art, science, and you. What you think, feel, and do is determined by it. Darwinian…
Several philosophical issues in connection with computer simulations rely on the assumption that results of simulations are trustworthy. Examples of these include the debate on the experimental role of computer simulations \cite{Parker2009,…
The essay consists of three parts. In the first part, it is explained how theory of algorithms and computations evaluates the contemporary situation with computers and global networks. In the second part, it is demonstrated what new…
In a previous paper, we provided a formal definition for the concept of computational irreducibility (CIR), i.e. the fact for a function f from N to N that it is impossible to compute f(n) without following approximately the same path than…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
We report a new limitation on the ability of physical systems to perform computation -- one that is based on generalizing the notion of memory, or storage space, available to the system to perform the computation. Roughly, we define memory…
The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild…
This paper delves into the intersection of computational theory and music, examining the concept of undecidability and its significant, yet overlooked, implications within the realm of modern music composition and production. It posits that…
We advance a Bayesian concept of 'intrinsic asymptotic universality' taking to its final conclusions previous conceptual and numerical work based upon a concept of a reprogrammability test and an investigation of the complex qualitative…
Landauer's principle claims that "Information is Physical." It is not surprising that its conceptual antithesis, Wheeler's "It from Bit," has been more popular among computer scientists --- in the form of the Church-Turing hypothesis: All…