21,764 research outputs found
A Hypercomputation in Brouwer's Constructivism
In contrast to other constructivist schools, for Brouwer, the notion of
"constructive object" is not restricted to be presented as `words' in some
finite alphabet of symbols, and choice sequences which are non-predetermined
and unfinished objects are legitimate constructive objects. In this way,
Brouwer's constructivism goes beyond Turing computability. Further, in 1999,
the term hypercomputation was introduced by J. Copeland. Hypercomputation
refers to models of computation which go beyond Church-Turing thesis. In this
paper, we propose a hypercomputation called persistently evolutionary Turing
machines based on Brouwer's notion of being constructive.Comment: This paper has been withdrawn by the author due to crucial errors in
theorems 4.6 and 5.2 and definition 4.
On Completeness of Cost Metrics and Meta-Search Algorithms in \$-Calculus
In the paper we define three new complexity classes for Turing Machine
undecidable problems inspired by the famous Cook/Levin's NP-complete complexity
class for intractable problems. These are U-complete (Universal complete),
D-complete (Diagonalization complete) and H-complete (Hypercomputation
complete) classes. We started the population process of these new classes. We
justify that some super-Turing models of computation, i.e., models going beyond
Turing machines, are tremendously expressive and they allow to accept arbitrary
languages over a given alphabet including those undecidable ones. We prove also
that one of such super-Turing models of computation -- the \$-Calculus,
designed as a tool for automatic problem solving and automatic programming, has
also such tremendous expressiveness. We investigate also completeness of cost
metrics and meta-search algorithms in \$-calculus
Compact Adaptively Secure ABE from k-Lin: Beyond NC1 and towards NL
We present a new general framework for constructing compact and adaptively secure attribute-based encryption (ABE) schemes from -Lin in asymmetric bilinear pairing groups. Previously, the only construction [Kowalczyk and Wee, Eurocrypt \u2719] that simultaneously achieves compactness and adaptive security from static assumptions supports policies represented by Boolean formulae. Our framework enables supporting more expressive policies represented by arithmetic branching programs.
Our framework extends to ABE for policies represented by uniform models of computation such as Turing machines. Such policies enjoy the feature of being applicable to attributes of arbitrary lengths. We obtain the first compact adaptively secure ABE for deterministic and non-deterministic finite automata (DFA and NFA) from -Lin, previously unknown from any static assumptions. Beyond finite automata, we obtain the first ABE for large classes of uniform computation, captured by deterministic and non-deterministic logspace Turing machines (the complexity classes and ) based on -Lin. Our ABE scheme has compact secret keys of size linear in the description size of the Turing machine . The ciphertext size grows linearly in the input length, but also linearly in the time complexity, and exponentially in the space complexity. Irrespective of compactness, we stress that our scheme is the first that supports large classes of Turing machines based solely on standard assumptions. In comparison, previous ABE for general Turing machines all rely on strong primitives related to indistinguishability obfuscation
On the possible Computational Power of the Human Mind
The aim of this paper is to address the question: Can an artificial neural
network (ANN) model be used as a possible characterization of the power of the
human mind? We will discuss what might be the relationship between such a model
and its natural counterpart. A possible characterization of the different power
capabilities of the mind is suggested in terms of the information contained (in
its computational complexity) or achievable by it. Such characterization takes
advantage of recent results based on natural neural networks (NNN) and the
computational power of arbitrary artificial neural networks (ANN). The possible
acceptance of neural networks as the model of the human mind's operation makes
the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of
Liverpool, UK. 23 page
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