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Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory最新文献

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Generic separations 通用的分离
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1996-02-01 DOI: 10.1109/SCT.1994.315809
L. Fortnow, T. Yamakami
{"title":"Generic separations","authors":"L. Fortnow, T. Yamakami","doi":"10.1109/SCT.1994.315809","DOIUrl":"https://doi.org/10.1109/SCT.1994.315809","url":null,"abstract":"M. Blum and R. Impagliazzo (Proc. 28th IEEE Symposium on Foundations of Computer Science, pp. 118-126, 1987), using techniques of Hartmanis and Hemachandra (1991) and Rackoff (1982), showed that if P = NP then P(G) = NP(G)/spl cap/co-NP(G) = UP(G), where G is a generic oracle. They left open the question as to whether these collapses occur at higher levels of the polynomial-time hierarchy. We give a surprising negative answer to this question. We show that relative to any generic oracle G and for any k/spl ges/ 2, there exists a tally set in U/spl Deltasub ksup P/(G)/spl capspl Pisub ksup P/(G) but not in /spl Deltasub ksup P/(G). An immediate corollary is that generic oracles separate /spl Sigmasub ksup Pspl capspl Pisub ksup P/ and /spl Deltasub ksup P/. We also show that related results hold for type-2 complexity.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133271102","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}
引用次数: 9
Approximable sets 可逼近的集
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1995-08-01 DOI: 10.1109/SCT.1994.315822
R. Beigel, M. Kummer, F. Stephan
{"title":"Approximable sets","authors":"R. Beigel, M. Kummer, F. Stephan","doi":"10.1109/SCT.1994.315822","DOIUrl":"https://doi.org/10.1109/SCT.1994.315822","url":null,"abstract":"Much structural work on NP-complete sets has exploited SAT's d-self-reducibility. We exploit the additional fact that SAT is a d-cylinder to show that NP-complete sets are p-superterse unless P=NP. In fact, every set that is NP-hard under polynomial-time n/sup o(1/)-tt reductions is p-superterse unless P=NP. In particular no p-selective set is NP-hard under polynomial-time n/sup o(1/)-tt reductions unless P=NP. In addition, no easily countable set is NP-hard under Turing reductions unless P=NP. Self-reducibility does not seem to suffice for our main result: in a relativized world, we construct a d-self-reducible set in NP-P that is polynomial-time 2-tt reducible to a p-selective set.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127499502","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}
引用次数: 93
Relationships among PL, #L, and the determinant PL， #L和行列式之间的关系
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-12-01 DOI: 10.1109/SCT.1994.315797
E. Allender, M. Ogihara
{"title":"Relationships among PL, #L, and the determinant","authors":"E. Allender, M. Ogihara","doi":"10.1109/SCT.1994.315797","DOIUrl":"https://doi.org/10.1109/SCT.1994.315797","url":null,"abstract":"Results by Toda (1991), Vinay (1991), Damm (1991), and Valiant (1992) have shown that the complexity of the determinant is characterized by the complexity of counting the number of accepting computations of a nondeterministic logspace-bounded machine. (This class of functions is known as L.) By using that characterization and by establishing a few elementary closure properties, we give a very simple proof of a theorem of Jung (1985), showing that probabilistic logspace-bounded (PL) machines lose none of their computational power if they are restricted to run in polynomial time. We also present new results comparing and contrasting the classes of functions reducible to PL, #L, and the determinant, using various notions of reducibility.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122716510","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}
引用次数: 135
Logical definability of counting functions 计数函数的逻辑可定义性
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-06-28 DOI: 10.1109/SCT.1994.315798
K. Compton, E. Grädel
{"title":"Logical definability of counting functions","authors":"K. Compton, E. Grädel","doi":"10.1109/SCT.1994.315798","DOIUrl":"https://doi.org/10.1109/SCT.1994.315798","url":null,"abstract":"The relationship between counting functions and logical expressibility is explored. The most well studied class of counting functions is P, which consists of the functions counting the accepting computation paths of a nondeterministic polynomial-time Turing machine. For a logic L, L is the class of functions on finite structures (of a fixed signature) counting the tuples (T~, c~) satisfying a given formula /spl psi/(T~, c~) in (L. Saluja et al., 1992) showed that on classes of ordered structures FO= P (where FO denotes first-order logic) and that every function in /spl Sigmasub 1/ has a fully polynomial randomized approximation scheme. We give a probabilistic criterion for membership in /spl Sigmasub 1/ (on unordered structures). A consequence is that functions counting the number of cliques, the number of Hamilton cycles, and the number of pairs with distance greater than two in a graph, are not contained in /spl Sigmasub 1/. It is shown that on ordered structures /spl Sigmasub 1/ captures the previously studied class span P. On unordered structures FO is a proper subclass of P and /spl Sigmasub 1/ is a proper subclass of spanP; in fact, no class L contains all polynomial-time computable functions on unordered structures. However, it is shown that on unordered structures every function in P is identical almost everywhere with some function #FO, and similarly for /spl Sigmasub 1/ and spanP. Finally, it is shown that FO is closed under various operations under which P is closed, but that FO is not closed under other operations under which P would be closed only if certain generally believed assumptions in complexity theory failed.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126690624","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}
引用次数: 8
Generalized CNF satisfiability problems and non-efficient approximability 广义CNF可满足性问题与非有效逼近性
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-06-28 DOI: 10.1109/SCT.1994.315789
H. Hunt, M. Marathe, R. Stearns
