92,832 research outputs found
Limits on Fundamental Limits to Computation
An indispensable part of our lives, computing has also become essential to
industries and governments. Steady improvements in computer hardware have been
supported by periodic doubling of transistor densities in integrated circuits
over the last fifty years. Such Moore scaling now requires increasingly heroic
efforts, stimulating research in alternative hardware and stirring controversy.
To help evaluate emerging technologies and enrich our understanding of
integrated-circuit scaling, we review fundamental limits to computation: in
manufacturing, energy, physical space, design and verification effort, and
algorithms. To outline what is achievable in principle and in practice, we
recall how some limits were circumvented, compare loose and tight limits. We
also point out that engineering difficulties encountered by emerging
technologies may indicate yet-unknown limits.Comment: 15 pages, 4 figures, 1 tabl
Simulation of Two-Way Pushdown Automata Revisited
The linear-time simulation of 2-way deterministic pushdown automata (2DPDA)
by the Cook and Jones constructions is revisited. Following the semantics-based
approach by Jones, an interpreter is given which, when extended with
random-access memory, performs a linear-time simulation of 2DPDA. The recursive
interpreter works without the dump list of the original constructions, which
makes Cook's insight into linear-time simulation of exponential-time automata
more intuitive and the complexity argument clearer. The simulation is then
extended to 2-way nondeterministic pushdown automata (2NPDA) to provide for a
cubic-time recognition of context-free languages. The time required to run the
final construction depends on the degree of nondeterminism. The key mechanism
that enables the polynomial-time simulations is the sharing of computations by
memoization.Comment: In Proceedings Festschrift for Dave Schmidt, arXiv:1309.455
Perspectives for proof unwinding by programming languages techniques
In this chapter, we propose some future directions of work, potentially
beneficial to Mathematics and its foundations, based on the recent import of
methodology from the theory of programming languages into proof theory. This
scientific essay, written for the audience of proof theorists as well as the
working mathematician, is not a survey of the field, but rather a personal view
of the author who hopes that it may inspire future and fellow researchers
Causality, Information and Biological Computation: An algorithmic software approach to life, disease and the immune system
Biology has taken strong steps towards becoming a computer science aiming at
reprogramming nature after the realisation that nature herself has reprogrammed
organisms by harnessing the power of natural selection and the digital
prescriptive nature of replicating DNA. Here we further unpack ideas related to
computability, algorithmic information theory and software engineering, in the
context of the extent to which biology can be (re)programmed, and with how we
may go about doing so in a more systematic way with all the tools and concepts
offered by theoretical computer science in a translation exercise from
computing to molecular biology and back. These concepts provide a means to a
hierarchical organization thereby blurring previously clear-cut lines between
concepts like matter and life, or between tumour types that are otherwise taken
as different and may not have however a different cause. This does not diminish
the properties of life or make its components and functions less interesting.
On the contrary, this approach makes for a more encompassing and integrated
view of nature, one that subsumes observer and observed within the same system,
and can generate new perspectives and tools with which to view complex diseases
like cancer, approaching them afresh from a software-engineering viewpoint that
casts evolution in the role of programmer, cells as computing machines, DNA and
genes as instructions and computer programs, viruses as hacking devices, the
immune system as a software debugging tool, and diseases as an
information-theoretic battlefield where all these forces deploy. We show how
information theory and algorithmic programming may explain fundamental
mechanisms of life and death.Comment: 30 pages, 8 figures. Invited chapter contribution to Information and
Causality: From Matter to Life. Sara I. Walker, Paul C.W. Davies and George
Ellis (eds.), Cambridge University Pres
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