22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)最新文献

{"title":"Towards separating nondeterministic time from deterministic time","authors":"R. Kannan","doi":"10.1109/SFCS.1981.51","DOIUrl":"https://doi.org/10.1109/SFCS.1981.51","url":null,"abstract":"It would be of interest to separate nondeterminism from determinism i.e., to show that for all \"nice\" functions t(n), NTIME (t(n)), (the class of languages accepted by multitape nondeterministic Turing machines in time O(t(n))) strictly contains DTIME (t(n)) (the class of languages accepted by multitape deterministic Turing machines in time O(t(n)). We establish a weaker form of the statement. We show that there is a universal constant k such that for all \"nice\" functions t(n), the class of languages that can be accepted simultaneously in deterministic time O(t(n)) and space o((t(n))1/k) is strictly contained in NTIME (t(n)). (We will use the notation SPACE, TIME (s(n),t(n)) to denote the class of languages accepted by a deterministic TM in time O(t(n)) and simultaneously space O(s(n)).) This result is proved using a time-alternation trade-off and several other applications of this trade-off are presented. For example, we show that for each language L in SPACE, TIME (nl-ε, ni) (where o≪ε≪l, ε, i constants) there exists a j such that L is accepted by a O(n) time bounded alternating Turing machine with j alternations. The trade-off also leads to the separation ∪SεSt SPACE, TIME (s,t)⊂+Σ2 TIME(t) where t(n) is any \"nice\" function and St is a class of \"nice\" functions in o(t). Here St includes most natural functions for natural t. For example, nj/log*n is in Snj.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127072020","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}

{"title":"A fast probabilistic parallel sorting algorithm","authors":"R. Reischuk","doi":"10.1109/SFCS.1981.6","DOIUrl":"https://doi.org/10.1109/SFCS.1981.6","url":null,"abstract":"We describe a probabilistic parallel algorithm to sort n keys drawn from some arbitrary total ordered set. This algorithm can be implemented on a parallel computer consisting of n RAMs, each with small private memory, and a common memory of size O(n) such that the average runtime is bounded by O(log n). Hence for this algorithm the product of time and number of processors meets the information theoretic lower bound for sorting.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114137452","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}

{"title":"A complexity calculus for classes of recursive search programs over tree structures","authors":"P. Flajolet, J. Steyaert","doi":"10.1109/SFCS.1981.2","DOIUrl":"https://doi.org/10.1109/SFCS.1981.2","url":null,"abstract":"We study a restricted programming language over tree structures. For this language, we give systematic translation rules which map programs into complexity descriptors. The descriptors are in the form of generating functions of average costs. Such a direct approach avoids the recourse to recurrences; it therefore simplifies the task of analyzing algorithms in the class considered and permits analysis of structurally complex programs. It also allows for a clear discussion of analytic properties of complexity descriptors whose singularities are related to the asymptotic behavior of average costs. Algorithms that are analyzed in this way include: formal differentiation, tree matching, tree embedding and simplification of expressions in a diversity of contexts. Some general results relating (average case) complexity properties to structural properties of programs in the class can also be derived in this framework.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130785753","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}

{"title":"A model of concurrent database transactions","authors":"R. Sethi","doi":"10.1109/SFCS.1981.8","DOIUrl":"https://doi.org/10.1109/SFCS.1981.8","url":null,"abstract":"When several transactions (processes) read and write items in a database, the question of consistency of the database arises. Consistency is maintained if transactions are serial: all actions of a transaction execute completely before the actions of the next transaction begin. A particular history of interleaved actions belonging to several transactions is correct if it is equivalent to a serial history. We provide a natural framework for studying serializability that encompasses models that have been considered in the literature. A history is represented by a dag in which there is a vertex for each instantaneous value taken by an item in the database. The main tool for determining serializability are \"exclusion rules\" which determine implied orderings between vertices. For example, a vertex that uses a value must be serialized before the value is overwritten. An exclusion closure -- the result of applying the rules as long as possible -- can be constructed in time cubic in the number of vertices. Since determining serializability is NP-complete, exclusion closures cannot always decide serializability, but useful sufficient conditions can be proven. Exclusion closures allow the largest known classes of polynomially serializable histories to be properly extended. When studying serializability it is not necessary to work solely with the dag containing instantaneous values of all items. Three abstractions of the dag are presented which correspond to models of transactions and to \"version graphs\" in the literature. Since serializability of histories is known to be NP-complete, subclasses of serializable histories have been studied. One such class consists of histories serializable in a strict sense: transactions that are already in serial in a history must remain in the same relative order. When there are no useless actions in a history, strict serializability can be determined in polynomial time. If useless actions are permitted then strict serializability becomes NP-complete. The above results apply to two step transactions in which there is a read step followed by a write step, Each step involves some subset of the items in the database. With multistep transactions strict serializability is NP-complete even if there are no useless actions.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133856193","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}

