Proceedings of the forty-seventh annual ACM symposium on Theory of Computing最新文献_第10页

Complexity measures and hierarchies for the evaluation of integers, polynomials, and n-linear forms 复杂性措施和层次结构的评估整数，多项式，和n-线性形式

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803746

R. Lipton, D. Dobkin

引用次数: 2

Intercalation theorems for tree transducer languages 树形换能器语言的插补定理

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803761

C. Raymond Perrault

引用次数: 6

On non-linear lower bounds in computational complexity 关于计算复杂度的非线性下界

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803752

L. Valiant

引用次数: 90

On the complexity of the Extended String-to-String Correction Problem 扩展字符串到字符串校正问题的复杂性

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803771

R. Wagner

引用次数: 111

Feasibly constructive proofs and the propositional calculus (Preliminary Version) 可行构造证明与命题演算(初版)

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803756

S. Cook

{"title":"Feasibly constructive proofs and the propositional calculus (Preliminary Version)","authors":"S. Cook","doi":"10.1145/800116.803756","DOIUrl":"https://doi.org/10.1145/800116.803756","url":null,"abstract":"The motivation for this work comes from two general sources. The first source is the basic open question in complexity theory of whether P equals NP (see [1] and [2]). Our approach is to try to show they are not equal, by trying to show that the set of tautologies is not in NP (of course its complement is in NP). This is equivalent to showing that no proof system (in the general sense defined in [3]) for the tautologies is “super” in the sense that there is a short proof for every tautology. Extended resolution is an example of a powerful proof system for tautologies that can simulate most standard proof systems (see [3]). The Main Theorem (5.5) in this paper describes the power of extended resolution in a way that may provide a handle for showing it is not super. The second motivation comes from constructive mathematics. A constructive proof of, say, a statement @@@@×A must provide an effective means of finding a proof of A for each value of x, but nothing is said about how long this proof is as a function of x. If the function is exponential or super exponential, then for short values of x the length of the proof of the instance of A may exceed the number of electrons in the universe. In section 2, I introduce the system PV for number theory, and it is this system which I suggest properly formalizes the notion of a feasibly constructive proof.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1975-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88281754","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: 227

On computing the minima of quadratic forms (Preliminary Report) 二次型最小值的计算(初步报告)

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803749

A. Yao

引用次数: 6

Proving assertions about programs that manipulate data structures 证明关于操作数据结构的程序的断言

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803758

D. Oppen, S. Cook

引用次数: 34

Degree-languages, polynomial time recognition, and the LBA problem 学位语言，多项式时间识别，和LBA问题

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803763

D. Wotschke

引用次数: 4

Two applications of a probabilistic search technique: Sorting X+Y and building balanced search trees 概率搜索技术的两个应用:排序X+Y和构建平衡搜索树

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803774

M. Fredman

{"title":"Two applications of a probabilistic search technique: Sorting X+Y and building balanced search trees","authors":"M. Fredman","doi":"10.1145/800116.803774","DOIUrl":"https://doi.org/10.1145/800116.803774","url":null,"abstract":"Let X = {x1,...,xN} and Y = {y1,...,yN} be sets of N real numbers. We denote by X + Y the multiset {xi + yj; 1 ≤ i, j ≤ N} of size N2. Berklekamp has posed the problem of sorting X + Y. Harper, Payne, Savage and Strauss [1] show that N21og2N comparisons suffice to sort X + Y, thereby saving a factor of 2 over sorting without exploiting the structure of X + Y. (Given u in X + Y, we assume that we know the i,j indices such that u = xi + yj.) Furthermore, they show that this bound is tight for a restricted class of comparison algorithms. However, without their restriction the order of magnitude comparison complexity of this problem has remained an open question. In this paper we show that X + Y can be sorted with O(N2) comparisons. Our proof is unusual for this type of problem in that we do not explicitly exhibit an algorithm. Instead, it is a particular application of a more general search technique whose behavior is easily related to information theoretic lower bounds. In the context of sorting, this search method translates into an insertion sort, where the insertions are not performed by means of the usual binary search, but rather as off-centered searches designed so that each comparison, roughly speaking, equally divides the space of remaining possibilities. We draw attention to this search technique because it might find application to other problems, and we illustrate this possibility with a second application. Our second application concerns the construction of probabilistically balanced binary search trees.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"97 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1975-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78676578","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: 67

Four models for the analysis and optimization of program control structures 程序控制结构分析与优化的四种模型

Proceedings of the forty-seventh annual ACM symposium on Theory of Computing Pub Date : 1975-05-05 DOI: 10.1145/800116.803766

T. W. Pratt

{"title":"Four models for the analysis and optimization of program control structures","authors":"T. W. Pratt","doi":"10.1145/800116.803766","DOIUrl":"https://doi.org/10.1145/800116.803766","url":null,"abstract":"The analysis of the relation between the structure of a program and the function that it computes requires a decomposition of the program into its components. Traditionally this decomposition has been based on the common division of a program into subprograms, and ultimately into statements, expressions and individual variables and constants. In this paper an alternative decomposition is proposed that is based on the decomposition of a program into a set of kernel elements, those program elements that participate in the direct computation of the outputs of the program, and a set of control elements, those elements that participate in the determination of the execution path. The kernel-control decomposition of a program leads to a series of progressively more abstract program representations, each of which has both theoretical and practical interest. The separation of control structure from kernel and the three abstract models presented here, which are based on this decomposition, are particularly valuable in the analysis and optimization of program control structures. This research summary outlines the major results, which will be reported in full in a journal article.","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"1975-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74125244","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: 2