منابع مشابه
Non-Turing Computers and Non-Turing Computability*
Various examples of Malament-Hogarth (hereafter, M-H) spacetimes are given in Hogarth (1992), but the following artificial example from Earman and Norton (1993) is perhaps the simplest. Start with Minkowski spacetime (R4, η) and choose a scalar field Ω on M such that Ω=1 outside a compact set C⊂M and Ω tends rapidly to infinity as a point r∈C is approached. The spacetime (R4-r, Ω2η), depicted i...
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In contrast to most kinds of computability studied in mathematical logic, feedback computability has a non-degenerate notion of parallelism. Here we study parallelism for the most basic kind of feedback, namely that of Turing computability. We investigate several different possible definitions of parallelism in this context, with an eye toward specifying what is so computable. For the determini...
متن کاملTuring and Post on Computability
[Turing then gives his formal definitions and in particular says that for a real number or function on the natural numbers to be computable it must be computable by amachine that gives an output for every input.] No attempt has yet been made to show that the "computable" numbers include all numbers which would naturally be regarded as computable. All arguments which can be given are bound to be...
متن کاملDice games and Arrows theorem
We observe that non-transitivity is not the most general way that Arrows impossibility theorem is reected in dice games. Non-transitivity in dice games is a well-known phenomenon. It was described in several Scienti c American columns in the 1970s, beginning with [3], and has since become a popular topic, discussed in articles like [4, 5] and textbooks on elementary mathematics and probabilit...
متن کاملGödel on Turing on Computability
In section 9 of his paper, “On Computable Numbers,” Alan Turing outlined an argument for his version of what is now known as the Church–Turing thesis: “the [Turing machine] ‘computable’ numbers include all numbers which would naturally be regarded as computable” [p. 135]. The argument, which relies on an analysis of calculation by an (ideal) human, has attracted much attention in recent years. ...
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ژورنال
عنوان ژورنال: Economic Theory
سال: 1997
ISSN: 0938-2259,1432-0479
DOI: 10.1007/s001990050157