PSPACE-complete - Factbites

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Topic: PSPACE-complete

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	PSPACE - Wikipedia, the free encyclopedia
		PSPACE is a strict superset of the set of context-sensitive languages.
		A logical characterization of PSPACE is that it is the set of problems expressible in second order logic with the addition of a transitive closure operator.
		In complexity theory the class PSPACE, which equals NPSPACE by Savitch's theorem, is the set of decision problems that can be solved by a deterministic or nondeterministic Turing machine using a polynomial amount of memory and unlimited time.
	en.wikipedia.org /wiki/PSPACE (320 words)

	Complete Problems
		In this presentation, complete problems are defined and the P-complete, NP-complete, and PSPACE-complete problems are discussed.
		A problem Q is complete for C under R-reduction if it is hard for C under R-reductions and is a member of C. Problems are hard for a class if they are as hard to solve as any other problem in the class.
		Complete problems are members of the class for which they are hard.
	www.geocities.com /s2swen/song.html (1657 words)

	308-506 Lecture Notes for 4 Dec 2001
		A language A is defined to be PSPACE complete if it is in PSPACE and for any language B in PSPACE, B is poly-time reducble to A. (As Pascal probably mentioned, all of our completeness results hold if we redefine completeness in terms of log-space or even more restricted reductions.
		We now finish our treatment of PSPACE completeness by revisiting the regular expression inequivalence language REI, consisting of pairs of regular expressions (R,S) such that L(R) and L(S) are not the same language.
		In PSPACE we can examine this tree and evaluate the truth of the statement -- the node for an existential quantifier is labeled true iff one of its children is true, and the node for a universal quantifier if true iff both of its children are true.
	www.cs.mcgill.ca /~barring/notes/21.htm (2798 words)

	Solutions to practice questions for CSCI 6420 exam 2
		That is, NP is a subset of DP and DP is a subset of PSPACE.
		DP is a complexity class that lies between NP and PSPACE.
		To show that PSPACE is a subset of P
	www.cs.ecu.edu /~karl/6420/spr04/solution2.html (1486 words)

	PSPACE-complete - Wikipedia, the free encyclopedia
		A decision problem is in PSPACE-complete if it is in PSPACE, and every problem in PSPACE can be reduced to it in polynomial time.
		Note that the definition of PSPACE-complete is based on asymptotic complexity: the time it takes to solve a problem of size n, in the limit as n grows without bound.
		The problems in PSPACE-complete can be thought of as the hardest problems in PSPACE.
	en.wikipedia.org /wiki/PSPACE-complete (400 words)

	msbean.long.doc
		If B, a PSPACE complete problem, is as difficult or more difficult than any other problem in PSPACE, then any PSPACE problem must be reducible to B, and that reduction must be comparatively simple.
		Proof that TQBF is PSPACE complete TQBF is in PSPACE.
		The tableau method used to prove that SAT is NP-complete doesn’t work here, simply because PSPACE may be bigger than NP, so we don’t know that we’re dealing with problems that can be solved in non-deterministic exponential time, and the tableau might have rows exponential on n.
	www.cs.brown.edu /courses/gs019/lectures/msbean.long.doc (2035 words)

	[12pt,letterpaper] A note on the power of the counting class \#P
		There are three complete problems we will focus on in this article; each problem is complete for one of P, NP, and PSPACE.
		We say a language L is complete for a class iff L is hard for that class, and L is a member of that class.
		In contrast, for problems in PSPACE, their solutions are extremely hard to verify, yet checking that a solution exists is just as hard as it is for the P problems.
	www.cs.cmu.edu /~ryanw/project.html (2259 words)

	Abstracts of Joseph Y. Halpern's Publications
		Porcedure declarations are completely explained in the usual framework of complete partial orders, but cpo's are inadequate for the semantics of blocks, and a new class of store models is developed.
		Finally, a complete axiomatization for deterministic propositional dynamic logic is given, based on the Segerberg axioms for propositional dynamic logic.
		The details of the proof that our axiom system is relatively complete in the sense of Cook may be of independent interest, because we introduce results about expressiveness for programs with higher types that are useful beyond the immediate problem of the language L4.
	www.cs.cornell.edu /home/halpern/abstract.html (17597 words)

	CMPT 652
		PSPACE is the class of problems such that determining whether a given X is a member of the set can be done in polynomial space by a deterministic computation.
		NP is the class of problems such that determining whether a given X is a member of the set can be done in polynomial time by a non-deterministic computation.
		EXPTIME is the class of problems such that determining whether a given X is a member of the set can be done in exponential time by a deterministic computation.
	www.cs.ualberta.ca /~jeffp/cmput652/ModalLogicComplexity.html (752 words)

