We give a parallel RAM algorithm for simulating a deterministic auxiliary pushdown machine. If the pushdown machine uses space s(n) ≥ log n and time 2O(s(n)) then our parallel simulation algorithm takes time O(s(n)) and requires 2 processors. Thus any deterministic context free language is accepted in time O(log n) by our parallel RAM algorithm using a polynomial number of processors. (Our algorithm can easily be extended to also accept the LR(k) languages in time O(log n) and 2O(k) Processors. Our simulation algorithm is near optimal for parallel RAMs, since we show that the language accepted in time T(n) by a parallel RAM is accepted by a deterministic auxiliary pushdown machine with space T(n) and time 2O(T(n)2).
{"title":"Parallel time O(log N) acceptance of deterministic CFLs","authors":"P. Klein, J. Reif","doi":"10.1137/0217027","DOIUrl":"https://doi.org/10.1137/0217027","url":null,"abstract":"We give a parallel RAM algorithm for simulating a deterministic auxiliary pushdown machine. If the pushdown machine uses space s(n) ≥ log n and time 2O(s(n)) then our parallel simulation algorithm takes time O(s(n)) and requires 2 processors. Thus any deterministic context free language is accepted in time O(log n) by our parallel RAM algorithm using a polynomial number of processors. (Our algorithm can easily be extended to also accept the LR(k) languages in time O(log n) and 2O(k) Processors. Our simulation algorithm is near optimal for parallel RAMs, since we show that the language accepted in time T(n) by a parallel RAM is accepted by a deterministic auxiliary pushdown machine with space T(n) and time 2O(T(n)2).","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124485124","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 show that the problem of deciding whether an instance of the traveling salesman problem has a uniquely optimal solution is complete for Δ2P.
我们证明了旅行推销员问题的一个实例对于Δ2P是否有唯一最优解的判定问题是完全的。
{"title":"On the complexity of unique solutions","authors":"C. Papadimitriou","doi":"10.1145/62.322435","DOIUrl":"https://doi.org/10.1145/62.322435","url":null,"abstract":"We show that the problem of deciding whether an instance of the traveling salesman problem has a uniquely optimal solution is complete for Δ2P.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122680408","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 Higher Reciprocity Laws are considered to be among the deepest and most fundamental results in number theory. Yet, they have until recently played no part in number theoretic algorithms. In this paper we explore the power of the laws in algorithms. The problem we consider is part of a group of well-studied problems about roots in finite fields and rings. Let F denote a finite field, let m denote a direct product of finite fields. Consider the following problems: Problem 1. Is Xn = a solvable in F; Problem 2. If Xn = a is solvable in F find X; Problem 3. Is Xn = a solvable in m; Problem 4. If Xn = a solvable in m find X.
{"title":"An application of higher reciprocity to computational number theory","authors":"L. Adleman, Robert McDonnell","doi":"10.1109/SFCS.1982.59","DOIUrl":"https://doi.org/10.1109/SFCS.1982.59","url":null,"abstract":"The Higher Reciprocity Laws are considered to be among the deepest and most fundamental results in number theory. Yet, they have until recently played no part in number theoretic algorithms. In this paper we explore the power of the laws in algorithms. The problem we consider is part of a group of well-studied problems about roots in finite fields and rings. Let F denote a finite field, let m denote a direct product of finite fields. Consider the following problems: Problem 1. Is Xn = a solvable in F; Problem 2. If Xn = a is solvable in F find X; Problem 3. Is Xn = a solvable in m; Problem 4. If Xn = a solvable in m find X.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114193349","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 analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an excellent agreement between the two. We also explain a certain empirically observed anomaly in the behaviour of the algorithm. Finally we establish that asymptotically perfect packing is possible when input items are drawn from a monotonically decreasing density function.
