Unlike finite-state machines, there exists no general algorithm of turning a NPDA into an equivalent DPDA if it exists, because that is the problem of determining whether a context-free language is deterministic, which is not decidable.

Suppose that the set of indices such that is decidable ; then, there exists a function that returns if, and otherwise.

In mathematics, logic and computer science, a formal language is called recursively enumerable ( also recognizable, partially decidable or Turing-acceptable ) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i. e., if there exists a Turing machine which will enumerate all valid strings of the language.

BAN logic, and logics in the same family, are decidable: there exists an algorithm taking BAN hypotheses and a purported conclusion, and that answers whether or not the conclusion is derivable from the hypotheses.

The space hierarchy theorem shows that, for every space-constructible function, there exists some language L which is decidable in space but not in space.

For every space-constructible function, there exists a language that is decidable in space

The specific question of aperiodic tiling first arose in 1961, when logician Hao Wang tried to determine whether the Domino Problem is decidable — that is, whether there exists an algorithm for deciding if a given finite set of prototiles admits a tiling of the plane.

This form has all universal quantifiers preceding any existential quantifiers, so that all sentences can be recast in the form This fact allowed Tarski to prove that Euclidean geometry is decidable: there exists an algorithm which can determine the truth or falsity of any sentence.

In 1929, Mojżesz Presburger showed that the theory of natural numbers with addition and equality ( now called Presburger arithmetic in his honor ) is decidable and gave an algorithm that could determine if a given sentence in the language was true or false.

A decision problem which can be solved by an algorithm, such as this example, is called decidable.

In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set.

For example, Tarski found an algorithm that can decide the truth of any statement in analytic geometry ( more precisely, he proved that the theory of real closed fields is decidable ).

In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas, or, more precisely, an algorithm that can and will return a Boolean true or false value ( instead of looping indefinitely ).

A proof of x = y is simply the trivial algorithm if x evaluates to the same number that y does ( which is always decidable for natural numbers ), otherwise there is no proof.

Questions about the provability of statements are represented as questions about the properties of numbers, which would be decidable by the theory if it were complete.

Equivalently, NC can be defined as those decision problems decidable by a uniform Boolean circuit ( which can be calculated from the length of the input ) with polylogarithmic depth and a polynomial number of gates.

Peano arithmetic, which is Presburger arithmetic augmented with multiplication, is not decidable, as a consequence of the negative answer to the Entscheidungsproblem.

The pure-group languages were the first interesting family of regular languages for which the star height problem was proved to be decidable.

An application of this notion is the decidability question: it follows from Post's theorem that a recursively axiomatized modal logic L which has FMP is decidable, provided it is decidable whether a given finite frame is a model of L. In particular, every finitely axiomatizable logic with FMP is decidable.

Questions about the provability of statements are represented as questions about the properties of numbers, which would be decidable by the theory if it were complete.

* Structure of the program: Locality occurs often because of the way in which computer programs are created, for handling decidable problems.

The word decidable stems from the German word Entscheidungsproblem which was used in the original papers of Turing and others.

* A formula A of the language of arithmetic is decidable if it represents a decidable set, i. e. if there is an effective method which, given a substitution of the free variables of A, says that either the resulting instance of A is provable or its negation is.

* In a Chemical Reaction Network ( a finite set of reactions like A + B → 2C + D operating on a finite number of molecules ), the ability to ever reach a given target state from an initial state is decidable, while even approximating the probability of ever reaching a given target state ( using the standard concentration-based probability for which reaction will occur next ) is undecidable.

A generalization of P is NP, which is the class of decision problems decidable by a non-deterministic Turing machine that runs in polynomial time.

L is a subclass of NL, which is the class of languages decidable in logarithmic space on a nondeterministic Turing machine.

State reachability is decidable for this sub-class, which is why it is an interesting formalism for formal verification.

These fragments of Q remain undecidable, but they are no longer essentially undecidable: they have consistent decidable extensions, as well as uninteresting models ( i. e., models which are not end-extensions of the standard natural numbers ).

For example, whether a machine runs for more than 100 steps on some input is a decidable property, even though it is non-trivial.

Similarly, whether a machine has more than 5 states is a decidable property of the machine, as the number of states can simply be counted.

Nevertheless it is decidable whether an equation holds of all Heyting algebras.

Therefore in a given case it is decidable whether or not the reduction is semistable, namely multiplicative reduction at worst.

A theory ( set of formulas closed under logical consequence ) in a fixed logical system is decidable if there is an effective method for determining whether arbitrary formulas are included in the theory.

A logical system is decidable if there is an effective method for determining whether arbitrary formulas are theorems of the logical system.

For example, propositional logic is decidable, because the truth-table method can be used to determine whether an arbitrary propositional formula is logically valid.

It might seem that the potentially infinite memory capacity is an unrealizable attribute, but any decidable problem solved by a Turing machine will always require only a finite amount of memory.

Moreover, any axiomatizable and complete theory is decidable.

Turing machines can decide any context-free language, in addition to languages not decidable by a push-down automaton, such as the language consisting of prime numbers.

Indeed, the proof that a logical system or theory is undecidable will use the formal definition of computability to show that an appropriate set is not a decidable set, and then invoke Church's thesis to show that the theory or logical system is not decidable by any effective method ( Enderton 2001, pp. 206ff.

First-order logic is not decidable in general ; in particular, the set of logical validities in any signature that includes equality and at least one other predicate with two or more arguments is not decidable ( provided the finitely axiomatizable theory Robinson Arithmetic is consistent ; this provison is implicit in every undecidability claim made in this article ).

A set of natural numbers is called computable ( synonyms: recursive, decidable ) if there is a computable, total function such that for any natural number, if is in and if is not in.