3,513 research outputs found
Computation Environments, An Interactive Semantics for Turing Machines (which P is not equal to NP considering it)
To scrutinize notions of computation and time complexity, we introduce and
formally define an interactive model for computation that we call it the
\emph{computation environment}. A computation environment consists of two main
parts: i) a universal processor and ii) a computist who uses the computability
power of the universal processor to perform effective procedures. The notion of
computation finds it meaning, for the computist, through his
\underline{interaction} with the universal processor.
We are interested in those computation environments which can be considered
as alternative for the real computation environment that the human being is its
computist. These computation environments must have two properties: 1- being
physically plausible, and 2- being enough powerful.
Based on Copeland' criteria for effective procedures, we define what a
\emph{physically plausible} computation environment is.
We construct two \emph{physically plausible} and \emph{enough powerful}
computation environments: 1- the Turing computation environment, denoted by
, and 2- a persistently evolutionary computation environment, denoted by
, which persistently evolve in the course of executing the computations.
We prove that the equality of complexity classes and
in the computation environment conflicts with the
\underline{free will} of the computist.
We provide an axiomatic system for Turing computability and
prove that ignoring just one of the axiom of , it would not be
possible to derive from the rest of axioms.
We prove that the computist who lives inside the environment , can never
be confident that whether he lives in a static environment or a persistently
evolutionary one.Comment: 33 pages, interactive computation, P vs N
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.
A Projective Simulation Scheme for Partially-Observable Multi-Agent Systems
We introduce a kind of partial observability to the projective simulation
(PS) learning method. It is done by adding a belief projection operator and an
observability parameter to the original framework of the efficiency of the PS
model. I provide theoretical formulations, network representations, and
situated scenarios derived from the invasion toy problem as a starting point
for some multi-agent PS models.Comment: 28 pages, 21 figure
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