The paper explores the difference between parallel and serial queries to an NP-complete oracle, SAT, from the perspective of functions with a limited number of output bits. For polynomial-time bounded query language classes, which can be considered as functions with 1 bit output, previous work has shown that 2 serial queries to SAT is equivalent to 3 parallel queries to SAT. In contrast, for function classes with no limit on the number of output bits, previous work has shown that there exists a function that can be computed in polynomial time using 3 parallel queries to SAT, but cannot be computed using 2 serial queries to SAT, unless P=NP. The results show that there exists a function with 2 bit output that can be computed using 3 parallel queries to SAT, but cannot be computed using 2 serial queries to SAT, unless the polynomial hierarchy collapses.
{"title":"Bounded query functions with limited output bits","authors":"Richard Chang, J. Squire","doi":"10.1109/CCC.2001.933876","DOIUrl":"https://doi.org/10.1109/CCC.2001.933876","url":null,"abstract":"The paper explores the difference between parallel and serial queries to an NP-complete oracle, SAT, from the perspective of functions with a limited number of output bits. For polynomial-time bounded query language classes, which can be considered as functions with 1 bit output, previous work has shown that 2 serial queries to SAT is equivalent to 3 parallel queries to SAT. In contrast, for function classes with no limit on the number of output bits, previous work has shown that there exists a function that can be computed in polynomial time using 3 parallel queries to SAT, but cannot be computed using 2 serial queries to SAT, unless P=NP. The results show that there exists a function with 2 bit output that can be computed using 3 parallel queries to SAT, but cannot be computed using 2 serial queries to SAT, unless the polynomial hierarchy collapses.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122201941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For Part I, see Theoretical Computer Science (to be published). Investigates the Kolmogorov complexity of the problem (a/spl rarr/c)/spl and/(b/spl rarr/d), defined as the minimum length of a program that, given a, outputs c and, given b, outputs d. We prove that, unlike all known problems of this kind, its complexity is not expressible in terms of the Kolmogorov complexity of a, b, c and d, their pairs, triples, etc. This solves the problem posed in Part I. We then consider the following theorem: there are two strings, whose mutual information is large but which have no common information in a strong sense. This theorem was proven by A. Muchnik et al. (1999) via a non-constructive argument. We present a constructive proof, thus solving a problem posed by Muchnik et al. We give also an interpretation of both results in terms of Shannon entropy.
{"title":"Logical operations and Kolmogorov complexity. II","authors":"A. Muchnik, N. Vereshchagin","doi":"10.1109/CCC.2001.933892","DOIUrl":"https://doi.org/10.1109/CCC.2001.933892","url":null,"abstract":"For Part I, see Theoretical Computer Science (to be published). Investigates the Kolmogorov complexity of the problem (a/spl rarr/c)/spl and/(b/spl rarr/d), defined as the minimum length of a program that, given a, outputs c and, given b, outputs d. We prove that, unlike all known problems of this kind, its complexity is not expressible in terms of the Kolmogorov complexity of a, b, c and d, their pairs, triples, etc. This solves the problem posed in Part I. We then consider the following theorem: there are two strings, whose mutual information is large but which have no common information in a strong sense. This theorem was proven by A. Muchnik et al. (1999) via a non-constructive argument. We present a constructive proof, thus solving a problem posed by Muchnik et al. We give also an interpretation of both results in terms of Shannon entropy.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"55 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113941055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We use hypotheses of structural complexity theory to separate various NP-completeness notions. In particular, we introduce a hypothesis from which we describe a set in NP that is /spl les//sub T//sup P/-complete but not /spl les//sub tt//sup P/-complete. We provide fairly thorough analyses of the hypotheses that we introduce.
{"title":"Separation of NP-completeness notions","authors":"A. Pavan, A. Selman","doi":"10.1109/CCC.2001.933875","DOIUrl":"https://doi.org/10.1109/CCC.2001.933875","url":null,"abstract":"We use hypotheses of structural complexity theory to separate various NP-completeness notions. In particular, we introduce a hypothesis from which we describe a set in NP that is /spl les//sub T//sup P/-complete but not /spl les//sub tt//sup P/-complete. We provide fairly thorough analyses of the hypotheses that we introduce.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132311381","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a new model for computing polynomials-a depth 2 circuit with a symmetric gate at the top and plus gates at the bottom, i.e. the circuit computes a symmetric function in linear functions-S/sub m//sup d/(l/sub 1/, l/sub 2/, ..., l/sub m/) (S/sub m//sup d/ is the d'th elementary symmetric polynomial in m variables, and the l/sub i/'s are linear functions). We refer to this model as the symmetric model. This new model is related to standard models of arithmetic circuits, especially to depth 3 circuits. In particular we show that, in order to improve the results of Shpilka and Wigderson (1999), i.e. to prove super-quadratic lower bounds for depth 3 circuits, one must first prove a super-linear lower bound for the symmetric model. We prove two nontrivial linear lower bounds for our model. The first lower bound is for computing the determinant, and the second is for computing the sum of two monomials. The main technical contribution relates the maximal dimension of linear subspaces on which S/sub m//sup d/ vanishes, and lower bounds to the symmetric model. In particular we show that an answer of the following problem (which is very natural, and of independent interest) will imply lower bounds on symmetric circuits for many polynomials: "what is the maximal dimension of a linear subspace of C/sup m/, on which S/sub m//sup d/ vanishes?" We give two partial solutions to the problem above, each enables us to prove a different lower bound.
