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Pspace is an English word. Below you'll find 10+ example sentences showing how it's used in practice.

Rare word

Pspace in a sentence

Pspace meaning

The set of all decision problems that can be solved by a Turing machine using an amount of memory which is a polynomial function of the input size.

Using Pspace

  • The main meaning on this page is: The set of all decision problems that can be solved by a Turing machine using an amount of memory which is a polynomial function of the input size.
  • In the example corpus, pspace often appears in combinations such as: in pspace, to pspace, pspace -complete.

Context around Pspace

  • Average sentence length in these examples: 22.9 words
  • Position in the sentence: 5 start, 8 middle, 3 end
  • Sentence types: 16 statements, 0 questions, 0 exclamations

Often before:

become 1× class 1× few 1×

Often after:

complete 11× problems 1× machine 1× either 1×

Sentence patterns with Pspace

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

to a pspace complete problem 2× a few pspace complete problems 1× are in pspace 1× are the pspace complete problems 1× because all pspace problems could 1× believed that pspace complete problems 1× characterization of pspace from descriptive 1× completeness for pspace or other 1×

Sentence openings and endings

Common sentence openings:

arora barak 2009 1× closure properties the 1× examples below are 1× finding a simple 1× in 1970 savitch 1× in other words 1×

Common sentence endings:

pspace complete problems 2× and kleene star 1× are in pspace 1× are pspace complete 1× bit more technical 1× e g citation 1×

Words around Pspace

Just before it in the word index:

psp 79 psovaya 3 psos 9 psoriatic 8 psoriasis 61 psophometric 2

Just after it in the word index:

pspc 8 pspca 2 pspcl 8 pspo 32 pspos 12 pspp 3

Similar in corpus frequency:

abad 22 abolishment 22 abr 22 abyad 22 accompanist 22 achmea 22

Corpus analysis for Pspace

  • In this selection, "pspace" usually appears in the middle of the sentence. The average example has 22.9 words, and this corpus slice is mostly made up of statements.
  • Around the word, become, class, few, complete, problems and machine stand out and add context to how "pspace" is used.
  • Recognizable usage signals include to a pspace complete problem and a few pspace complete problems. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "pspace" sits close to words such as abad, abolishment and abr, which helps place it inside the broader word index.

Example types with pspace

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

The hardest problems in PSPACE are the PSPACE-Complete problems. (10 words)

Examples Below are descriptions of a few PSPACE-complete problems. (10 words)

More precisely, this language is PSPACE-complete ; see e.g. citation. (11 words)

Longer example sentences

That means a finite game like checkers (which is played on an 8 8 board) could never be PSPACE-complete, since they can be solved in constant time and space using a very large lookup table (checkers is already solved in this way). (43 words)

In other words, there is a context-sensitive grammar G such that deciding whether a certain string s belongs to the language of G is PSPACE-complete (so G is fixed and only s is part of the input of the problem). (42 words)

Arora & Barak (2009) p.100 A logical characterization of PSPACE from descriptive complexity theory is that it is the set of problems expressible in second-order logic with the addition of a transitive closure operator. (35 words)

Example sentences (16)

Finding a simple solution to a PSPACE -complete problem would mean we have a simple solution to all other problems in PSPACE because all PSPACE problems could be reduced to a PSPACE -complete problem.

In 1970, Savitch's theorem showed that PSPACE is closed under nondeterminism, implying that even non-deterministic context-sensitive grammars are in PSPACE.

NP is contained in PSPACE —to show this, it suffices to construct a PSPACE machine that loops over all proof strings and feeds each one to a polynomial-time verifier.

The hardest problems in PSPACE are the PSPACE-Complete problems.

Arora & Barak (2009) p.100 A logical characterization of PSPACE from descriptive complexity theory is that it is the set of problems expressible in second-order logic with the addition of a transitive closure operator.

But they will become PSPACE-complete if a polynomial bound on the number of moves is enforced.

Closure properties The class PSPACE is closed under operations union, complementation, and Kleene star.

Examples Below are descriptions of a few PSPACE-complete problems.

Advertentie

If P is not equal to NP, then P is not equal to PSPACE either.

In other words, there is a context-sensitive grammar G such that deciding whether a certain string s belongs to the language of G is PSPACE-complete (so G is fixed and only s is part of the input of the problem).

It is widely believed that PSPACE-complete problems are strictly harder than any problem in NP, although this has not yet been proved.

More precisely, this language is PSPACE-complete ; see e.g. citation.

Morever, there are context-sensitive grammars whose languages are PSPACE-complete.

See Game complexity for more games whose completeness for PSPACE or other complexity classes has been determined.

That means a finite game like checkers (which is played on an 8 8 board) could never be PSPACE-complete, since they can be solved in constant time and space using a very large lookup table (checkers is already solved in this way).

The proof that QBF is a PSPACE-complete problem is essentially a restatement of the proof of Savitch's theorem in the language of logic, and is a bit more technical.

Advertentie

Common combinations with pspace

These word pairs occur most frequently in English texts:

  • in pspace 5×
  • to pspace 3×
  • pspace -complete 3×
  • pspace is 2×
  • of pspace 2×

Frequently asked questions

How do you use "pspace" in a sentence?
An example: "Finding a simple solution to a PSPACE -complete problem would mean we have a simple solution to all other problems in PSPACE because all PSPACE problems could be reduced to a PSPACE -complete problem." This page contains 10+ example sentences with the word "pspace" from authentic English texts.
What does "pspace" mean?
Pspace means: The set of all decision problems that can be solved by a Turing machine using an amount of memory which is a polynomial function of the input size.
How many example sentences with "pspace" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "pspace", drawn from a database of millions of English sentences.