3,406 research outputs found
Addressing Machines as models of lambda-calculus
Turing machines and register machines have been used for decades in
theoretical computer science as abstract models of computation. Also the
-calculus has played a central role in this domain as it allows to
focus on the notion of functional computation, based on the substitution
mechanism, while abstracting away from implementation details. The present
article starts from the observation that the equivalence between these
formalisms is based on the Church-Turing Thesis rather than an actual encoding
of -terms into Turing (or register) machines. The reason is that these
machines are not well-suited for modelling \lam-calculus programs.
We study a class of abstract machines that we call \emph{addressing machine}
since they are only able to manipulate memory addresses of other machines. The
operations performed by these machines are very elementary: load an address in
a register, apply a machine to another one via their addresses, and call the
address of another machine. We endow addressing machines with an operational
semantics based on leftmost reduction and study their behaviour. The set of
addresses of these machines can be easily turned into a combinatory algebra. In
order to obtain a model of the full untyped -calculus, we need to
introduce a rule that bares similarities with the -rule and the rule
from combinatory logic
The Mode of Computing
The Turing Machine is the paradigmatic case of computing machines, but there
are others, such as Artificial Neural Networks, Table Computing,
Relational-Indeterminate Computing and diverse forms of analogical computing,
each of which based on a particular underlying intuition of the phenomenon of
computing. This variety can be captured in terms of system levels,
re-interpreting and generalizing Newell's hierarchy, which includes the
knowledge level at the top and the symbol level immediately below it. In this
re-interpretation the knowledge level consists of human knowledge and the
symbol level is generalized into a new level that here is called The Mode of
Computing. Natural computing performed by the brains of humans and non-human
animals with a developed enough neural system should be understood in terms of
a hierarchy of system levels too. By analogy from standard computing machinery
there must be a system level above the neural circuitry levels and directly
below the knowledge level that is named here The mode of Natural Computing. A
central question for Cognition is the characterization of this mode. The Mode
of Computing provides a novel perspective on the phenomena of computing,
interpreting, the representational and non-representational views of cognition,
and consciousness.Comment: 35 pages, 8 figure
On Modelling and Analysis of Dynamic Reconfiguration of Dependable Real-Time Systems
This paper motivates the need for a formalism for the modelling and analysis
of dynamic reconfiguration of dependable real-time systems. We present
requirements that the formalism must meet, and use these to evaluate well
established formalisms and two process algebras that we have been developing,
namely, Webpi and CCSdp. A simple case study is developed to illustrate the
modelling power of these two formalisms. The paper shows how Webpi and CCSdp
represent a significant step forward in modelling adaptive and dependable
real-time systems.Comment: Presented and published at DEPEND 201
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
The impossibility of an effective theory of policy in a complex economy
theory of policy,dynamical system,computation universality,recursive rule,complex economy
A Primer on the Tools and Concepts of Computable Economics
Computability theory came into being as a result of Hilbert's attempts to meet Brouwer's challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, constructive mathematics should be one vision of computability theory. However, there are fundamental differences between computability theory and constructive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economic an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formalization of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. The context is that of a digital economy embedded in an information society
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