Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185355
A. Feldmann, J. Sgall, S. Teng
The problem of online job scheduling on various parallel architectures is studied. An O((log log n)/sup 1/2/)-competitive algorithm for online dynamic scheduling on an n*n mesh is given. It is proved that this algorithm is optimal up to a constant factor. The algorithm is not greedy, and the lower bound proof shows that no greedy-like algorithm can be very good. The upper bound result can be generalized to any fixed-dimensional meshes. Competitive scheduling algorithms for other architectures are given.<>
{"title":"Dynamic scheduling on parallel machines","authors":"A. Feldmann, J. Sgall, S. Teng","doi":"10.1109/SFCS.1991.185355","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185355","url":null,"abstract":"The problem of online job scheduling on various parallel architectures is studied. An O((log log n)/sup 1/2/)-competitive algorithm for online dynamic scheduling on an n*n mesh is given. It is proved that this algorithm is optimal up to a constant factor. The algorithm is not greedy, and the lower bound proof shows that no greedy-like algorithm can be very good. The upper bound result can be generalized to any fixed-dimensional meshes. Competitive scheduling algorithms for other architectures are given.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124089850","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}
The communication complexity of zero-knowledge proof systems is improved. Let C be a Boolean circuit of size n. Previous zero-knowledge proof systems for the satisfiability of C require the use of Omega (kn) bit commitments in order to achieve a probability of undetected cheating not greater than 2/sup -k/. In the case k=n, the communication complexity of these protocols is therefore Omega (n/sup 2/) bit commitments. A zero-knowledge proof is given for achieving the same goal with only O(n/sup m/+k square root n/sup m/) bit commitments, where m=1+ epsilon /sub n/ and epsilon /sub n/ goes to zero as n goes to infinity. In the case k=n, this is O(n square root n/sup m/). Moreover, only O(k) commitments need ever be opened, which is interesting if committing to a bit is significantly less expensive than opening a commitment.<>
{"title":"Subquadratic zero-knowledge","authors":"J. Boyar, G. Brassard, R. Peralta","doi":"10.1145/227683.227686","DOIUrl":"https://doi.org/10.1145/227683.227686","url":null,"abstract":"The communication complexity of zero-knowledge proof systems is improved. Let C be a Boolean circuit of size n. Previous zero-knowledge proof systems for the satisfiability of C require the use of Omega (kn) bit commitments in order to achieve a probability of undetected cheating not greater than 2/sup -k/. In the case k=n, the communication complexity of these protocols is therefore Omega (n/sup 2/) bit commitments. A zero-knowledge proof is given for achieving the same goal with only O(n/sup m/+k square root n/sup m/) bit commitments, where m=1+ epsilon /sub n/ and epsilon /sub n/ goes to zero as n goes to infinity. In the case k=n, this is O(n square root n/sup m/). Moreover, only O(k) commitments need ever be opened, which is interesting if committing to a bit is significantly less expensive than opening a commitment.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124755473","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185387
N. Bshouty, Richard Cleve, Wayne Eberly
Some tradeoffs between the size and depth of algebraic formulas are proved. It is shown that, for any fixed in >0, any algebraic formula of size S can be converted into an equivalent formula of depth O(log S) and size O(S/sup 1+ in /). This result is an improvement over previously known results where, to obtain the same depth bound, the formula size is Omega (S/sup alpha /), with alpha >or=2.<>
证明了代数公式的大小和深度之间的一些权衡。结果表明，对于任意大于0的定值，任意大小为S的代数公式都可以转化为深度为O(log S)，大小为O(S/sup 1+ in /)的等效公式。这个结果是对先前已知结果的改进，其中，为了获得相同的深度边界，公式大小为Omega (S/sup alpha /)， alpha >或=2。
{"title":"Size-depth tradeoffs for algebraic formulae","authors":"N. Bshouty, Richard Cleve, Wayne Eberly","doi":"10.1109/SFCS.1991.185387","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185387","url":null,"abstract":"Some tradeoffs between the size and depth of algebraic formulas are proved. It is shown that, for any fixed in >0, any algebraic formula of size S can be converted into an equivalent formula of depth O(log S) and size O(S/sup 1+ in /). This result is an improvement over previously known results where, to obtain the same depth bound, the formula size is Omega (S/sup alpha /), with alpha >or=2.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125065582","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185397
N. Kahalé
The expansion properties of regular graphs are investigated. The best previously known expansion of subsets of linear size of explicit k-regular graphs is k/4. This bound is achieved by nonbipartite Ramanujan graphs of degree k=p+1, which have the property that all but the largest eigenvalue have absolute value at most 2 square root p. The expansion coefficient for linear subsets for nonbipartite Ramanujan graphs is improved to 3(k-2)/8. Other results are established, including improved results about random walks on expanders.<>
