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Topic: PSPACE

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EXPSPACE

Complexity classes P and NP

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	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.
		These problems are widely suspected to be outside of P and NP, but that is not known.
		Some other generalized games, such as chess, checkers (draughts), and go are EXPTIME-complete because a game between two perfect players can be very long, so they are unlikely to be in PSPACE.
	en.wikipedia.org /wiki/PSPACE-Complete (400 words)

	[12pt,letterpaper] A note on the power of the counting class \#P
		PSPACE represents the class of languages that can be solved by a polynomial space bounded Turing machine.
		Also, if one is given an unbounded amount of time yet a bound on space, it seems one should be able to solve more problems with those resources than if one were constrained to the same bound on time, yet unbounded space to work with, since time is required to use the unbounded space.
		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)

	PSPACE (Site not responding. Last check: 2007-11-07)
		In complexity theory the class PSPACE is the set of decision problems that can be solved by a Turing machine using a polynomial amount of memory, and unlimited time.
		So The set PSPACE is a strict superset of the set of context-sensitive languages.
		See PSPACE-Complete for examples of problems that are suspected to be in PSPACE but not in NP.
	www.theezine.net /p/pspace.html (101 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.
		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)

	Some Algebraic and Geometric Computations in PSPACE (Site not responding. Last check: 2007-11-07)
		We give a PSPACE algorithm for determining the signs of multivariate polynomials at the common zeros of a system of polynomial equations.
		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].
		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)

	[No title]
		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.
		Otherwise, reject.” The space complexity for this algorithm is linear, because we have a recursion depth equal to the number of variables in w, and we store the value of a single variable at each level of recursion.
		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)

	VIZLAB Virtual Environments
		The projectors are each placed approximately 1.35 times the width of the screen behind the screens and this distance can be further shortened by the use of mirrors to fold the optical path.
		The first public installation to use pSpace was the Powerhouse Museum in Sydney, for the exhibition The Universal Machine.
		A two wall Wedge is now running as a permanent public exhibit, with an environment created by visualization programmers at the ANUSF Vizlab, namely Drew Whitehouse, Stuart Ramsden and Ajay Limaye.
	anusf.anu.edu.au /pSpace (879 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		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/cmpt308/lectures/18.txt (138 words)

	Citations: Journal of the ACM - Shamir, PSPACE (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		For definitions of classes such as P, NP, and PSPACE, see [8, 4] If a language L has an Arthur Merlin game where Arthur asks only a constant number of questions, we say that L 2 AM[2] NP corresponds to Arthur Merlin games where Arthur says nothing, and thus clearly NP AM[2] Restricting....
		For definitions of classes such as P, NP, and PSPACE, see [7, 4] If a language L has an Arthur Merlin game where Arthur asks only a constant number of questions, we say that L AM[2] NP corresponds to Arthur Merlin games where Arthur says nothing, and thus clearly NP AM[2] Restricting....
		Applying enough polynomial padding to a PSPACE complete language it remains PSPACE complete but the interactive proof for it becomes sub linear in length and thus in the knowledge it reveals.
	citeseer.ist.psu.edu /context/34073/0 (1962 words)

	Autocad 3D FREE training - Auto cad 3D and the mviews, mspace, and pspace commands.
		Having completed the first stage of creating drawings from an Auto cad 3D model by creating 4 mviews, the second stage is to ACTIVATE one view to show a plan, ACTIVATE another view to show the front elevation, and activate a third view to show a side elevation.
		De-activate an Mview by typing 'Pspace >' (Pspace is short for paperspace / paper space.)
		If you need to use the 'Mspace / Pspace' method, note the command down for use later on when activating and de-activating Mviews.
	www.3d-cadcea.co.uk /html/task10.htm (956 words)

	The Corewar Lexicon
		When pspace was first implemented on the hills, one of the first switching algorithms was the simple 'switch on loss' or 'switch on tie or loss'.
		The second, and more important, change is that the pspace value is not re-stored unless it has changed (note that it still always undergoes a mod before being used); this saves a cycle and leads to exactly the same behaviour.
		One method is to simply load a number into pspace on the first round and check it every remaining round to see if it's been tampered with.
	www.corewar.info /lexicon/p-switcher.htm (5022 words)

	Hardness and completeness
		Since an easier class is included as a subset of a harder one, it is helpful to have a notion of a language (i.e., problem) being among the hardest possible within a class.
		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.
	msl.cs.uiuc.edu /planning/node314.html (215 words)

	Interactive Proof Systems
		Shamir, 1990, showed in a very elegant proof that IP is equivalent to PSPACE.
		The difference between a deterministic interactive proof system (DIP) and an interactive proof system (IP) is that the verifier V in IP is now a probabilistic Turing machine with a polynomial time bound.
		In order to determine if a word w is in the language L or not, one must calculate the probability with which V accepts w in polynomial space.
	www2.hawaii.edu /~hmauch/subdir2/IPSystemsnew.htm (1856 words)

	Computational Complexity: Extreme Oracles
		In one of your previous posts you mentioned that what you like about TCS is that what we now know will remain true for ever.
		But as evidence that P = NP, this is circular: if you believe that PSPACE is a realistic oracle, then you believe a lot more than P = NP.
		Despite the result that IP = PSPACE, you could still make a case for realism of random oracles (at least to a bystander like me), because the realism of IP and PSPACE is debatable.
	weblog.fortnow.com /2005/08/extreme-oracles.html (806 words)

