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Topic: PSPACE complete

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	Complete Problems
		Because a log-space transformation is a DTM that has a ready-only input tape, a write-only output tape, and a work tape or tapes on which it uses O(log n) cells to process an input string w of length n.
		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 (Site not responding. Last check: 2007-10-20)
		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.
		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.
		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.
	www.cs.mcgill.ca /~barring/notes/21.htm (2798 words)

	PSPACE-complete
		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.
		These problems are widely suspected to be outside of P and NP, but that is not known.
		So are the generalized versions of the games Hex and Reversi and the solitaire games Rush Hour, Mahjong, Atomix and Sokoban.
	publicliterature.org /en/wikipedia/p/ps/pspace_complete_1.html (378 words)

	[No title]
		We show here that both domi- complete, even for the propositional case, by exhibiting in nance and consistency testing for general CP-nets Section 4 a PSPACE-hardness proof for dominance testing.
		For every x V, we set Dx = {x, ¬x} complete if for every x V, the formula p- (x) p+ (x) is a C C (thus, we overload the notation and write x both for the vari- tautology.
		We define S () to the paper, the membership in PSPACE can be demonstrated be the sequence of actions in S (ACT) obtained by replacing by considering nondeterministic algorithms consisting of re- each action a in by a1,.
	www.ijcai.org /papers/0737.txt (4400 words)

	Hex Game Index \| Tela Communications
		The players alternately place one of their pieces, also referred to as "stones", on any one of the hexagons, provided that the cell is not already occupied by another piece.
		The objective of "blue" is to complete an unbroken chain of pieces of one color, from one edge to the opposite edge.
		The players continue placing their pieces until one of them has made a complete chain.
	www.telacommunications.com /misc/games/hex/index.html (342 words)

	ECCC Report TR05-011 and related Papers
		Complete sets of any level of PH, MODPH, or the Boolean hierarchy over NP are many-one autoreducible.
		These results solve several of the open questions raised by Buhrman and Torenvliet in their 1994 survey paper on the structure of complete sets.
		You may contribute to the discussion of this ECCC Report; see the detailed instructions.
	eccc.hpi-web.de /eccc-reports/2005/TR05-011/index.html (135 words)

	Dr. Dobb's \| Algorithm Alley \| July 22, 2001
		If n is equal to 1 million, and if a computer can perform one iteration per microsecond, it can complete a constant algorithm in a microsecond, a linear algorithm in a second, and a quadratic algorithm in 11.6 days.
		It would take 32,000 years to complete a cubic algorithm; not terribly practical, but a computer built to withstand the next ice age would eventually deliver a solution.
		PSPACE includes NP, but there are problems in PSPACE that are thought to be harder than NP.
	www.ddj.com /184409316?pgno=5 (2036 words)

	Hex
		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.
		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.
	maarup.net /thomas/hex (5616 words)

	Undecidability and Intractability in Theoretical Physics
		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.
		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.
	www.stephenwolfram.com /publications/articles/physics/85-undecidability/2/text.html (2128 words)

	CSCI 6420, Spring 2002
		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.
		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.
	www.cs.ecu.edu /~karl/6420/spr02/index.html (975 words)

	PSPACE-complete problems for subgroups of free groups and inverse finite automata - Birget, Margolis, Meakin, Weil ... (Site not responding. Last check: 2007-10-20)
		In the process, we show that certain problems about finite automata which are pspace-complete in general remain...
		...numbers is in PSPACE, where a semigroup S is an inverse semigroup if every element x in S has a pseudo inverse x.
		] have shown that the membership problem for inverse semigroups is PSPACE hard and hence it follows that it is PSPACE complete.
	citeseer.ist.psu.edu /176029.html (645 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		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.
		Proof Idea: (1) TQBF is in PSPACE, by a simple recursive algorithm for testing the truth a qbf.
		(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/308/lectures/18.txt (130 words)

	[No title]
		Specifically, such a study will be important in the remote possibility that NP turns out to be equal to P -- the same reason the study was important for NP in the first place.
		However, if NP turns out to be different from P, then the study of PSPACE might provide some insight into the factors that increase the complexity of problems.
		5.5.2 that the language L is in PSPACE.
	www.cse.ohio-state.edu /~gurari/theory-bk/theory-bk-fivese5.html (2564 words)

	Computational Complexity of Games and Puzzles
		The arrows eventually block the movement of the queens; the last player to complete a move wins.
		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 object is to control empty squares by surrounding them; after both players are unwilling to continue play, these squares are counted and the scores adjusted by the numbers of stones that had been removed.
	www.ics.uci.edu /~eppstein/cgt/hard.html (2681 words)

	PSPACE-complete : PSPACE-Complete
		In complexity theory, PSPACE-complete is a set of decision problems.
		A problem is in PSPACE-complete if it is in PSPACE, and every problem in PSPACE can be reduced to it in polynomial time.
		These problems are widely suspected to be outside of P and NP, but that isn't known.
	www.mik.fastload.org /ps/PSPACE-Complete.html (431 words)

