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[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference最新文献

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Gap-definable counting classes 间隙可定义的计数类
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-11-22 DOI: 10.1109/SCT.1991.160241
Stephen A. Fenner, L. Fortnow, S. Kurtz
{"title":"Gap-definable counting classes","authors":"Stephen A. Fenner, L. Fortnow, S. Kurtz","doi":"10.1109/SCT.1991.160241","DOIUrl":"https://doi.org/10.1109/SCT.1991.160241","url":null,"abstract":"The function class Hash P lacks a crucial closure property: it is not closed under subtraction. To remedy this problem, the authors introduce the function class GapP as a natural alternative to Hash P. GapP is the closure of Hash P under subtraction, and has all the other useful closure properties of Hash P as well. It is shown that most previously studied counting classes are gap-definable, i.e., definable using the values of GapP functions alone. It is shown that there is a smallest gap-definable class, SPP, which is still large enough to contain Few. It is also shown that SPP consists of exactly those languages low for GapP, and thus SSP languages are low for any gap-definable class. It is further shown that any countable collection of languages is contained in a unique minimum gap-definable class, which implies that the gap-definable classes form a lattice under inclusion. Subtraction seems necessary for this result, since nothing similar is known for the Hash P-definable classes.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114410589","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: 205
Connections between the complexity of unique satisfiability and the threshold behavior of randomized reductions 唯一可满足性的复杂性与随机化约的阈值行为之间的联系
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160268
Richard Chang, Jim Kadin, P. Rohatgi
{"title":"Connections between the complexity of unique satisfiability and the threshold behavior of randomized reductions","authors":"Richard Chang, Jim Kadin, P. Rohatgi","doi":"10.1109/SCT.1991.160268","DOIUrl":"https://doi.org/10.1109/SCT.1991.160268","url":null,"abstract":"The present research is motivated by new results on the complexity of the unique satisfiability problem (USAT). Some new results are obtained, using the concept of randomized reductions. The proofs use only the fact that USAT is complete for D/sup P/ under randomized reductions, even though the probability bound of these reductions may be low. Furthermore, the results show that the structural complexities of USAT and D/sup P/ many-one complete sets are very similar, lending support to the argument that even sets complete under 'weak' randomized reductions can capture the properties of the many-one complete sets. The authors generalize these results for the Boolean hierarchy and give upper and lower bounds on the thresholds for these classes.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123107200","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: 18
On one query, self-reducible sets 在一个查询上，自约集
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160254
M. Ogihara, A. Lozano
{"title":"On one query, self-reducible sets","authors":"M. Ogihara, A. Lozano","doi":"10.1109/SCT.1991.160254","DOIUrl":"https://doi.org/10.1109/SCT.1991.160254","url":null,"abstract":"The authors study one-word-decreasing self-reducible sets, which are the usual self-reducible sets with the peculiarity that the self-reducibility machine makes at most one query to a word lexicographically smaller than the input. It is first shown that for all counting classes defined by a predicate on the number of accepting paths there exist complete sets which are one-word-decreasing self-reducible. Using this fact it is proved that, for any class K chosen from a certain set of complexity classes, it holds that (1) if there is a sparse polynomial-time bounded-truth-table-hard set for K, then K=P, and (2) if there is a sparse strongly nondeterministic bounded-truth-table-hard set for K, then K contained in NP intersection co-NP. The main result also shows that the same facts hold for the class PSPACE.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116949599","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: 29
Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits 计数辅助下推自动机和半无界算术电路
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160269
V. Vinay
{"title":"Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits","authors":"V. Vinay","doi":"10.1109/SCT.1991.160269","DOIUrl":"https://doi.org/10.1109/SCT.1991.160269","url":null,"abstract":"The author examines various counting measures on space bounded nondeterministic auxiliary pushdown machines. In the main theorem, it is shown how a NAuxPDA may be simulated efficiently by a uniform family of Boolean circuits, which preserve the number of accepting paths in the NAuxPDA as the number of accepting subtrees in the Boolean circuit. The techniques used simulate the NAuxPDA in a novel way by considering the height and reversal bounds of an AuxPDA. One of the highlights of the present work is an exact characterization of the important class DET. It is shown that DET is exactly the class of functions that can be computed as the difference between the outputs of two counting logspace machines.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122894721","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: 127
A pseudorandom oracle characterization of BPP BPP的伪随机oracle表征
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160261
J. H. Lutz
{"title":"A pseudorandom oracle characterization of BPP","authors":"J. H. Lutz","doi":"10.1109/SCT.1991.160261","DOIUrl":"https://doi.org/10.1109/SCT.1991.160261","url":null,"abstract":"It is known from work of C.H. Bennett and J. Gill (1981) and K. Ambos-Spies (1986) that the following conditions are equivalent: (i) L in BPP; (ii); for almost all oracles A, l in P/sup A/. It is shown here that the following conditions are also equivalent to (i) and (ii): (iii) the set of oracles A for which L in P/sup A/ has pspace-measure 1; (iv) for every pspace-random oracle A, L in P/sup A/. It follows from this characterization that almost every A in DSPACE (2/sup poly/) is polynomial-time hard for BPP. Succinctly, the main content of the proof is that pseudorandom generators exist relative to every pseudorandom oracle.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115806017","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: 21
