A Formalization and Proof of the Extended Church-Turing Thesis -Extended Abstract-
نویسندگان
چکیده
منابع مشابه
A Formalization and Proof of the Extended Church-Turing Thesis
One of the important parameters in the description of a modern algorithm is its complexity, or—more precisely—the complexity class it belongs to. To determine the latter, one counts the number of steps required by the algorithm to perform the calculation, relative to input size. That, of course, means that the analysis is sensitive to the chosen measure of the domain elements and to the definit...
متن کاملA Formalization and Proof of the Extended Church-Turing Thesis -Extended Abstract-
state machines (ASMs) [7, 8, 5] provide a perfect language for descriptions of algorithmic transition functions. They consist of generalized assignment statements f (s1, . . . ,sk) := u, conditional tests if C then P or if C then P else Q, where C is a Boolean combination of equations between terms, and parallel composition. A program as such defines a single transition; it is executed repeated...
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Our goal is to formalize the Church-Turing Thesis for a very large class of computational models. Specifically, the notion of an “effective model of computation” over an arbitrary countable domain is axiomatized. This is accomplished by modifying Gurevich’s “Abstract State Machine” postulates for state-transition models. A proof is provided that all models satisfying these axioms, regardless of...
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We show that a random-access machine (RAM) can simulate any effective algorithm with only constant overhead of time, thereby supporting the Extended Church-Turing Thesis.
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cell containing a left end marker ` (never written over) and extends to infinitely many cells to the right. This machine has a head that can move left or right one cell in each step, and in each step it reads the current symbol it is currently scanning and overwrites it before moving on. Initally, the tape contains the input string, which is finite, on cells numbered 1 onwards (cell 0 contains ...
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ژورنال
عنوان ژورنال: Electronic Proceedings in Theoretical Computer Science
سال: 2012
ISSN: 2075-2180
DOI: 10.4204/eptcs.88.6