{"title":"Better expansion for Ramanujan graphs","authors":"N. Kahalé","doi":"10.1109/SFCS.1991.185397","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185397","url":null,"abstract":"The expansion properties of regular graphs are investigated. The best previously known expansion of subsets of linear size of explicit k-regular graphs is k/4. This bound is achieved by nonbipartite Ramanujan graphs of degree k=p+1, which have the property that all but the largest eigenvalue have absolute value at most 2 square root p. The expansion coefficient for linear subsets for nonbipartite Ramanujan graphs is improved to 3(k-2)/8. Other results are established, including improved results about random walks on expanders.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117351414","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185342
D. Lapidot, A. Shamir
A major open problem in the theory of multiprover protocols is to characterize the languages which can be accepted by fully parallelized protocols which achieve an exponentially low probability of cheating in a single round. The problem was motivated by the observation that the probability of cheating the n parallel executions of a multiprover protocol can be exponentially higher than the probability of cheating in n sequential executions of the same protocol. The problem is solved by proving that any language in NEXP-time has a fully parallelized multiprover protocol. By combining this result with a fully parallelized version of the protocol of M. Ben-Or et al. (ACM Symp. on Theory of Computing, 1988), a one-round perfect zero-knowledge protocol (under no cryptographic assumptions) can be obtained for every NEXPTIME language.<>
多证明者协议理论中的一个主要开放问题是描述可以被完全并行化协议接受的语言，从而在单轮中实现指数级低的作弊概率。这个问题的动机是观察到在多个证明者协议的n次并行执行中作弊的概率可以指数地高于在同一协议的n次连续执行中作弊的概率。通过证明在NEXP-time中的任何语言都具有完全并行的多证明程序协议，可以解决这个问题。通过将该结果与M. Ben-Or等人的协议的完全并行化版本相结合。在《计算理论》(Theory of Computing, 1988)中，对于每一种NEXPTIME语言，都可以获得一轮完美的零知识协议(在没有密码学假设的情况下)。
{"title":"Fully parallelized multi prover protocols for NEXP-time","authors":"D. Lapidot, A. Shamir","doi":"10.1109/SFCS.1991.185342","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185342","url":null,"abstract":"A major open problem in the theory of multiprover protocols is to characterize the languages which can be accepted by fully parallelized protocols which achieve an exponentially low probability of cheating in a single round. The problem was motivated by the observation that the probability of cheating the n parallel executions of a multiprover protocol can be exponentially higher than the probability of cheating in n sequential executions of the same protocol. The problem is solved by proving that any language in NEXP-time has a fully parallelized multiprover protocol. By combining this result with a fully parallelized version of the protocol of M. Ben-Or et al. (ACM Symp. on Theory of Computing, 1988), a one-round perfect zero-knowledge protocol (under no cryptographic assumptions) can be obtained for every NEXPTIME language.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"351 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124447895","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185377
B. Awerbuch, G. Varghese
The notion of distributed program checking as a means of making a distributed algorithm self-stabilizing is explored. A compiler that converts a deterministic synchronous protocol pi for static networks into a self-stabilizing version of pi for dynamic networks is described. If T/sub pi / is the time complexity of pi and D is a bound on the diameter of the final network, the compiled version of pi stabilizes in time O(D+T/sub pi /) and has the same space complexity as pi . The general method achieves efficient results for many specific noninteractive tasks. For instance, solutions for the shortest paths and spanning tree problems take O(D) to stabilize, an improvement over the previous best time of O(D/sup 2/).<>
{"title":"Distributed program checking: a paradigm for building self-stabilizing distributed protocols","authors":"B. Awerbuch, G. Varghese","doi":"10.1109/SFCS.1991.185377","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185377","url":null,"abstract":"The notion of distributed program checking as a means of making a distributed algorithm self-stabilizing is explored. A compiler that converts a deterministic synchronous protocol pi for static networks into a self-stabilizing version of pi for dynamic networks is described. If T/sub pi / is the time complexity of pi and D is a bound on the diameter of the final network, the compiled version of pi stabilizes in time O(D+T/sub pi /) and has the same space complexity as pi . The general method achieves efficient results for many specific noninteractive tasks. For instance, solutions for the shortest paths and spanning tree problems take O(D) to stabilize, an improvement over the previous best time of O(D/sup 2/).<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134397868","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 general theory of using a congruence closure based simplifier (CCNS) proposed by P. Chew (1980) for computing normal forms is developed, and several applications are presented. An independent set of postulates is given, and it is proved that CCNS can be used for any system that satisfies them. It is then shown that CCNS can be used for consistent convergent systems and for various kinds of priority rewrite systems. A simple translation scheme for converting priority systems into effectively nonoverlapping convergent systems is presented.<>