{"title":"Probabilistic analysis of some bin-packing problems","authors":"N. Karmarkar","doi":"10.1109/SFCS.1982.37","DOIUrl":"https://doi.org/10.1109/SFCS.1982.37","url":null,"abstract":"We analyze the average-case behaviour of the Next-Fit algorithm for bin-packing, and obtain closed-form expressions for distributions of interest. Our analysis is based on a novel technique of partitioning the interval (0, 1) suitably and then formulating the problem as a matrix-differential equation. We compare our analytic results with previously known simulation results and show that there is an excellent agreement between the two. We also explain a certain empirically observed anomaly in the behaviour of the algorithm. Finally we establish that asymptotically perfect packing is possible when input items are drawn from a monotonically decreasing density function.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133901014","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 purpose of our research whose prel iminary resul ts are reported here is to examine the following question: ~iven chiP ~ A, 1!!! 19 optimalli .!lloc.!~ .il 8IImJ 1/Q, !UD9.!:Y, and wiriy (internal
我们的研究，其初步结果在这里报告是为了检验以下问题:~给定芯片~ A, 1!!19 .最优。[1] [8] [1] [1] [9]:Y，和线形(内部
{"title":"Optimal allocation of computational resources in VLSI","authors":"Z. Kedem","doi":"10.1109/SFCS.1982.32","DOIUrl":"https://doi.org/10.1109/SFCS.1982.32","url":null,"abstract":"The purpose of our research whose prel iminary resul ts are reported here is to examine the following question: ~iven chiP ~ A, 1!!! 19 optimalli .!lloc.!~ .il 8IImJ 1/Q, !UD9.!:Y, and wiriy (internal <XIIIDUD.i.cation) so that sane function of interest can ~ cauputed .!p th;m:~~!Y minimtm !~.!? -P-;;h. suprisingly, the geanetric nature of the model makesit sufficiently \"structured\" so that meaningful study of the consequences of such allocatim for the purpose of designing provably optimal chips is feasibl e. ( I t is interesting to contrast this situation with the one in unstructured models, where simi! ar attempts at fomsal treatment of optimal allocation 00 not seem to be as fruitful.) Our resul ts pennit us to CXJDPletely characterize both the 8llount of resources required and their allocation for certain ccmputations, and to obtain previously proved lower bounds (which generally accomted for sane of the resources, or restricted their util ization in sane way) for certain fmctions as special cases, by invoking explicit constraints.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127755350","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 define two generalized types of a priority queue by allowing some forms of changing the priorities of the elements in the queue. We show that they can be implemented efficiently. Consequently, each operation takes O(log n) time. We use these generalized priority queues to construct an O(EV log V) algorithm for finding a maximal weighted matching in general graphs.
{"title":"Priority queues with variable priority and an O(EV log V) algorithm for finding a maximal weighted matching in general graphs","authors":"Z. Galil, S. Micali, H. Gabow","doi":"10.1137/0215009","DOIUrl":"https://doi.org/10.1137/0215009","url":null,"abstract":"We define two generalized types of a priority queue by allowing some forms of changing the priorities of the elements in the queue. We show that they can be implemented efficiently. Consequently, each operation takes O(log n) time. We use these generalized priority queues to construct an O(EV log V) algorithm for finding a maximal weighted matching in general graphs.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128967730","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}
This paper deals with the complexity of context-free grammars with 1-1etter terminal alphabet. We study the complexity of the membership problem and the inequivalence problem. We show that the first problem is NP-complete and the second one is Σ2p- complete with respect to log-space reduction. The second result also implies that the inequivalence problem is in PSPACE, solving an open problem stated in [3] by Hunt III, Rosenkrantz and Szymanski.
{"title":"Deciding the inequivalence of context-free grammars with 1-letter terminal alphabet is S2p-complete","authors":"Thiet-Dung Huynh","doi":"10.1109/SFCS.1982.65","DOIUrl":"https://doi.org/10.1109/SFCS.1982.65","url":null,"abstract":"This paper deals with the complexity of context-free grammars with 1-1etter terminal alphabet. We study the complexity of the membership problem and the inequivalence problem. We show that the first problem is NP-complete and the second one is Σ2p- complete with respect to log-space reduction. The second result also implies that the inequivalence problem is in PSPACE, solving an open problem stated in [3] by Hunt III, Rosenkrantz and Szymanski.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115656457","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 Ellipsoid Algorithm (EA) for linear programming attracted recently great attention. EA was proposed in [N76] and developed in [K79, G81] and other works. It is a modification of Method of Centralized Splitting presented in [L65], which differs from EA in two essential respects. Firstly, [L65] uses simplexes instead of ellipsoids; it is admitted, secondly, that, several (q(n))splittings of the n-dimensional simplex may be needed before the remaining polyhedron can be enclosed into a simplex of a smaller volume. Only a very rough upper bound q(n) ≪ nlog(n)follows from the reasoning of [L65]. This does not imply polynomiality of the computation time, since n, log(n) splittings may make the simplex very complex. We prove below that, q(n)= 1. Let the problem be to find x∈Rn such that Ax ≫ 0, where A is an m × n matrix of rank n. We normalize solutions by a restriction (e - Ax) = 1 where e ≫ 0. On every step the algorithm considers a simplex BAx ≥ 0 containing all solutions, where B is a non-negative n × m matrix with det(BA) ≠ 0. Let us denote this simplex by ΔB, its volume by VB and its center by CB. Initially we take an arbitrary B and e = BT(1,..,1).
