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On this page you'll find 10+ example sentences with Undecidable. Discover the meaning, how to use the word correctly in a sentence.

Rare word

Undecidable in a sentence

Undecidable meaning

  1. Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
  2. (of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)

Using Undecidable

  • The main meaning on this page is: Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included. | (of a WFF) logically independent from the axioms of a given theory; i.e., that it can never be either proved or disproved (i.e., have its negation proved) on the basis of the axioms of the given theory. (Note: this latter definition is independent of any time bounds or computability issues, i.e., more Platonic.)
  • In the example corpus, undecidable often appears in combinations such as: is undecidable, undecidable in, be undecidable.

Context around Undecidable

  • Average sentence length in these examples: 24.8 words
  • Position in the sentence: 3 start, 12 middle, 5 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

formally 2× word 1× see 1× provably 1×

Often after:

questions 2× problem 1× statements 1× sentence 1× meaning 1× propositions 1×

Sentence patterns with Undecidable

These short patterns come directly from the example sentences and show how the word is often embedded:

1 is undecidable by representing 1× are formally undecidable questions about 1× functions is undecidable the class 1× hypothesis is undecidable and it 1× instead of undecidable for the 1× investigated is undecidable in the 1× is provably undecidable and so 1× it is undecidable 1×

Sentence openings and endings

Common sentence openings:

conway proved that 1× douglas s robertson 1× for example rice 1× for instance first 1× gödel s paper 1× he went on 1×

Common sentence endings:

algorithm is impossible 1× always parse perl 1× and its complement 1× axiom is canonical 1× be undecidable i 1× but undecidable sentence 1×

Words around Undecidable

Just before it in the word index:

undecidability 5 undeceived 2 undeceive 1 undebated 2 undebatable 2 undead 160

Just after it in the word index:

undecided 244 undecideds 7 undecipherable 3 undeciphered 3 undeclared 90 undecodable 2

Similar in corpus frequency:

ablation 39 abure 39 abvp 39 acheampong 39 adieu 39 adjectival 39

Corpus analysis for Undecidable

  • In this selection, "undecidable" usually appears in the middle of the sentence. The average example has 24.8 words, and this corpus slice is mostly made up of statements.
  • Around the word, formally, word, see, questions, problem and statements stand out and add context to how "undecidable" is used.
  • Recognizable usage signals include 1 is undecidable by representing and are formally undecidable questions about. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "undecidable" sits close to words such as ablation, abure and abvp, which helps place it inside the broader word index.

Example types with undecidable

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

However, many problems are undecidable even for context-free grammars. (10 words)

In general, it is undecidable whether a given axiom is canonical. (11 words)

As with many undecidable questions, one can still attempt to give useful approximate solutions. (14 words)

Longer example sentences

He went on to prove that there was no solution to the decision problem by first showing that the halting problem for Turing machines is undecidable : It is not possible to decide algorithmically whether a Turing machine will ever halt. (40 words)

It follows that an automated theorem prover will fail to terminate while searching for a proof precisely when the statement being investigated is undecidable in the theory being used, even if it is true in the model of interest. (39 words)

Gödel's paper was published in the Monatshefte in 1931 under the title Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I ( On Formally Undecidable Propositions in Principia Mathematica and Related Systems I ). (35 words)

Example sentences (20)

Because of the two meanings of the word undecidable, the term independent is sometimes used instead of undecidable for the "neither provable nor refutable" sense.

Such a problem is said to be undecidable if there is no computable function that correctly answers every question in the problem set (see undecidable problem ).

Undecidable statements provable in larger systems These are natural mathematical equivalents of the Gödel "true but undecidable" sentence.

As with many undecidable questions, one can still attempt to give useful approximate solutions.

Conway proved that the problem: : Given g and n, does the sequence of iterates reach 1? is undecidable, by representing the halting problem in this way.

Douglas S. Robertson offers Conway's game of life as an example: citation The underlying rules are simple and complete, but there are formally undecidable questions about the game's behaviors.

For example, Rice's theorem shows that each of the following sets of computable functions is undecidable: * The class of computable functions that return 0 for every input, and its complement.

For instance, first-order logic is undecidable, meaning a sound, complete and terminating decision algorithm is impossible.

Advertentie

Gödel's paper was published in the Monatshefte in 1931 under the title Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I ( On Formally Undecidable Propositions in Principia Mathematica and Related Systems I ).

He went on to prove that there was no solution to the decision problem by first showing that the halting problem for Turing machines is undecidable : It is not possible to decide algorithmically whether a Turing machine will ever halt.

However, given a grammar, the problem of determining if there exists a parser for some that recognizes it is undecidable.

However, many problems are undecidable even for context-free grammars.

However the halting problem is provably undecidable and so such an algorithm does not exist.

In 1973, Saharon Shelah showed that the Whitehead problem in group theory is undecidable, in the first sense of the term, in standard set theory.

In general, it is undecidable whether a given axiom is canonical.

In the following table, Turing's original model allowed only the first three lines that he called N1, N2, N3 (cf Turing in Undecidable, p. 126).

In this sense, the continuum hypothesis is undecidable, and it is the most widely known example of a natural statement that is independent from the standard ZF axioms of set theory.

It follows that an automated theorem prover will fail to terminate while searching for a proof precisely when the statement being investigated is undecidable in the theory being used, even if it is true in the model of interest.

It is a long-standing result that the halting problem is undecidable, and therefore not even perl can always parse Perl.

Kleene's definition of "general recursion" (known now as mu-recursion) was used by Church in his 1935 paper An Unsolvable Problem of Elementary Number Theory that proved the "decision problem" to be "undecidable" (i.

Advertentie

Common combinations with undecidable

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "undecidable" in a sentence?
An example: "Because of the two meanings of the word undecidable, the term independent is sometimes used instead of undecidable for the "neither provable nor refutable" sense." This page contains 10+ example sentences with the word "undecidable" from authentic English texts.
What does "undecidable" mean?
Undecidable means: Incapable of being algorithmically decided in finite time. For example, a set of strings is undecidable if it is impossible to program a computer (even one with infinite memory) to determine whether or not specified strings are included.
How many example sentences with "undecidable" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "undecidable", drawn from a database of millions of English sentences.