Results 1  10
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425
DAGwidth is PSPACEcomplete
, 2014
"... Berwanger et al. show in [BDH+12] that for every graph G of size n and DAGwidth k there is a DAG decomposition of width k of size nO(k). This gives a polynomial time algorithm for determining the DAGwidth of a graph for any fixed k. However, if the DAGwidth of the graphs from a class is not boun ..."
Complexity Issues in Finding Succinct Solutions of PSPACEComplete Problems
, 2005
"... We study the problem of deciding whether some PSPACEcomplete problems have models of bounded size. Contrary to problems in NP, models of PSPACEcomplete problems may be exponentially large. However, such models may take polynomial space in a succinct representation. For example, the models of a QBF ..."
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Cited by 3 (0 self)
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We study the problem of deciding whether some PSPACEcomplete problems have models of bounded size. Contrary to problems in NP, models of PSPACEcomplete problems may be exponentially large. However, such models may take polynomial space in a succinct representation. For example, the models of a
Complexity Issues in Finding Succinct Solutions of PSPACEComplete Problems
, 2008
"... We study the problem of deciding whether some PSPACEcomplete problems have models of bounded size. Contrary to problems in NP, models of PSPACEcomplete problems may be exponentially large. However, such models may take polynomial space in a succinct representation. For example, the models of a QBF ..."
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We study the problem of deciding whether some PSPACEcomplete problems have models of bounded size. Contrary to problems in NP, models of PSPACEcomplete problems may be exponentially large. However, such models may take polynomial space in a succinct representation. For example, the models of a
Finding paths between . . .
, 2007
"... Suppose we are given a graph G together with two proper vertex kcolourings of G, α and β. How easily can we decide whether it is possible to transform α into β by recolouring vertices of G one at a time, making sure we always have a proper kcolouring of G? This decision problem is trivial for k = ..."
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= 2, and decidable in polynomial time for k = 3. Here we prove it is PSPACEcomplete for all k ≥ 4. In particular, we prove that the problem remains PSPACEcomplete for bipartite graphs, as well as for: (i) planar graphs and 4 ≤ k ≤ 6, and (ii) bipartite planar graphs and k = 4. Moreover, the values
Finding Paths Between 3Colourings
, 2007
"... Given a 3colourable graph G and two proper vertex 3colourings α and β of G, consider the following question: is it possible to transform α into β by recolouring vertices of G one at a time, making sure that all intermediate colourings are proper 3colourings? We prove that this question is answera ..."
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Cited by 8 (4 self)
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Given a 3colourable graph G and two proper vertex 3colourings α and β of G, consider the following question: is it possible to transform α into β by recolouring vertices of G one at a time, making sure that all intermediate colourings are proper 3colourings? We prove that this question
Improving Exhaustive Search Implies Superpolynomial Lower Bounds
, 2009
"... The P vs NP problem arose from the question of whether exhaustive search is necessary for problems with short verifiable solutions. We do not know if even a slight algorithmic improvement over exhaustive search is universally possible for all NP problems, and to date no major consequences have been ..."
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Cited by 40 (7 self)
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given that similar improvements have been found for many other hard problems. Optimistically, one might hope our results suggest a new path to lower bounds; pessimistically, they show that carrying out the seemingly modest program of finding slightly better algorithms for all search problems may
Checking Computations in Polylogarithmic Time
, 1991
"... . Motivated by Manuel Blum's concept of instance checking, we consider new, very fast and generic mechanisms of checking computations. Our results exploit recent advances in interactive proof protocols [LFKN92], [Sha92], and especially the MIP = NEXP protocol from [BFL91]. We show that every no ..."
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Cited by 274 (11 self)
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nondeterministic computational task S(x; y), defined as a polynomial time relation between the instance x, representing the input and output combined, and the witness y can be modified to a task S 0 such that: (i) the same instances remain accepted; (ii) each instance/witness pair becomes checkable
Superpolynomial Circuits, Almost Sparse Oracles and the Exponential Hierarchy
 In Proceedings of the 12th Conference on the Foundations of Software Technology and Theoretical Computer Science
, 1992
"... Several problems concerning superpolynomial size circuits and superpolynomialtime advice classes are investigated. First we consider the implications of NP (and other fun damental complexity classes) having circuits slightly bigger than polynomial. We prove that if such circuits exist, for examp ..."
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Cited by 19 (6 self)
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Several problems concerning superpolynomial size circuits and superpolynomialtime advice classes are investigated. First we consider the implications of NP (and other fun damental complexity classes) having circuits slightly bigger than polynomial. We prove that if such circuits exist
TimeSpace Tradeoffs in Resolution: Superpolynomial Lower Bounds For Superlinear Space
 STOC'12
, 2012
"... We give the first timespace tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size N that have Resolution refutations of space and size each roughly N log2 N (and like all formulas have Resolution refutations of space N) ..."
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Cited by 14 (1 self)
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We give the first timespace tradeoff lower bounds for Resolution proofs that apply to superlinear space. In particular, we show that there are formulas of size N that have Resolution refutations of space and size each roughly N log2 N (and like all formulas have Resolution refutations of space N) for which any Resolution refutation using space S and length T requires T ≥ (N0.58 log2 N/S)Ω(log logN / log log logN). By downward translation, a similar tradeoff applies to all smaller space bounds. We also show somewhat stronger timespace tradeoff lower bounds for Regular Resolution, which are also the first to apply to superlinear space. Namely, for any space bound S at most 2o(N 1/4) there are formulas of size N, having clauses of width 4, that have Regular Resolution proofs of space S and slightly larger size T = O(NS), but for which any Regular Resolution proof of space S1− requires length TΩ(log logN / log log logN).
Results 1  10
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425