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Characterizations of flowchartable recursions short version 流程图递归的特征描述
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804893
S. A. Walker, H. Strong
{"title":"Characterizations of flowchartable recursions short version","authors":"S. A. Walker, H. Strong","doi":"10.1145/800152.804893","DOIUrl":"https://doi.org/10.1145/800152.804893","url":null,"abstract":"In this paper we give new characterizations for the flowchartability of recursive functionals. The general question of flowchartability is recursively undecidable. We present here an effective map from recursions to representatives for which the question is decidable. The decision provides a good approximation to a characterization for general flowchartability in the following senses: (1) if a representative is flowchartable then the recursions it represents are, and (2) there is a straightforward method of flowcharting, depending only on recursion structure, such that a recursion is flowchartable by this method if and only if its representative is flowchartable. The main results of the paper are (1) that such a representative is flowchartable if, and only if, it is simple or linear, and (2) that, when the context is restricted so that only invertible operations are considered, such a representative is flowchartable if, and only if, it is nested. The terms “simple” and “linear” have been defined in previous papers in the area, although they are extended slightly in this one. The term nested is introduced here. Simple, linear, and nested recursions are very easy to identify by inspection.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134250819","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: 11
Developmental systems and languages 发展系统和语言
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804917
A. Lindenmayer, G. Rozenberg
{"title":"Developmental systems and languages","authors":"A. Lindenmayer, G. Rozenberg","doi":"10.1145/800152.804917","DOIUrl":"https://doi.org/10.1145/800152.804917","url":null,"abstract":"Developmental systems were introduced (Lindenmayer, 1968, 1971) in order to model morphogenetic (pattern-generating) processes in growing, multicellular, filamentous organisms. These systems were originally conceived as linear arrays of interconnected finite automata, each automaton corresponding to a living cell, with the possibility that new automata can be added to the array (cells divide) or be deleted from the array (cells die). Each cell in the array is supposed to have the same state-transition and output functions. As required by biological considerations these functions must be applied to all cells in the array simultaneously at each time step. Thus one obtains infinite sequences of arrays once the functions and the initial arrays are specified. Simplified constructs are defined (and used in this paper) by considering the states and outputs to be identical and thus omitting the output functions. Such filamentous developmental systems have been called “Lindenmayer models” Herman, 1969, 1970) or “L-systems” (Van Dalen, 1971).","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121222721","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: 440
On the equivalence of schemes 论方案的等价性
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804897
Stephen J. Garland, D. Luckham
{"title":"On the equivalence of schemes","authors":"Stephen J. Garland, D. Luckham","doi":"10.1145/800152.804897","DOIUrl":"https://doi.org/10.1145/800152.804897","url":null,"abstract":"One objective of the study of schemes for computation is that of finding general methods for checking or verifying a given program against its specifications. If one views the program and its specification as presenting two supposedly equivalent schemes for a computation, then the objective reduces to one of finding general methods for determining whether, in fact, the two schemes are equivalent. Unfortunately, for many classes of schemes which are sufficiently powerful, this “equivalence problem” is not decidable, i.e. there are no general methods capable of determining, in all cases, whether two schemes in the class are equivalent. In this report we investigate the question of which classes of schemes have decidable equivalence problems, or, in otherwords the question of for which classes of schemes there exist general methods capable of determining equivalence.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"218 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122361675","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: 7
Maze recognizing automata (Extended Abstract) 迷宫识别自动机(扩展摘要)
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804908
W. Savitch
{"title":"Maze recognizing automata (Extended Abstract)","authors":"W. Savitch","doi":"10.1145/800152.804908","DOIUrl":"https://doi.org/10.1145/800152.804908","url":null,"abstract":"In [2], computations of nondeterministic machines are shown to correspond to threadings of certain mazes. We briefly summarize these results and then obtain some new extentions of them. A new device called a maze-recognizing automaton is introduced. This is a type of finite-state device that crawls through mazes. The following statements are proven equivalent. (i) There is a maze-recognizing automaton which recognizes the threadable mazes. (ii) Every nondeterministic L(n) tape-bounded Turing machine is equivalent to some deterministic L(n) tape-bounded Turing machine, provided L(n) ≥ log2n.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114055298","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
Recursion schemes with lists 带列表的递归方案
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804894
James H. Morris
