Epimenides, Gödel, Turing: an Eternal Gölden Tangle
نویسنده
چکیده
The Halting Problem is a version of the Liar's Paradox.
منابع مشابه
Gödel on computability * Wilfried
The identification of an informal concept of “effective calculability”with a rigorous mathematical notion like “recursiveness” or “Turingcomputability” is still viewed as problematic, and I think rightly so. I analyzethree different and conflicting perspectives Gödel articulated in the three decadesfrom 1934 to 1964. The significant shifts in Gödel's position underline thedi...
متن کاملAn Effective Procedure for Computing "Uncomputable" Functions
We give an effective procedure that produces a natural number in its output from any natural number in its input, that is, it computes a total function. The elementary operations of the procedure are Turingcomputable. The procedure has a second input which can contain the Gödel number of any Turing-computable total function whose range is a subset of the set of the Gödel numbers of all Turing-c...
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. ...
متن کاملModels of Computation Lecture : Turing Machines [fa''']
Although Turing did not know it at the time, he was not the first to prove that the Entscheidungsproblem had no algorithmic solution. The first such proof is implicit in the work of Kurt Gödel; in lectures on his incompleteness theorems2 at Princeton in 1934, Gödel described a model of general recursive functions, which he largely credited to Jacques Herbrand.3 Gödel’s incompleteness theorem ca...
متن کاملInformal Physical Reasoning Processes
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the application of any Turing-computable function to this Turing program. The existence principle overcomes the limitation of the outputs of Turing machines to li...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1606.08722 شماره
صفحات -
تاریخ انتشار 2016