{"title":"An old linear programming algorithm runs in polynomial time","authors":"Boris Yamnitsky, L. Levin","doi":"10.1109/SFCS.1982.63","DOIUrl":"https://doi.org/10.1109/SFCS.1982.63","url":null,"abstract":"The Ellipsoid Algorithm (EA) for linear programming attracted recently great attention. EA was proposed in [N76] and developed in [K79, G81] and other works. It is a modification of Method of Centralized Splitting presented in [L65], which differs from EA in two essential respects. Firstly, [L65] uses simplexes instead of ellipsoids; it is admitted, secondly, that, several (q(n))splittings of the n-dimensional simplex may be needed before the remaining polyhedron can be enclosed into a simplex of a smaller volume. Only a very rough upper bound q(n) ≪ nlog(n)follows from the reasoning of [L65]. This does not imply polynomiality of the computation time, since n, log(n) splittings may make the simplex very complex. We prove below that, q(n)= 1. Let the problem be to find x∈Rn such that Ax ≫ 0, where A is an m × n matrix of rank n. We normalize solutions by a restriction (e - Ax) = 1 where e ≫ 0. On every step the algorithm considers a simplex BAx ≥ 0 containing all solutions, where B is a non-negative n × m matrix with det(BA) ≠ 0. Let us denote this simplex by ΔB, its volume by VB and its center by CB. Initially we take an arbitrary B and e = BT(1,..,1).","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126856330","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 author investigates the following problem: Suppose m people wish to compute the value of a function f(x1, x2, x3, ..., xm), which is an integer-valued function of m integer variables xi of bounded range. Assume initially person Pi knows the value of xi and no other x's. Is it possible for them to compute the value of f, by communicating among themselves, without unduly giving away any information about the values of their own variables? The author gives a precise formulation of this general problem and describe three ways of solving it by use of one-way functions (i.e., functions which are easy to evaluate but hard to invert). These results have applications to secret voting, private querying of database, oblivious negotiation, playing mental poker, etc.. He also discusses the complexity question "How many bits need to be exchanged for the computation," and describes methods to prevent participants from cheating. Finally, he studies the question "What cannot be accomplished with one-way functions."
{"title":"Protocols for secure computations","authors":"A. Yao","doi":"10.1109/SFCS.1982.88","DOIUrl":"https://doi.org/10.1109/SFCS.1982.88","url":null,"abstract":"The author investigates the following problem: Suppose m people wish to compute the value of a function f(x1, x2, x3, ..., xm), which is an integer-valued function of m integer variables xi of bounded range. Assume initially person Pi knows the value of xi and no other x's. Is it possible for them to compute the value of f, by communicating among themselves, without unduly giving away any information about the values of their own variables? The author gives a precise formulation of this general problem and describe three ways of solving it by use of one-way functions (i.e., functions which are easy to evaluate but hard to invert). These results have applications to secret voting, private querying of database, oblivious negotiation, playing mental poker, etc.. He also discusses the complexity question \"How many bits need to be exchanged for the computation,\" and describes methods to prevent participants from cheating. Finally, he studies the question \"What cannot be accomplished with one-way functions.\"","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123907660","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}
Some models of parallel computation consist of copies of a single finite automaton, connected together in a regular fashion. In such computers clerks can be a useful data structure, enabling one to simulate a more powerful computer for which optimal algorithms are easier to design. Clerks are used here to give optimal algorithms for the 3-dimensional connected is problem on a parallel processing array, and a circle construction problem on a pyramid cellular automaton.
{"title":"Using clerk in parallel processing","authors":"Q. Stout","doi":"10.1109/SFCS.1982.48","DOIUrl":"https://doi.org/10.1109/SFCS.1982.48","url":null,"abstract":"Some models of parallel computation consist of copies of a single finite automaton, connected together in a regular fashion. In such computers clerks can be a useful data structure, enabling one to simulate a more powerful computer for which optimal algorithms are easier to design. Clerks are used here to give optimal algorithms for the 3-dimensional connected is problem on a parallel processing array, and a circle construction problem on a pyramid cellular automaton.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122417149","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：