{"title":"Recursion schemes with lists","authors":"James H. Morris","doi":"10.1145/800152.804894","DOIUrl":"https://doi.org/10.1145/800152.804894","url":null,"abstract":"Scheme translation is used to compare the abilities of languages obtained by augmenting recursion schemes with lists, markers, and functional values. It is shown that the first two additions make orthogonal contributions to the language's power. Theorems 4 and 5 appear to be new results.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122231499","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
A hierarchy for nondeterministic time complexity 不确定时间复杂度的层次结构
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804913
S. Cook
{"title":"A hierarchy for nondeterministic time complexity","authors":"S. Cook","doi":"10.1145/800152.804913","DOIUrl":"https://doi.org/10.1145/800152.804913","url":null,"abstract":"The purpose of this paper is to prove the following result: Theorem 1 For any real numbers r1, r2, 1 ≤ r1 < r2, there is a set A of strings which has nondeterministic time complexity nr2 but not nondeterministic time complexity nr1 The computing devices are non-deterministic multitape Turing machines.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117172923","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: 183
Program schemas with equality 具有相等性的程序模式
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804896
A. K. Chandra, Z. Manna
{"title":"Program schemas with equality","authors":"A. K. Chandra, Z. Manna","doi":"10.1145/800152.804896","DOIUrl":"https://doi.org/10.1145/800152.804896","url":null,"abstract":"We discuss the class of program schemas augmented with equality tests, that is, tests of equality between terms. In the first part of the paper we discuss and illustrate the “power” of equality tests. It turns out that the class of program schemas with equality is more powerful than the “maximal” classes of schemas suggested by other investigators. In the second part of the paper we discuss the decision problems of program schemas with equality. It is shown for example that while the decision problems normally considered for schemas (such as halting, divergence, equivalence, isomorphism and freedom) are solvable for Ianov schemas, they all become unsolvable if general equality tests are added. We suggest, however, limited equality tests which can be added to certain subclasses of program schemas while preserving their solvable properties.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133565244","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
Validating register allocations for straight line programs 验证直线程序的寄存器分配
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804918
R. Sethi
{"title":"Validating register allocations for straight line programs","authors":"R. Sethi","doi":"10.1145/800152.804918","DOIUrl":"https://doi.org/10.1145/800152.804918","url":null,"abstract":"Straight line programs are essentially sequences of assignment statements. A general program consists of straight line segments with flow of control between these segments. The interfaces between a straight line segment and the rest of the program place constraints on register allocations for the segment. These constraints may render a register allocation for a straight line program unrealizable. An algorithm is given to determine if a register allocation for a straight line program is realizable. It is shown that the algorithm takes 0(n3) steps, where n is the number of statements in the program. An unrealizable assignment may be made realizable by introducing stores into memory at appropriate points. It is shown how the minimum number of such stores may be found.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"29 21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131372109","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: 4
Polynomial evaluation via the division algorithm the fast Fourier transform revisited 通过除法算法对多项式求值进行了快速傅立叶变换
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1972-05-01 DOI: 10.1145/800152.804900
C. M. Fiduccia
{"title":"Polynomial evaluation via the division algorithm the fast Fourier transform revisited","authors":"C. M. Fiduccia","doi":"10.1145/800152.804900","DOIUrl":"https://doi.org/10.1145/800152.804900","url":null,"abstract":"A polynomial p(x) can be evaluated at several points x1,...,xm by first constructing a polynomial d(x) which has x1,...,xm as roots, then dividing p(x) by d(x), and finally evaluating the remainder r(x) at x1,...,xm. This method is useful if the coefficient sequence of d(x) can be chosen to be sparse, thus simplifying the construction of r(x). The case m=1 and d(x) = x−x1 is Horner's rule, while the case d(x) = xm−1 yields the fast Fourier transform algorithm.","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1972-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131982952","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
Proceedings of the fourth annual ACM symposium on Theory of computing 第四届ACM计算理论年会论文集
Proceedings of the fourth annual ACM symposium on Theory of computing Pub Date : 1969-05-05 DOI: 10.1145/800152
P. C. Fischer, S. Ginsburg, M. Harrison
{"title":"Proceedings of the fourth annual ACM symposium on Theory of computing","authors":"P. C. Fischer, S. Ginsburg, M. Harrison","doi":"10.1145/800152","DOIUrl":"https://doi.org/10.1145/800152","url":null,"abstract":"","PeriodicalId":229726,"journal":{"name":"Proceedings of the fourth annual ACM symposium on Theory of computing","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1969-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126083583","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: 7
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