{"title":"Affine projections of symmetric polynomials","authors":"Amir Shpilka","doi":"10.1109/CCC.2001.933883","DOIUrl":"https://doi.org/10.1109/CCC.2001.933883","url":null,"abstract":"We introduce a new model for computing polynomials-a depth 2 circuit with a symmetric gate at the top and plus gates at the bottom, i.e. the circuit computes a symmetric function in linear functions-S/sub m//sup d/(l/sub 1/, l/sub 2/, ..., l/sub m/) (S/sub m//sup d/ is the d'th elementary symmetric polynomial in m variables, and the l/sub i/'s are linear functions). We refer to this model as the symmetric model. This new model is related to standard models of arithmetic circuits, especially to depth 3 circuits. In particular we show that, in order to improve the results of Shpilka and Wigderson (1999), i.e. to prove super-quadratic lower bounds for depth 3 circuits, one must first prove a super-linear lower bound for the symmetric model. We prove two nontrivial linear lower bounds for our model. The first lower bound is for computing the determinant, and the second is for computing the sum of two monomials. The main technical contribution relates the maximal dimension of linear subspaces on which S/sub m//sup d/ vanishes, and lower bounds to the symmetric model. In particular we show that an answer of the following problem (which is very natural, and of independent interest) will imply lower bounds on symmetric circuits for many polynomials: \"what is the maximal dimension of a linear subspace of C/sup m/, on which S/sub m//sup d/ vanishes?\" We give two partial solutions to the problem above, each enables us to prove a different lower bound.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134113134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove a general lower bound on the complexity of unbounded error probabilistic communication protocols. This result improves on a lower bound for bounded error protocols from Krause (1996). As a simple consequence we get the, to our knowledge, first linear lower bound on the complexity of unbounded error probabilistic communication protocols for the functions defined by Hadamard matrices. We also give an upper bound on the margin of any embedding of a concept class in half spaces.
{"title":"A linear lower bound on the unbounded error probabilistic communication complexity","authors":"J. Forster","doi":"10.1109/CCC.2001.933877","DOIUrl":"https://doi.org/10.1109/CCC.2001.933877","url":null,"abstract":"We prove a general lower bound on the complexity of unbounded error probabilistic communication protocols. This result improves on a lower bound for bounded error protocols from Krause (1996). As a simple consequence we get the, to our knowledge, first linear lower bound on the complexity of unbounded error probabilistic communication protocols for the functions defined by Hadamard matrices. We also give an upper bound on the margin of any embedding of a concept class in half spaces.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132627799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is: /spl Sigma//sub 3//sup p/-hard to approximate to within a factor 2-/spl epsiv/ for any /spl epsiv/>0; approximable in A/spl Mscr/ to within a factor 2; and A/spl Mscr/-hard to approximate to within a factor N/sup /spl epsiv// for some constant /spl epsiv/>0. To obtain the /spl Sigma//sub 3//sup 9/-hardness results we solve a randomness extraction problem using list-decodable binary codes; for the positive results we utilize the Sauer-Shelah(-Perles) Lemma. The exact value of /spl epsiv/ in the A/spl Mscr/-hardness result depends on the degree achievable by explicit disperser constructions.