{"title":"A theory of using history for equational systems with applications","authors":"Rakesh M. Verma","doi":"10.1145/210118.210130","DOIUrl":"https://doi.org/10.1145/210118.210130","url":null,"abstract":"A general theory of using a congruence closure based simplifier (CCNS) proposed by P. Chew (1980) for computing normal forms is developed, and several applications are presented. An independent set of postulates is given, and it is proved that CCNS can be used for any system that satisfies them. It is then shown that CCNS can be used for consistent convergent systems and for various kinds of priority rewrite systems. A simple translation scheme for converting priority systems into effectively nonoverlapping convergent systems is presented.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133361872","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185366
Howard Aizenstein, L. Pitt
A polynomial-time algorithm is presented for exactly learning the class of read-twice DNF formulas, i.e. Boolean formulas in disjunctive normal form where each variable appears at most twice. The (standard) protocol used allows the learning algorithm to query whether a given assignment of Boolean variables satisfies the DNF formula to be learned (membership queries), as well as to obtain counterexamples to the correctness of its current hypothesis which can be any arbitrary DNF formula (equivalence queries). The formula output by the learning algorithm is logically equivalent to the formula to be learned.<>
{"title":"Exact learning of read-twice DNF formulas","authors":"Howard Aizenstein, L. Pitt","doi":"10.1109/SFCS.1991.185366","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185366","url":null,"abstract":"A polynomial-time algorithm is presented for exactly learning the class of read-twice DNF formulas, i.e. Boolean formulas in disjunctive normal form where each variable appears at most twice. The (standard) protocol used allows the learning algorithm to query whether a given assignment of Boolean variables satisfies the DNF formula to be learned (membership queries), as well as to obtain counterexamples to the correctness of its current hypothesis which can be any arbitrary DNF formula (equivalence queries). The formula output by the learning algorithm is logically equivalent to the formula to be learned.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124740604","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185363
M. Kunde
Sorting and routing on r-dimensional n*. . .*n grids of processors is studied. Deterministic algorithms are presented for h-h problems, h>or=1, where each processor initially and finally contains h elements. It is shown that the classical 1-1 sorting can be solved with (2r-1.5)n+o(n) transport steps, i.e. in about 2.5n steps for r=2. The general h-h sorting problem, h>or=4r-4 can be solved within a number of transport steps that asymptotically differs by a factor of at most 3 from the trivial bisection bound. Furthermore, the bisection bound is asymptotically tight for sequences of h permutation routing problems, h=4cr, c>or=1, and for so-called offline routing.<>
{"title":"Concentrated regular data streams on grids: sorting and routing near to the bisection bound","authors":"M. Kunde","doi":"10.1109/SFCS.1991.185363","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185363","url":null,"abstract":"Sorting and routing on r-dimensional n*. . .*n grids of processors is studied. Deterministic algorithms are presented for h-h problems, h>or=1, where each processor initially and finally contains h elements. It is shown that the classical 1-1 sorting can be solved with (2r-1.5)n+o(n) transport steps, i.e. in about 2.5n steps for r=2. The general h-h sorting problem, h>or=4r-4 can be solved within a number of transport steps that asymptotically differs by a factor of at most 3 from the trivial bisection bound. Furthermore, the bisection bound is asymptotically tight for sequences of h permutation routing problems, h=4cr, c>or=1, and for so-called offline routing.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121657349","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185423
N. Alon
The Lovasz local lemma (1975) is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of losing a little in the estimates, but his method does not seem to be parallelizable. His technique is modified to achieve an algorithmic version that can be parallelized, thus providing deterministic NC/sup 1/ algorithms for various interesting algorithmic search problems.<>
{"title":"A parallel algorithmic version of the local lemma","authors":"N. Alon","doi":"10.1109/SFCS.1991.185423","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185423","url":null,"abstract":"The Lovasz local lemma (1975) is a tool that enables one to show that certain events hold with positive, though very small probability. It often yields existence proofs of results without supplying any efficient way of solving the corresponding algorithmic problems. J. Beck has recently found a method for converting some of these existence proofs into efficient algorithmic procedures, at the cost of losing a little in the estimates, but his method does not seem to be parallelizable. His technique is modified to achieve an algorithmic version that can be parallelized, thus providing deterministic NC/sup 1/ algorithms for various interesting algorithmic search problems.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125243438","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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