A Formalization and Proof of the Extended Church-Turing Thesis -Extended Abstract-
نویسندگان
چکیده
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 repeatedly, as a unit, until no assignments have their conditions are enabled. If no assignments are enabled, then there is no next state. A triplet 〈M ,S,S0〉 is called abstract state machine (ASM) if S0 are initial states and S are states of an ASM program M , such that 〈M ,S,S0〉 satisfy the conditions for being an algorithm given in Definition 1. Every algorithm is emulated step-by step, state-by-state by an ASM. Theorem 8 ([8]). Let 〈τ ,S,S0〉 be an algorithm over vocabulary F. Then there exists an ASM 〈M ,S,S0〉 over the same vocabulary, such that τ = M ↾S, with the terms (and subterms) appearing in the ASM program serving as critical terms. Definition 9 (ESM). An effective state machine (ESM) is an effective implementation of an ASM M . Constructors are part and parcel of the states, though they need not appear in an ESM program. 76 Extended Church-Turing Thesis
منابع مشابه
A Formalization of the Church-Turing Thesis
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...
متن کاملA 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 of the Church-Turing Thesis for State-Transition Models
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 statetransition systems. A proof is provided that all models satisfying our axioms, regardless of u...
متن کاملRandom-Access Machines and the Extended Church-Turing Thesis
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.
متن کامل