{"title":"On the complexity of approximating the VC dimension","authors":"Elchanan Mossel, C. Umans","doi":"10.1109/CCC.2001.933889","DOIUrl":"https://doi.org/10.1109/CCC.2001.933889","url":null,"abstract":"We study the complexity of approximating the VC dimension of a collection of sets, when the sets are encoded succinctly by a small circuit. We show that this problem is: /spl Sigma//sub 3//sup p/-hard to approximate to within a factor 2-/spl epsiv/ for any /spl epsiv/>0; approximable in A/spl Mscr/ to within a factor 2; and A/spl Mscr/-hard to approximate to within a factor N/sup /spl epsiv// for some constant /spl epsiv/>0. To obtain the /spl Sigma//sub 3//sup 9/-hardness results we solve a randomness extraction problem using list-decodable binary codes; for the positive results we utilize the Sauer-Shelah(-Perles) Lemma. The exact value of /spl epsiv/ in the A/spl Mscr/-hardness result depends on the degree achievable by explicit disperser constructions.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132451056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A secret-sharing scheme enables a dealer to distribute a secret among no parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f: {0, 1}/sup n//spl rarr/{0, 1}. A family of secret-sharing schemes is called efficient if the total length of the n shares is polynomial in n. Most previously known secret-sharing schemes belonged to a class of linear schemes, whose complexity coincides with the monotone span program size of their access structure. Prior to this work there was no evidence that nonlinear schemes can be significantly more efficient than linear schemes, and in particular there were no candidates for schemes efficiently realizing access structures which do not lie in NC. The main contribution of this work is the construction of two efficient nonlinear schemes: (1) A scheme with perfect privacy whose access structure is conjectured not to lie in NC; (2) A scheme with statistical privacy whose access structure is conjectured not to lie to P/poly. Another contribution is the study of a class of nonlinear schemes, termed quasi-linear schemes, obtained by composing linear schemes over different fields. We show that while these schemes are possibly (super-polynomially) more powerful than linear schemes, they cannot efficiently realize access structures outside NC.
{"title":"On the power of nonlinear secret-sharing","authors":"A. Beimel, Y. Ishai","doi":"10.1109/CCC.2001.933886","DOIUrl":"https://doi.org/10.1109/CCC.2001.933886","url":null,"abstract":"A secret-sharing scheme enables a dealer to distribute a secret among no parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f: {0, 1}/sup n//spl rarr/{0, 1}. A family of secret-sharing schemes is called efficient if the total length of the n shares is polynomial in n. Most previously known secret-sharing schemes belonged to a class of linear schemes, whose complexity coincides with the monotone span program size of their access structure. Prior to this work there was no evidence that nonlinear schemes can be significantly more efficient than linear schemes, and in particular there were no candidates for schemes efficiently realizing access structures which do not lie in NC. The main contribution of this work is the construction of two efficient nonlinear schemes: (1) A scheme with perfect privacy whose access structure is conjectured not to lie in NC; (2) A scheme with statistical privacy whose access structure is conjectured not to lie to P/poly. Another contribution is the study of a class of nonlinear schemes, termed quasi-linear schemes, obtained by composing linear schemes over different fields. We show that while these schemes are possibly (super-polynomially) more powerful than linear schemes, they cannot efficiently realize access structures outside NC.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133800142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. Ambos-Spies, W. Merkle, Jan Reimann, F. Stephan
In this paper we investigate effective versions of Hausdorff dimension which have been recently introduced by Lutz. We focus on dimension in the class E of sets computable in linear exponential time. We determine the dimension of various classes related to fundamental structural properties including different types of autoreducibility and immunity. By a new general invariance theorem for resource-bounded dimension we show that the class of p-m-complete sets for E has dimension 1 in E. Moreover, we show that there are p-m-lower spans in E of dimension /spl Hscr/(/spl beta/) for any rational /spl beta/ between 0 and 1, where /spl Hscr/(/spl beta/) is the binary entropy function. This leads to a new general completeness notion for E that properly extends Lutz's concept of weak completeness. Finally we characterize resource-bounded dimension in terms of martingales with restricted betting ratios and in terms of prediction functions.
{"title":"Hausdorff dimension in exponential time","authors":"K. Ambos-Spies, W. Merkle, Jan Reimann, F. Stephan","doi":"10.1109/CCC.2001.933888","DOIUrl":"https://doi.org/10.1109/CCC.2001.933888","url":null,"abstract":"In this paper we investigate effective versions of Hausdorff dimension which have been recently introduced by Lutz. We focus on dimension in the class E of sets computable in linear exponential time. We determine the dimension of various classes related to fundamental structural properties including different types of autoreducibility and immunity. By a new general invariance theorem for resource-bounded dimension we show that the class of p-m-complete sets for E has dimension 1 in E. Moreover, we show that there are p-m-lower spans in E of dimension /spl Hscr/(/spl beta/) for any rational /spl beta/ between 0 and 1, where /spl Hscr/(/spl beta/) is the binary entropy function. This leads to a new general completeness notion for E that properly extends Lutz's concept of weak completeness. Finally we characterize resource-bounded dimension in terms of martingales with restricted betting ratios and in terms of prediction functions.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115025635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We use a Ramsey-theoretic argument to obtain the first lower bounds for approximations over Z/sub m/ by nonlinear polynomials: (i) A degree-2 polynomial over Z/sub m/ (m odd) must differ from the parity function on at least a 1/2-1/2((log n)/sup /spl Omega/(1)/) fraction of all points in the Boolean n-cube. A degree-O(1) polynomial over Z/sub m/ (m odd) must differ from the parity function on at least a 1/2-o(1) fraction of all points in the Boolean n-cube. These nonapproximability results imply the first known lower bounds on the top fanin of MAJoMOD/sub m/oAND/sub O(1)/ circuits (i.e., circuits with a single majority-gate at the output node, MOD/sub m/-gates at the middle level, and constant-fanin AND-gates at the input level) that compute parity: (i) MAJoMOD/sub m/oAND/sub 2/ circuits that compute parity must have top fanin 2((log n)/sup /spl Omega/(1)/). (ii) Parity cannot be computed by MAJoMODmoAND/sub O(1)/ circuits with top fanin O(1). Similar results hold for the MOD/sub q/ function as well.
