PSPACE oor Spaans
PSPACE
Vertalings in die woordeboek Engels - Spaans
ESPACIOP
Geskatte vertalings
Vertoon algoritmies gegenereerde vertalings
voorbeelde
Advanced filtering
Voorbeelde moet herlaai word.
By contrast, generalized games that can last for a number of moves that is polynomial in the size of the board are often PSPACE-complete.
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Note that the definition of PSPACE-completeness is based on asymptotic complexity: the time it takes to solve a problem of size n, in the limit as n grows without bound.
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If such a collapse did occur, we could deduce that P ≠ PSPACE, since it is a well-known theorem that DTIME(f(n)) is strictly contained in DSPACE(f(n)).
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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.
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Not surprisingly, many puzzles turn out to be NP-complete, and many games turn out to be PSPACE-complete.
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An alternative characterization of PSPACE is the set of problems decidable by an alternating Turing machine in polynomial time, sometimes called APTIME or just AP.
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Savitch's theorem establishes that PSPACE = NPSPACE and EXPSPACE = NEXPSPACE.
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Correspondingly, the PSPACE-complete problem there resembles games: is there some move I can make, such that for all moves my opponent might make, there will then be some move I can make to win?
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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).
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The PSPACE-complete problems are widely suspected to be outside the more famous complexity classes P and NP, but that is not known.
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The hardest problems in PSPACE are the PSPACE-Complete problems.
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EXPSPACE is a strict superset of PSPACE, NP, and P and is believed to be a strict superset of EXPTIME.
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This places it in the important complexity class PSPACE.
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It is widely believed that PSPACE-complete problems are strictly harder than any problem in NP, although this has not yet been proved.
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If both quantifiers are allowed, the problem is called the quantified Boolean formula problem (QBF), which can be shown to be PSPACE-complete.
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Any cryptosystem that uses pspace algorithms, which is essentially their entire infrastructure, could easily be accessed.
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A major result of complexity theory is that PSPACE can be characterized as all the languages recognizable by a particular interactive proof system, the one defining the class IP.
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Examples of games that are PSPACE-complete (when generalized so that they can be played on an n × n board) are the games Hex and Reversi and the solitaire games Rush Hour, Mahjong, Atomix, and Sokoban.
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The PSPACE-hardness of robot motion planning was shown in a seminal paper by Reif (1979).
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This is supposed to be hard, at least PSPACE-complete.
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Membership of a string in a language defined by an arbitrary context-sensitive grammar, or by an arbitrary deterministic context-sensitive grammar, is a PSPACE-complete problem.
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L is strictly contained in PSPACE.
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See Game complexity for more games whose completeness for PSPACE or other complexity classes has been determined.
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However, the time hierarchy theorems provide no means to relate deterministic and non-deterministic complexity, or time and space complexity, so they cast no light on the great unsolved questions of computational complexity theory: whether P and NP, NP and PSPACE, PSPACE and EXPTIME, or EXPTIME and NEXPTIME are equal or not.
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Bylander (1992) shows simple STRIPS planning to be PSPACE-complete.
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