	Introduction
		In this paper we show that we can emulate a Turing Machine (TM) in linear time using an infinite version of the puzzle in which only a finite number of containers are initially out of storage.
		Restricting the tape to finite length (linear bounded automata) shows that finite puzzles are PSPACE hard.
		Since the problem is in PSPACE [1], this means the puzzles are PSPACE complete, solving the open problem posed by Dorit and Zwick[1].
	www.cs.ualberta.ca /~joe/Preprints/Sokoban/node1.html (473 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)

	A New Kind of Science: The NKS Forum - PSPACE: explanantion?
		I've been reading NKS and come across the discussion of computational complexity.
		As a non-mathematician, I am trying to get a handle on what this means and, in particular, the notion of PSPACE.
		I am currently working on a go application and it is indicated as PSPACE hard.
	forum.wolframscience.com /showthread.php?s=&threadid=587 (99 words)

	Provability Logic
		Looking at the procedure a bit more precisely, it can be shown that GL is decidable in the computational complexity class PSPACE, like the well-known modal logics K, T and S4.
		This means that there is a Turing machine that, given a formula A as input, answers whether A follows from GL or not; the size of the memory that the Turing machine needs for its computation is only polynomial in the length of A.
		To give some more perspective on complexity, the class P of functions computable in an amount of time polynomial in the length of the input, is included in PSPACE, which in turn is included in the class EXPTIME of functions computable in exponential time.
	plato.stanford.edu /entries/logic-provability (4840 words)

	Vizlab Virtual Environments - Tools (Site not responding. Last check: 2007-11-07)
		Written by VIZLAB founder Drew Whitehouse, pSpace (short for 'pointer to Space/python Space') is our proprietary flexible scripting language-based software for developing Interactive Virtual Environments.
		pSpace supports environments with mono or stereo displays on single or multiple screens and will run under SGI IRIX and Windows-based systems.
		Discovery Centre VR theatre and was used in early prototyping of
	anusf.anu.edu.au /Vizlab/VE/tools.html (171 words)

	foo
		Three Musketeers 1998-04-29 [Redcode Maniacs Tournament (round 7)] pspace, stone, scan, clear, imp, gate, boot
		Psst 2.0 1998-04-29 [Redcode Maniacs Tournament (round 4)] pspace, boot, stone, clear, paper, scan, stun
		Mason 2.0 1996-02-09 [post] pspace, boot, stone, stun
	pauillac.inria.fr /~doligez/corewar/by-author/XMacrae-Robert.htm (299 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Our main results are: o R_KS and R_Kt are complete for PSPACE and EXP, respectively, under P/poly-truth-table reductions.
		Our techniques also allow us to show that all recursively-enumerable sets are reducible to RK via P/poly-truth-table reductions.
		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.
	www.eccc.uni-trier.de /eccc-reports/2002/TR02-028/revisn01.txt (222 words)

	Entailment of Atomic Set Constraints is PSPACE-Complete (Site not responding. Last check: 2007-11-07)
		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 /papers/abstracts/atomic:98.html (127 words)

	foo
		Loh_tst_1.3 (Calvin Loh) 1995-12-31 [post] pspace, imp, scan, paper, stone, boot, stun, gate
		Bigboy (Robert Macrae) 1995-12-20 [NSFCWT round 8] pspace, quick, scan, stun, stone
		Obvious (John K. Lewis) 1995-09-13 [posts] pspace, scan, stone, imp, boot, gate
	pauillac.inria.fr /~doligez/corewar/by-date/X1995second.htm (2199 words)

	Importing DWGs with Pspace & Mspace into Visio Technical (Site not responding. Last check: 2007-11-07)
		Importing DWGs with Pspace and Mspace into Visio Technical
		AutoCAD and IntelliCAD use paper space and model space concepts that allow you to create and view objects of different scales on one sheet of paper.
		If the drawing you want to convert includes additional model space objects, create a background page for each file you created in step 5 from the “Preparing a DWG…” section above, then open each file in its corresponding Visio background page.
	www.design-drawing.com /visio/DWG2VSD.htm (641 words)

	Strong Bisimilarity on Basic Parallel Processes is PSPACE-complete. (Site not responding. Last check: 2007-11-07)
		Abstract: 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.
	www.informatik.uni-hamburg.de /TGI/pnbib/j/jancar_p1.html (124 words)

	CoreWar "Koenigstuhl" Page
		The difference is that I separated the hill into several categories and let every program fight every other program:
		94nop ('94 instruction set, no Pspace, no '88 warriors
		Pspace-hill(s), "-r 1000", Pspace ok (188 entries: pspace.tar.gz)
	www.ociw.edu /~birk/COREWAR/koenigstuhl.html (867 words)

	The Computational Complexity of Motion Planning
		In particular, we show that the problem is PSPACE-complete.
		We begin with a review of NP-completeness and polynomial-time reductions, introduce the class PSPACE, and motivate the significance of PSPACE-complete problems.
		Afterwards, we prove that determining whether a given instance of a generalized Lunar Lockout puzzle is solvable is PSPACE-complete.
	epubs.siam.org /sam-bin/dbq/article/39517 (112 words)

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