{"title":"Generalized CNF satisfiability problems and non-efficient approximability","authors":"H. Hunt, M. Marathe, R. Stearns","doi":"10.1109/SCT.1994.315789","DOIUrl":"https://doi.org/10.1109/SCT.1994.315789","url":null,"abstract":"We use variants of the generalized CNF satisfiability problems SAT(S) of T.J. Schhaefer (1978) to characterize the efficient approximability of a number of basic NP and PSPACE-hard optimization problems in the literature. In contrast with the recent results, none of our proofs make use of interactive proof systems or of probabilistically checkable debate systems. In particular assuming P/spl ne/NP- or P/spl ne/PSPACE, we show that a number of the optimization problems shown not to be efficiently approximable can be shown not to be efficiently approximable by direct reductions, often of variants of the problems MAX NSF and ambiguous 3SAT. Moreover, often we show this, not only for arbitrary problem instances but also for planar problem instances and for f(n)-treewidth-bounded instances. Thus analogous to Zuckerman (1993), we show that: \"Planar NP-complete, PSPACE-complete, planar PSPACE-complete problems, etc. also have versions that are hard to approximate\".<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123872960","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}
引用次数: 20
Some consequences of our failure to prove non-linear lower bounds on explicit functions 未能证明显式函数的非线性下界的一些后果
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-06-28 DOI: 10.1109/SCT.1994.315815
R. Lipton
{"title":"Some consequences of our failure to prove non-linear lower bounds on explicit functions","authors":"R. Lipton","doi":"10.1109/SCT.1994.315815","DOIUrl":"https://doi.org/10.1109/SCT.1994.315815","url":null,"abstract":"Investigates the consequences of assuming that no explicit function has non-polynomial size Boolean circuit complexity. There are many consequences of this assumption. For example, it immediately proves that P does not equal NP. It also has ramifications for the length of certain interactive proofs.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"2012 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125653094","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}
引用次数: 11
NL/poly /spl sube/ /spl oplus/L/poly NL/poly /spl subbe / /spl oplus/L/poly
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-06-28 DOI: 10.1109/SCT.1994.315817
A. Wigderson
{"title":"NL/poly /spl sube/ /spl oplus/L/poly","authors":"A. Wigderson","doi":"10.1109/SCT.1994.315817","DOIUrl":"https://doi.org/10.1109/SCT.1994.315817","url":null,"abstract":"The article provides logspace analogs of the results of Valiant-Vazirani (L.G. Valiant and V.V. Vazirsni, 1986). We first show that solving STCONN for graphs with at most one st-path is essentially as hard as the general problem, via a probabilistic logspace reduction. We derive from it a nonuniform logspace reduction from NL to /spl oplus/L.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114982373","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}
引用次数: 25
Collapsing degrees in subexponential time 次指数时间内的坍缩度
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-06-28 DOI: 10.1109/SCT.1994.315788
D. Joseph, R. Pruim, Paul Young
{"title":"Collapsing degrees in subexponential time","authors":"D. Joseph, R. Pruim, Paul Young","doi":"10.1109/SCT.1994.315788","DOIUrl":"https://doi.org/10.1109/SCT.1994.315788","url":null,"abstract":"We show that there are subexponential deterministic time classes that have collapsing degrees. In particular, we prove the following: Let t be any effectively superpolynomial time bound. Then there is a set A/spl isin/DTIME(t) such that every set B/spl isin/deg/sub msup p/(A) is p-isomorphic to A.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"421 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122120704","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}
引用次数: 4
Multi-prover encoding schemes and three-prover proof systems 多证明者编码方案和三证明者证明系统
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-06-28 DOI: 10.1109/SCT.1994.315793
G. Tardos
{"title":"Multi-prover encoding schemes and three-prover proof systems","authors":"G. Tardos","doi":"10.1109/SCT.1994.315793","DOIUrl":"https://doi.org/10.1109/SCT.1994.315793","url":null,"abstract":"Suppose two provers agree in a polynomial p and want to reveal a single value y=p(x) to a verifier where m is chosen arbitrarily by the verifier. Whereas honest provers should be able to agree on any polynomial p the verifier wants to be sure that with any (cheating) pair of provers the value y he receives is a polynomial function of x. We formalize this question and introduce multi-prover (quasi-)encoding schemes to solve it. Multi-prover quasi-encoding schemes are used to develop new interactive proof techniques. The main result of M. Bellare et al. (1993) is the existence of one-round four-prover interactive proof system for any language an NP achieving any constant error probability with O(log n) random bits and poly(log log n) answer-sizes. We improve this result in two respects. First we decrease the number of provers to three, and then we decrease the answer-size to a constant. Reduction of each parameter de critical for applications. When the error-probability is required to approach zero, our technique is efficient in the number of random bits and in the answer size.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"371 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124643151","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}
引用次数: 10
The complexity of optimal queueing network control 最优排队网络控制的复杂性
Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory Pub Date : 1994-06-28 DOI: 10.1109/SCT.1994.315792
C. Papadimitriou, J. Tsitsiklis
{"title":"The complexity of optimal queueing network control","authors":"C. Papadimitriou, J. Tsitsiklis","doi":"10.1109/SCT.1994.315792","DOIUrl":"https://doi.org/10.1109/SCT.1994.315792","url":null,"abstract":"We consider the classical problem of optimal control (routing and sequencing) of a network of queues. We prove that this problem is EXP-complete and, therefore, provably intractable. Similar results are established for restricted versions of the problem. A weaker result is also established for the restless bandit problem.<<ETX>>","PeriodicalId":386782,"journal":{"name":"Proceedings of IEEE 9th Annual Conference on Structure in Complexity Theory","volume":"97 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114185281","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}
引用次数: 284
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