	Papers about Sokoban (Site not responding. Last check: 2007-10-20)
		Joe Culberson of the University of Alberta proved Sokoban to be PSPACE complete in Sokoban is PSPACE-complete (1997).
		Dorit Dor and Uri Zwick of Tel Aviv University proved Sokoban to be PSPACE hard in 1995 in Sokoban and other motion planning problems and considered a few generalizations.
		Andreas Junghanns and Jonathan Schaeffer at the University of Alberta wrote about solving sokoban problems in Sokoban: A Challenging Single-Agent Search Problem, which was presented at the IJCAI workshop on Using Games as an Experimental Testbed for Artificial Intelligence Research in August, 1997.
	members.aol.com /SokobanMac/papers.html (150 words)

	CS-15855 Complexity Theory - Syllabus
		Palindromes require time on a one-tape machine, but can be done in linear time on a 2-tape machine.
		Not all sets in NP - P are complete.
		Examples of how the use of randomness give surprising algorithms to solve seemly difficult problems: Schwartz-Zippel, verifying arithmetic, communication complexity, and strong CNF equality.
	www.andrew.cmu.edu /user/hardt/syllabus.html (315 words)

	[No title]
		Indicate (by words if necessary) which containments are not known to be strict.
		Note: this is an open-ended question, but at a minimum include the Kleene hierarchy, the polynomial-time hierarchy, PSPACE, NP-complete languages, and regular languages ¡
		Note: this is an open-ended question, but at a minimum include the Kleene hierarchy, the polynomial-time hierarchy, PSPACE, NP-complete languages, and regular languages ¡< R«ª,Ç `aóóóó ¨÷Problem 2: State the time hierarchy theorem (consult Sipser).
	www.cs.unm.edu /~gemmell/C500/hw8.ppt (977 words)

	topic8.html
		DSPACE(log n) is a proper subset of PSPACE.
		A language L is complete, for some class C of languages, with respect to polynomial-time (or, respectively, log-space) reductions, if
		When the weights are restricted to the numbers 0 and 1, this becomes exactly the Hamiltonial Circuit problem.
	www.soi.city.ac.uk /~bernie/tcomp/topic9.html (1547 words)

	Entailment of Atomic Set Constraints is PSPACE-Complete (Site not responding. Last check: 2007-10-20)
		Also, entailment of atomic set constraints has been claimed decidable in polynomial time.
		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.
	www.ps.uni-sb.de /PapersOz/abstracts/atomic:98.html (138 words)

	TCS - Research - Publications - Model Checking with Finite Complete Prefixes is PSPACE-complete (Site not responding. Last check: 2007-10-20)
		The method constructs a finite complete prefix, which can be seen as a symbolic representation of an interleaved reachability graph.
		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.
		This proof employs a class of 1-safe Petri nets for which it is easy to generate a finite complete prefix in polynomial time.
	www.tcs.hut.fi /Publications/info/kepa.Heljanko:Concur2000.shtml (197 words)

	CSC280: Course Schedule
		Sections 8.2 & 8.3 — PSPACE and PSPACE-complete Problems
		NL — those of languages with algorithms that require space proportional to only the log of the input length.
		We present a complete problem for NL and show that NL is a subclass of P. Also We show that the class NL is closed under complement.
	www.cs.rochester.edu /~schubert/280/schedule.html (805 words)

	Consilience
		However, there are problems in graph theory that are in polynomial space, where each variable takes up more than one "piece of space." A complete discussion of space would be superfluous, because it would very much mirror the discussion of time.
		However, the idea of PSPACE brings up a couple of interesting questions:
		Is a PSPACE problem necessarily a PTIME problem?
	www.princeton.edu /~complex/site/seminar2/notes.html (1730 words)

	Strong Bisimilarity on Basic Parallel Processes is PSPACE-complete (Site not responding. Last check: 2007-10-20)
		The paper shows an algorithmwhich, given a Basic Parallel Processes (BPP) system, constructs a set of linear mappings which characterize the (strong) bisimulation equivalence on the system.
		Though the number of the constructed mappings can be exponential, they can be generated in polynomial space; this shows that the problem of deciding bisimulation equivalence on BPP is in PSPACE.
		Combining with the PSPACE-hardness result by Srba, PSPACE-completeness is thus established.
	csdl.computer.org /comp/proceedings/lics/2003/1884/00/18840218abs.htm (150 words)

	[No title]
		=========================================================================== CSC 363H Lecture Summary for Week 13 Fall 2004 =========================================================================== ---------------- Space complexity (cont'd) ---------------- Given we can't prove P =/= PSPACE, what to do?
		Same as for NP: identify "hardest" problems in PSPACE.
		Language A is PSPACE-complete if: - A in PSPACE.
	www.cs.toronto.edu /~fpitt/20059/CSC363/lectures/LN13.txt (428 words)

	[No title]
		Due to the negative-requirement nature of the sets of coNP, it is not known how to find useful verifiers for these problems — i.e., it is not known whether NP = coNP.
		(Compare this to the fact that negative requirements such as uncountability, logical completeness, and nonhomeomorphic require complicated, nonconstructive proofs, often using proofs by contradictions.) Surprisingly, it has never been proven that NP is different from P: no one has ever found a way to replace brute force searching or to show that it is unreplaceable.
		We can prove some simple theorems, using this very important fact: EMBED Equation.3 EMBED Equation.3 PSPACE EMBED Equation.3 EXPSPACE.
	www.media.mit.edu /physics/pedagogy/babbage/texts/ct.doc (1567 words)

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