	Some Algebraic and Geometric Computations in PSPACE
		One of the consequences of this result is that the "Generalized Movers' Problem" in robotics drops from EXPTIME into PSPACE, and is therefore PSPACE-complete by a previous hardness result [Rei].
		We give a PSPACE algorithm for determining the signs of multivariate polynomials at the common zeros of a system of polynomial equations.
		Other geometric problems that also drop into PSPACE include the 3-d Euclidean Shortest Path Problem, and the "2-d Asteroid Avoidance Problem" described in [RS].
	sunsite.berkeley.edu /TechRepPages/CSD-88-439 (284 words)

	EXPTIME
		EXPTIME is known to be a subset of EXPSPACE and a superset of PSPACE, NP-complete, NP, and P.
		That is significant because it is currently unknown which (if any) of those four sets are equal to each other.
		If p(n) is a linear function, the resulting class is often called E, and is obviously a subset of EXPTIME.
	www.theezine.net /e/exptime.html (298 words)

	Computational Complexity of Games and Puzzles
		When a group of stones of one color is completely surrounded by stones of the other color, the surrounded group is removed from the board.
		The arrows eventually block the movement of the queens; the last player to complete a move wins.
		Even and R. Tarjan, A combinatorial problem which is complete in polynomial space, Proc.
	www.ics.uci.edu /~eppstein/cgt/hard.html (2681 words)

	Practice Final Exam Solutions for Comp Sc 341s
		We saw in lecture that TQBF, the set of true quantified boolean formulas, is complete for PSPACE under P-reductions.
		It is in PSPACE because we can search the entire tree of possible settings to the variables using PSPACE (the depth of this tree is bounded by the input size).
		An arbitrary language in PSPACE can be decided by reference to the PATH problem on the exponential-sized configuration graph.
	www.mtholyoke.edu /courses/barring/341/exams/pracfinsol.htm (1378 words)

	Hex
		In a game with complete information, such as chess, both players can predict the effects of their own moves and the winner is often the one who is able to predict most moves.
		The assumption that there is a winning strategy is sound since in all finite games with complete information and no chance events there is a winning strategy if it cannot end in a draw.
		Even and Tarjan showed in 1976 that a generalization of Hex to The Shannon Switching Game (which is Hex, played on an arbitrary graph) does belong to PSPACE and that if Hex is solvable in polynomial time, then any problem in PSPACE (and thus also in NP) is solvable in polynomial time.
	maarup.net /thomas/hex (5616 words)

	Nordic Journal of Computing, Volume 1
		Heuristics for completion in automatic proofs by structural induction.
	www.cs.helsinki.fi /njc/njc1.html (136 words)

	18.txt
		A language L is PSPACE-complete if (i) L is in PSPACE, and (ii) every language A in PSPACE is polytime reducible to L. phi is a true quantified Boolean formula } Thm: TQBF is PSPACE-complete.
		CMPT 308 Lecture 18 (PSPACE completeness) Read: pp.
		(2) To reduce a PSPACE language to TQBF, we define a qbf phi_{c1,c2,t} such that phi_{c1,c2,t} is True iff a given pspace-bounded TM M on a given input w gets from configuration c1 to configuration c2 in at most t steps.
	www.cs.sfu.ca /~kabanets/cmpt308/lectures/18.txt (138 words)

	Local Temporal Logic is Expressively Complete for Cograph Dependence Alphabets
		The main result of the paper shows such an expressive completeness result, if the underlying dependence alphabet is a cograph, i.e., if all traces are series parallel graphs.
		But now the difficult problem is to obtain expressive completeness results with respect to first order logic.
		Moreover, we show that this is the best we can expect in our setting: If the dependence alphabet is not a cograph, then we cannot express all first order properties.
	www.liafa.jussieu.fr /web9/rapportrech/description_en.php?idrapportrech=326 (207 words)

	Undecidability and Intractability in Theoretical Physics
		Certain problems are ``complete'' with respect to PSPACE, so that particular instances of them correspond to arbitrary PSPACE problems.
		[18] To determine whether there is any complete infinite configuration that satisfies a particular predicate (such as being invariant under the CA rule) is in general undecidable[18]: It is equivalent to finding the infinite-time behavior of a universal computer that lays down each row on the lattice in turn.
		The second, denoted PSPACE, are those that can be solved with polynomial storage capacity, but may require exponential time, and so are in practice effectively intractable.
	www.stephenwolfram.com /publications/articles/physics/85-undecidability/2/text.html (2128 words)

	CSCI 6420, Spring 2002
		It requires a generic reduction.) We proved that the generalized geography problem is PSPACE-complete by showing that it is in PSPACE and by reducing TQBF to it.
		We noted that PSPACE is the same as NPSPACE (nondeterministic polynomial space).
		Each of these classes has a natural notion of a complete problem, and each has examples of complete problems.
	www.cs.ecu.edu /~karl/6420/spr02 (975 words)

