12,733 research outputs found
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
Zeno machines and hypercomputation
This paper reviews the Church-Turing Thesis (or rather, theses) with
reference to their origin and application and considers some models of
"hypercomputation", concentrating on perhaps the most straight-forward option:
Zeno machines (Turing machines with accelerating clock). The halting problem is
briefly discussed in a general context and the suggestion that it is an
inevitable companion of any reasonable computational model is emphasised. It is
hinted that claims to have "broken the Turing barrier" could be toned down and
that the important and well-founded role of Turing computability in the
mathematical sciences stands unchallenged.Comment: 11 pages. First submitted in December 2004, substantially revised in
July and in November 2005. To appear in Theoretical Computer Scienc
Artificial Brains and Hybrid Minds
The paper develops two related thought experiments exploring variations on an âanimatâ theme. Animats are hybrid devices with both artificial and biological components. Traditionally, âcomponentsâ have been construed in concrete terms, as physical parts or constituent material structures. Many fascinating issues arise within this context of hybrid physical organization. However, within the context of functional/computational theories of mentality, demarcations based purely on material structure are unduly narrow. It is abstract functional structure which does the key work in characterizing the respective âcomponentsâ of thinking systems, while the âstuffâ of material implementation is of secondary importance. Thus the paper extends the received animat paradigm, and investigates some intriguing consequences of expanding the conception of bio-machine hybrids to include abstract functional and semantic structure. In particular, the thought experiments consider cases of mind-machine merger where there is no physical Brain-Machine Interface: indeed, the material human body and brain have been removed from the picture altogether. The first experiment illustrates some intrinsic theoretical difficulties in attempting to replicate the human mind in an alternative material medium, while the second reveals some deep conceptual problems in attempting to create a form of truly Artificial General Intelligence
Mapping Big Data into Knowledge Space with Cognitive Cyber-Infrastructure
Big data research has attracted great attention in science, technology,
industry and society. It is developing with the evolving scientific paradigm,
the fourth industrial revolution, and the transformational innovation of
technologies. However, its nature and fundamental challenge have not been
recognized, and its own methodology has not been formed. This paper explores
and answers the following questions: What is big data? What are the basic
methods for representing, managing and analyzing big data? What is the
relationship between big data and knowledge? Can we find a mapping from big
data into knowledge space? What kind of infrastructure is required to support
not only big data management and analysis but also knowledge discovery, sharing
and management? What is the relationship between big data and science paradigm?
What is the nature and fundamental challenge of big data computing? A
multi-dimensional perspective is presented toward a methodology of big data
computing.Comment: 59 page
The "paradox" of computability and a recursive relative version of the Busy Beaver function
In this article, we will show that uncomputability is a relative property not
only of oracle Turing machines, but also of subrecursive classes. We will
define the concept of a Turing submachine, and a recursive relative version for
the Busy Beaver function which we will call Busy Beaver Plus function.
Therefore, we will prove that the computable Busy Beaver Plus function defined
on any Turing submachine is not computable by any program running on this
submachine. We will thereby demonstrate the existence of a "paradox" of
computability a la Skolem: a function is computable when "seen from the
outside" the subsystem, but uncomputable when "seen from within" the same
subsystem. Finally, we will raise the possibility of defining universal
submachines, and a hierarchy of negative Turing degrees.Comment: 10 pages. 0 figures. Supported by the National Council for Scientific
and Technological Development (CNPq), Brazil. Book chapter published in
Information and Complexity, Mark Burgin and Cristian S. Calude (Editors),
World Scientific Publishing, 2016, ISBN 978-981-3109-02-5, available at
http://www.worldscientific.com/worldscibooks/10.1142/10017. arXiv admin note:
substantial text overlap with arXiv:1612.0522
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