{"title":"Lower bounds for approximations by low degree polynomials over Z/sub m/","authors":"N. Alon, R. Beigel","doi":"10.1109/CCC.2001.933885","DOIUrl":"https://doi.org/10.1109/CCC.2001.933885","url":null,"abstract":"We use a Ramsey-theoretic argument to obtain the first lower bounds for approximations over Z/sub m/ by nonlinear polynomials: (i) A degree-2 polynomial over Z/sub m/ (m odd) must differ from the parity function on at least a 1/2-1/2((log n)/sup /spl Omega/(1)/) fraction of all points in the Boolean n-cube. A degree-O(1) polynomial over Z/sub m/ (m odd) must differ from the parity function on at least a 1/2-o(1) fraction of all points in the Boolean n-cube. These nonapproximability results imply the first known lower bounds on the top fanin of MAJoMOD/sub m/oAND/sub O(1)/ circuits (i.e., circuits with a single majority-gate at the output node, MOD/sub m/-gates at the middle level, and constant-fanin AND-gates at the input level) that compute parity: (i) MAJoMOD/sub m/oAND/sub 2/ circuits that compute parity must have top fanin 2((log n)/sup /spl Omega/(1)/). (ii) Parity cannot be computed by MAJoMODmoAND/sub O(1)/ circuits with top fanin O(1). Similar results hold for the MOD/sub q/ function as well.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"155 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132670533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Gives an extension of the result due to Paul, Pippenger, Szemeredi and Trotter (1983) that deterministic linear time (DTIME) is distinct from nondeterministic linear time (NTIME). We show that NTIME[n/spl radic/log*(n)] /spl ne/ DTIME[n/spl radic/log*(n)]. We show that if the class of multi-pushdown graphs has {o(n), o[n/log(n)]} segregators, then NTIME[n log(n)] /spl ne/ DTIME[n log(n)]. We also show that at least one of the following facts holds: (1) P /spl ne/ L, and (2) for all polynomially bounded constructible time bounds t, NTIME(t) /spl ne/ DTIME(t). We consider the problem of whether NTIME(t) is distinct from NSPACE(t) for constructible time bounds t. A pebble game on graphs is defined such that the existence of a "good" strategy for the pebble game on multi-pushdown graphs implies a "good" simulation of nondeterministic time-bounded machines by nondeterministic space-bounded machines. It is shown that there exists a "good" strategy for the pebble game on multi-pushdown graphs if the graphs have sublinear separators. Finally, we show that nondeterministic time-bounded Turing machines can be simulated by /spl Sigma//sub 4/ machines with an asymptotically smaller time bound, under the assumption that the class of multi-pushdown graphs has sublinear separators.
{"title":"On separators, segregators and time versus space","authors":"R. Santhanam","doi":"10.1109/CCC.2001.933895","DOIUrl":"https://doi.org/10.1109/CCC.2001.933895","url":null,"abstract":"Gives an extension of the result due to Paul, Pippenger, Szemeredi and Trotter (1983) that deterministic linear time (DTIME) is distinct from nondeterministic linear time (NTIME). We show that NTIME[n/spl radic/log*(n)] /spl ne/ DTIME[n/spl radic/log*(n)]. We show that if the class of multi-pushdown graphs has {o(n), o[n/log(n)]} segregators, then NTIME[n log(n)] /spl ne/ DTIME[n log(n)]. We also show that at least one of the following facts holds: (1) P /spl ne/ L, and (2) for all polynomially bounded constructible time bounds t, NTIME(t) /spl ne/ DTIME(t). We consider the problem of whether NTIME(t) is distinct from NSPACE(t) for constructible time bounds t. A pebble game on graphs is defined such that the existence of a \"good\" strategy for the pebble game on multi-pushdown graphs implies a \"good\" simulation of nondeterministic time-bounded machines by nondeterministic space-bounded machines. It is shown that there exists a \"good\" strategy for the pebble game on multi-pushdown graphs if the graphs have sublinear separators. Finally, we show that nondeterministic time-bounded Turing machines can be simulated by /spl Sigma//sub 4/ machines with an asymptotically smaller time bound, under the assumption that the class of multi-pushdown graphs has sublinear separators.","PeriodicalId":240268,"journal":{"name":"Proceedings 16th Annual IEEE Conference on Computational Complexity","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127314528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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