{"title":"On the asymptotic complexity of matrix multiplication","authors":"D. Coppersmith, S. Winograd","doi":"10.1137/0211038","DOIUrl":"https://doi.org/10.1137/0211038","url":null,"abstract":"The main results of this paper have the following flavor: given one algorithm for multiplying matrices, there exists another, better, algorithm. A consequence of these results is that ω, the exponent for matrix multiplication, is a limit point, that is, cannot be realized by any single algorithm. We also use these results to construct a new algorithm which shows that ω ≪ 2.495364.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134030715","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}

{"title":"An O(N4/3) lower bound on the mono tone network complexity of N-TH degree convolution","authors":"Norbert Blum","doi":"10.1109/SFCS.1981.10","DOIUrl":"https://doi.org/10.1109/SFCS.1981.10","url":null,"abstract":"We prove an Ω(n4/3) lower bound for the number of ∧-gates in any monotone network computing n-th degree convolution.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124052908","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}

{"title":"Time-space trade-offs for general recursion","authors":"R. Verbeek","doi":"10.1109/SFCS.1981.50","DOIUrl":"https://doi.org/10.1109/SFCS.1981.50","url":null,"abstract":"A lower bound for the time-space trade-off of pebble games on PD-Graphs (which represent computations of push-down automata or recursion schemes) is proved, that is only a bit lower than the best known upper bound (the lower and upper time bound is about n ¿ 2 logn/log(s/log n)). The best lower bound known up to now is the bound for linear recursion (about n ¿ log n/log(s/log n) for s ≫ log n.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129892002","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}

{"title":"Worst-case ration for planar graphs and the method of induction on faces","authors":"C. Papadimitriou, M. Yannakakis","doi":"10.1109/SFCS.1981.55","DOIUrl":"https://doi.org/10.1109/SFCS.1981.55","url":null,"abstract":"The fact that several inlportant combinatorial optimiz.ation problems are NP-colnplete has motivated research on the worst-case analysis of approximation heuristics for these problems [Jol, GIl, Ch). TIlcse inve.stigations have produced some very interesting results\" and considerable insight has been gained by nov into the power and limitations of existing techniques. The most inlportnnt paradigm in this area is bin packing [JDGGU, J02, Yao, GJ2, GJ3] and its generalizations [GOJY, CGJT). '[his is so because of the elegance and depth of the cOlnbinatorial arguments employed in the proofs of the upper bounds, and the intricate constnlctions of exanlples that achieve them. Despite the presence of the unifying cotlcept of a weighting [unction, the arguments are usually ingenious yet ad hoc, and the construction of worst-case exmnp)es is largely decoupled from the upper bounding process. In this paper we present a fanlily of results concerning certain extrenlal properties of planar graphs. In particular we show the folloving: (1) The greedy heuristic (i.e., repeatedly pick the node with smallest degree and delete its neighborhood) applied to a planar graph with n nodes yields an independent set of size at least 4n/21. (2) l'he greedy heuristic yields an independent set at )etlst 23/63 times the optimum. (3) A planar graph with n nodes and minimum degree 3 has ahvays a nzatching with fewer than n/3 free nodes.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126785934","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}

{"title":"Probabilistic algorithms in finite fields","authors":"M. Ben-Or","doi":"10.1109/SFCS.1981.37","DOIUrl":"https://doi.org/10.1109/SFCS.1981.37","url":null,"abstract":"We present probabilistic algorithms for the problems of finding an irreducible polynomial of degree n over a finite field, finding roots of a polynomial, and factoring a polynomial into its irreducible factors over a finite field. All of these problems are of importance in algebraic coding theory, algebraic symbol manipulation, and number theory. These algorithms have a very transparent, easy to program structure. For finite fields of large characteristic p, so that exhaustive search through ${text{Z}}_p $, is not feasible, our algorithms are of lower order in the degrees of the polynomial and fields in question, than previously published algorithms.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1980-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124135582","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}

{"title":"The complexity of searching a graph","authors":"N. Megiddo, S. Hakimi, M. Garey, David S. Johnson, C. Papadimitriou","doi":"10.1145/42267.42268","DOIUrl":"https://doi.org/10.1145/42267.42268","url":null,"abstract":"T. Parsons proposed and partially analyzed the following pursuit-evasion problem on graphs: A team of searchers traverse the edges of a graph G in pursuit of a fugitive, who moves along the edges of the graph with complete knowledge of the locations of the pursuers. What is the smallest number s(G) of searchers that will suffice for guaranteeing capture of the fugitive? We show that determining whether s(G) ≤ K, for a given integer K, is NP-hard for general graphs but can be solved in linear time for trees. We also provide a structural characterization of those graphs with s(G) ≤ K for K = 1,2,3.","PeriodicalId":224735,"journal":{"name":"22nd Annual Symposium on Foundations of Computer Science (sfcs 1981)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129669764","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}