On the computational complexity of small descriptions 小描述的计算复杂度
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160247
Ricard Gavaldà, O. Watanabe
{"title":"On the computational complexity of small descriptions","authors":"Ricard Gavaldà, O. Watanabe","doi":"10.1109/SCT.1991.160247","DOIUrl":"https://doi.org/10.1109/SCT.1991.160247","url":null,"abstract":"For a set L that is polynomial time reducible to some sparse set, the authors investigate the computational complexity of such sparse sets relative to L. They construct sets A and B such that both of them are polynomial time reducible to some sparse set, but A (resp., B) is polynomial time reducible to no sparse set in P/sup A/ (resp., NP/sup B/ intersection co-NP/sup B/); that is, the complexity of sparse sets to which A (resp., B) is reducible is more than P/sup A/ (resp., NP/sup B/ intersection co-NP/sup B/). From these results and/or application of their proof technique the authors obtain: (1) lower bounds for the relative complexity of finding polynomial size circuits for some sets in P/poly, and (2) separations of the equivalence classes of sparse sets under various reducibilities.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124562516","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: 27
Monotone separation of logspace from NC/sup 1/ NC/sup的对数空间单调分离
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160272
M. Grigni, M. Sipser
{"title":"Monotone separation of logspace from NC/sup 1/","authors":"M. Grigni, M. Sipser","doi":"10.1109/SCT.1991.160272","DOIUrl":"https://doi.org/10.1109/SCT.1991.160272","url":null,"abstract":"It is shown that the monotone analog of logspace computation is more powerful than monotone log-depth circuits: monotone circuits for a certain function in monotone logspace require depth Omega (lg/sup 2/n). It is proved that mNC/sup 1/ not=mL. This result shows that the process of pointer jumping, i.e. following a chain of pointers to the end, cannot be simulated by a monotone NC/sup 1/ circuit. The proof is based upon the communication game method of A. Karchmer and A. Wigderson (1990).<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126837787","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: 3
On the random-self-reducibility of complete sets 完备集的随机自约性
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160252
J. Feigenbaum, L. Fortnow
{"title":"On the random-self-reducibility of complete sets","authors":"J. Feigenbaum, L. Fortnow","doi":"10.1109/SCT.1991.160252","DOIUrl":"https://doi.org/10.1109/SCT.1991.160252","url":null,"abstract":"Informally, a function f is random-self-reducible if the evaluation of f at any given instance x can be reduced in polynomial time to the evaluation of f at one or more random instances y/sub i/. A set is random-self-reducible if its characteristic function is. The authors generalize the previous formal definitions of random-self-reducibility. They show that, even under this very general definition, sets that are complete for any level of the polynomial hierarchy are not random-self-reducible, unless the hierarchy collapses. In particular, NP-complete sets are not random-self-reducible, unless the hierarchy collapses at the third level. By contrast, the authors show that sets complete for the classes PP and MOD/sub m/P are random-self-reducible.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"243 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115588094","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: 206
DSPACE (n/sup k/)=VAR(k+1) DSPACE (n/sup k/)=VAR(k+1)
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160278
Neil Immerman
{"title":"DSPACE (n/sup k/)=VAR(k+1)","authors":"Neil Immerman","doi":"10.1109/SCT.1991.160278","DOIUrl":"https://doi.org/10.1109/SCT.1991.160278","url":null,"abstract":"The author proves that the set of properties checkable by a Turing machine in DSPACE(n/sup k/) is exactly equal to the set of properties describable by a uniform sequence of first-order sentences using at most k+1 distinct variables. He proves that this is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity k. This is a refinement of the theorem PSPACE=VAR(O(1)). The author suggests some directions for exploiting this result to derive tradeoffs between the number of variables and the quantifier-depth in descriptive complexity. This has applications to parallel complexity.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115399865","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: 6
Exponential time and subexponential time sets 指数时间和次指数时间集合
[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference Pub Date : 1991-06-30 DOI: 10.1109/SCT.1991.160265
Shouwen Tang, B. Fu, Tian Liu
{"title":"Exponential time and subexponential time sets","authors":"Shouwen Tang, B. Fu, Tian Liu","doi":"10.1109/SCT.1991.160265","DOIUrl":"https://doi.org/10.1109/SCT.1991.160265","url":null,"abstract":"The authors prove that the symmetric difference of a <or=/sup P//sub k-parity/-hard set for E and a subexponential time computable set is still <or=P/sub k-parity/-hard for E. This remains true for a <or=/sup P//sub m/-hard set for E since 1-parity reduction is many-one reduction. In addition, it is shown that it is not the case with respect to some other types of reductions. The authors introduce and study the notions of E-complete and E-hard kernels.<<ETX>>","PeriodicalId":158682,"journal":{"name":"[1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130335992","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: 17
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