Examples of using Computability theory in English and their translations into Serbian
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Computability theory for digital computation is well developed.
Computable functions are the basic objects of study in computability theory.
Research in computability theory has typically focused on decision problems.
Many mathematicians andcomputational theorists who study recursion theory will refer to it as computability theory.
In computability theory in computer science, it is common to consider formal languages.
Therefore, formal language theory is a major application area of computability theory and complexity theory. .
Computability theory proves that these recursive-only languages are Turing complete;
Robert I. Soare, a prominent researcher in the field, has proposed(Soare 1996)that the field should be called"computability theory" instead.
In computability theory, the halting problem is a decision problem which can be stated as follows.
According to Gregory Chaitin,it is"the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously.".
In computability theory in computer science, it is common to consider formal languages.
Technically, the breakdown into decidable andundecidable pertains more to the study of computability theory but is useful for putting the complexity classes in perspective.
Computability theory deals primarily with the question of the extent to which a problem is solvable on a computer.
It[algorithmic information theory] is the result of putting Shannon's information theory and Turing's computability theory into a cocktail shaker and shaking vigorously.".
Reductions are also used in computability theory to show whether problems are or are not solvable by machines at all;
This contrasts with the theory of subrecursive hierarchies, formal methods andformal languages that is common in the study of computability theory in computer science.
Mortality(computability theory), a property of a Turing machine if it halts when run on any starting configuration.
The statement that the halting problem cannot be solved by a Turing machine is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine.
In computability theory, a machine that always halts, also called a decider or a total Turing machine, is a Turing machine that eventually halts for every input.
A cellular automaton is a discrete model studied in computability theory, mathematics, physics, complexity science, theoretical biology and microstructure modelling.
Computability theory is closely related to the branch of mathematical logic called recursion theory, which removes the restriction of studying only models of computation which are close to physically realizable.
Some commentators argue that both the names recursion theory and computability theory fail to convey the fact that most of the objects studied in recursion theory are not computable.
The computability theory is closely related to branch of the mathematical logic called the recursion theory, which removes restriction of studying only models of the computation which are reducible to Turing model.
This point of view relies on the history of computability theory(degrees of unsolvability,computability over functions, real numbers and ordinals), as also mentioned above.
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct a single algorithm that always leads to a correct yes-or-no answer….
The second sense, which will not be discussed here, is used in relation to computability theory and applies not to statements but to decision problems, which are countably infinite sets of questions each requiring a yes or no answer.
Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.
The halting problem is one of the most important results in computability theory, as it is an example of a concrete problem that is both easy to formulate and impossible to solve using a Turing machine.
Computability theory is less well developed for analog computation that occurs in analog computers, analog signal processing, analog electronics, neural networks and continuous-time control theory, modelled by differential equations and continuous dynamical systems(Orponen 1997; Moore 1996).
The second sense is used in relation to computability theory and applies not to statements but to decision problems, which are countably infinite sets of questions each requiring a yes or no answer.