Primjeri korištenja Computable na Engleski i njihovi prijevodi na Hrvatskom
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In practice, many functions of interest are computable by machines that always halt.
An integer sequence is a computable sequence, if there exists an algorithm which given n, calculates an, for all n> 0.
Computational complexity theory deals with the relative computational difficulty of computable functions.
Then he assumes that this predicate is computable, and can hence be expressed in lambda calculus.
All this is a computable fact if we look at the total cost of heating systems that include maintenance, consumption, useful life and investment.
Turing's toy computer had turned out to be universal-simple as it was, it could be programmed to compute anything that was computable at all.
If g were a total computable function extending f then g would be computable by some Turing machine; fix e as the index of such a machine.
The development of geomatics led to geography being reunited, as the complexities of the human andnatural environments could be assessed on new computable models.
A recursively enumerable language is a formal language for which there exists a Turing machine(or other computable function) which will enumerate all valid strings of the language.
The second question asks, in essence, whether there is another reasonable model of computation which computes only total functions and computes all the total computable functions.
For three distinct and complete achievements: 1 LCF,the mechanization of Scott's Logic of Computable Functions, probably the first theoretically based yet practical tool for machine assisted proof construction;
S and K can be composed to produce combinators that are extensionally equal to any lambda term, and therefore,by Church's thesis, to any computable function whatsoever.
The following theorem shows that the functions computable by machines that always halt do not include extensions of all partial computable functions, which implies the first question above has a negative answer.
To some extent, the development of geomatics helped obscure the binary between physical and human geography to some extent, as the complexities of the human andnatural environments could be assessed on new computable models.
Indeed, PCF(for Programming language for Computable Functions) is a prototypical, typed functional programming language, where types are used to ensure that programs are well-behaved but not necessarily terminating.
Two questions can be asked about the relationship between partial Turing machines and total Turing machines: Can every partial function computable by a partial Turing machine be extended(that is, have its domain enlarged)to become a total computable function?
A function F: N→ N of natural numbers is a computable function if and only if there exists a lambda expression f such that for every pair of x, y in N, F(x)=y if and only if f x=β y, where x and y are the Church numerals corresponding to x and y, respectively and=β meaning equivalence with beta reduction.
Thus if this new model of computation consisted of a sequence M 1, M 2,…{\displaystyle M_{1}, M_{2},\ldots} of machines, there would be a recursively enumerable sequence T 1,… T 2,…{\displaystyle T_{1},\ldots T_{2},\ldots}of Turing machines that compute total functions and so that every total computable function is computable by one of the machines Ti.
A recursively enumerable language is a formal language for which there exists a Turing machine(or other computable function) that will halt and accept when presented with any string in the language as input but may either halt and reject or loop forever when presented with a string not in the language.
The arithmetical hierarchy, degrees of computability, computable ordinals and hyperarithmetic theory, finite automata and regular sets with enormous consequences for computer science, computability on higher types, recursive realizability for intuitionistic arithmetic with consequences for philosophy and for program correctness in computer science.