	Hardness and completeness
		If it is known that the language is both hard for some class X and is also a member of X, then it is called X-complete (i.e., NP-complete, PSPACE-complete, etc.).
		Note that because of this uncertainty regarding P, NP, and PSPACE, one cannot say that a problem is intractable if it is NP-hard or PSPACE-hard; one can, however, if the problem is EXPTIME-hard.
		Let X refer to either P, NP, PSPACE, or EXPTIME.
	msl.cs.uiuc.edu /planning/node314.html (215 words)

	r-kt.html
		Our hardness result for PSPACE gives rise to fairly natural problems that are complete for PSPACE under polynomial-time Turing reductions, but not under logarithmic-space many-one reductions.
		We show that sets consisting of strings of high Kolmogorov complexity provide examples of sets that are complete for several complexity classes under probabilistic and non-uniform reductions.
		These sets are provably not complete under the usual many-one reductions.
	www.cs.wisc.edu /~dieter/Research/r-kt.html (209 words)

	revisn01.txt
		Our hardness result for PSPACE gives rise to fairly natural problems that are complete for PSPACE under poly-time Turing reductions, but not under logspace-many-one reductions.
		We present efficient reductions, showing that these sets are hard and complete for various complexity classes.
		Our hardness results for EXP and PSPACE rely on nonrelativizing proof techniques.
	www.eccc.uni-trier.de /eccc-reports/2002/TR02-028/revisn01.txt (222 words)

	FI Abstracts vol. 58
		The information about the uncertainty of cell states is expressed by an indeterminate X called information variable and its dynamics is investigated by extending CA to CA[X] whose cell states are polynomials in X. For the global configuration of extended CA[X], new notions of completeness and degeneracy are defined and their dynamical properties are investigated.
		A theorem is proved that completeness equals non-degeneracy.
		With respect to the reversibility, we prove that a CA is reversible, if and only if its extension CA[X] preserves the set of complete configurations.
	fi.mimuw.edu.pl /abs58.html (3829 words)

	Model Checking with Finite Complete Prefixes Is PSPACE-complete - Heljanko (ResearchIndex)
		We show that model checking a fixed size formula of several temporal logics, including LTL, CTL, and CTL #, is PSPACE-complete in the size of a finite complete prefix of a 1-safe Petri net.
		The method constructs a finite complete prefix, which can be seen as a symbolic representation of an interleaved reachability graph.
		11 A complete finite prefix for process algebra - Langerak, Brinksma - 1999
	citeseer.lcs.mit.edu /heljanko00model.html (575 words)

	Abstract: PSpace Reasoning with the Description Logic ALCF(D).
		We show that, for both logics, the standard reasoning tasks concept satisfiability, concept subsumption, and ABox consistency are PSpace-complete if the concrete domain D satisfies some natural conditions.
		Abstract: PSpace Reasoning with the Description Logic ALCF(D).
		Description Logics (DLs), a family of formalisms for reasoning about conceptual knowledge, can be extended with concrete domains to allow an adequate representation of "concrete qualities" of real-worlds entities such as their height, temperature, duration, and size.
	lat.inf.tu-dresden.de /~clu/papers/abstracts/igpl02.html (100 words)

	math lessons - PSPACE-Hard
		PSPACE-hardness is distinguished from PSPACE-completeness by the fact that PSPACE-hardness does not require the problem to be in PSPACE.
		A decision problem p is said to be PSPACE-Hard if, given any decision problem q in PSPACE, q can be reduced to p in polynomial time.
	www.mathdaily.com /lessons/PSPACE-Hard (72 words)

	PSPACE
		Los problemas más duros de PSPACE son los problemas de PSPACE-Complete.
		Una caracterización alternativa de PSPACE es el grupo de problemas decidibles por una máquina de Turing que se alterna en tiempo polinómico.
		El grupo PSPACE es un sobreconjunto terminante del grupo de idiomas sensibles al contexto.
	www.yotor.net /wiki/es/ps/PSPACE.htm (271 words)

	TCS - Research - Publications - Deadlock and Reachability Checking with Finite Complete Prefixes
		Computational complexity of using finite complete prefixes as a symbolic representation of the state space is discussed.
		In addition a novel way of deadlock and reachability checking using the finite complete prefix approach is devised.
		(iii) The translations of the problems of deadlock and reachability checking using finite complete prefixes into the problem of finding a stable model of a logic program are devised.
	www.tcs.hut.fi /Publications/A56.shtml (312 words)

	Regular expression star-freeness is PSPACE-complete
		The paper also includes a new proof of the PSPACE -completeness of the finite automaton aperiodicity problem.
		It is proved that the problem of deciding if a regular expression denotes a star-free language is PSPACE -complete.
	www.inf.u-szeged.hu /kutatas/actacybernetica/vol13n1/cikk1.xml (68 words)

	Entailment of Atomic Set Constraints is PSPACE-Complete
		We show that entailment between atomic set constraints can express quantified boolean formulas and is thus PSPACE hard.
		For infinite signatures, we also present a PSPACE-algorithm for solving atomic set constraints with negation.
		Also, entailment of atomic set constraints has been claimed decidable in polynomial time.
	www.ps.uni-sb.de /papers/abstracts/atomic:98.html (127 words)

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