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Proceedings of the fifth annual ACM symposium on Theory of computing 第五届ACM计算理论年会论文集
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1977-05-04 DOI: 10.1145/800125
J. Hopcroft, E. P. Friedman, M. Harrison
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引用次数: 78
Tree transductions and families of tree languages 树状转导和树状语言的家族
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804051
B. S. Baker
{"title":"Tree transductions and families of tree languages","authors":"B. S. Baker","doi":"10.1145/800125.804051","DOIUrl":"https://doi.org/10.1145/800125.804051","url":null,"abstract":"Interest in the study of sets of trees, tree languages, has led to the definition of finite automata which accept trees [2,11] and transducers which map trees into other trees [7,9,10]. These generalized machines may read treesfinite automata which accept trees [2,11] and of transducers which map trees into other trees [7,9,10]. These generalized machines may read trees either “top-down” (from the root toward the leaves) or “bottom-up” (from the leaves toward the root). Here it is shown that both the class of top-down transductions and the class of bottom-up transductions can be characterized in terms of two restricted classes of tree transductions. From these ductions and the class of bottom-up transductions can be characterized in terms of two restricted classes of tree transductions. From these characterizations, it is shown that the composition of any n bottom-up transductions can be realized by the composition of n+1 top-down transductions, and similarly, the composition of any n top-down transductions can be realized by the composition of n+1 bottom-up transductions. Next, we study the families of tree languages which can be obtained from the recognizable sets (sets accepted by finite tree automata) by the composition of n top-down or bottom-up transductions, n>0. The yield operation, which concatenates the leaves of a tree from left to right to form a of string, languages from the hierarchy of families of tree languages. It is shown that each family of string languages in this hierarchy is properly contained in the family of context-sensitive languages.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116593897","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: 38
Polynominal time reducibility 多标称时间可约性
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804042
R. Ladner
{"title":"Polynominal time reducibility","authors":"R. Ladner","doi":"10.1145/800125.804042","DOIUrl":"https://doi.org/10.1145/800125.804042","url":null,"abstract":"Several of the results that appear in [4] are stated to be true of polynominal time reducibility (≤p) but are not proved explicitly. We shall prove several of these results with the hope of shedding some light on the “determinism vs. nondeterminism” problem. The ideas behind these proofs already exist in [4] but appear here in a different setting. We shall spend most of our time on two theorems: (i) If φ <p Β then there exists an Α such that φ<p Α <p Β and (ii) there exist Α and Β neither of which is polynominal time computable but such that if C ≤p Α and C ≤p Β then C is polynominal time computable. We show how the techniques used in the proofs of these theorems may be extended to prove other results.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131153896","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
Elementary bounds for presburger arithmetic presburger算术的初等界
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804033
D. Oppen
{"title":"Elementary bounds for presburger arithmetic","authors":"D. Oppen","doi":"10.1145/800125.804033","DOIUrl":"https://doi.org/10.1145/800125.804033","url":null,"abstract":"We consider the first-order theory whose language has as nonlogical symbols the constant symbols 0 and 1, the binary relation symbols = and <, the unary function symbol − and the binary function symbol + This theory of integers under addition is commonly called the 'Presburger Arithmetic' and is known to be decidable for truth [Presburger (1929), Hilbert and Bernays (1968)]. We prove here that there exists a decision procedure for this theory, involving quantifier elimination, for which there is a superexponential upper bound on the size of formula produced when all variables have been eliminated.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"158 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123716843","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: 42
Duality applied to the complexity of matrix multiplications and other bilinear forms 对偶性应用于矩阵乘法和其他双线性形式的复杂性
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804038
J. Hopcroft, J. Musinski
{"title":"Duality applied to the complexity of matrix multiplications and other bilinear forms","authors":"J. Hopcroft, J. Musinski","doi":"10.1145/800125.804038","DOIUrl":"https://doi.org/10.1145/800125.804038","url":null,"abstract":"The paper considers the complexity of bilinear forms in a noncommutative ring. The dual of a computation is defined and applied to matrix multiplication and other bilinear forms. It is shown that the dual of an optimal computation gives an optimal computation for a dual problem. An nxm by mxp matrix product is shown to be the dual of an nxp by pxm or an mxn by nxp matrix product implying that each of the matrix products requires the same number of multiplications to compute. Finally an algorithm for computing a single bilinear form over a noncommutative ring with a minimum number of multiplications is derived by considering a dual problem.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128198137","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: 36
The computational complexity of algebraic numbers 代数数的计算复杂性
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804046
H. T. Kung
{"title":"The computational complexity of algebraic numbers","authors":"H. T. Kung","doi":"10.1145/800125.804046","DOIUrl":"https://doi.org/10.1145/800125.804046","url":null,"abstract":"Let {xi} be a sequence approximating an algebraic number α of degree r, and let [equation], for some rational function @@@@ with integral coefficients. Let M denote the number of multiplications or divisions needed to compute @@@@ and let M¯ denote the number of multiplications or divisions, except by constants, needed to compute @@@@. Define the multiplication efficiency measure of {xi} as [equation] or as [equation], where p is the order of convergence of {xi}. Kung [1] showed that Ē({xi}) ≤ 1 or equivalently, [equation]. In this paper we show that (i) [equation]; (ii) if E({xi}) = 1 then α is a rational number; (iii) if Ē({xi}) = 1 then α is a rational or quadratic irrational number. This settles the question of when the multiplication efficiency E({xi}) or Ē({xi}) achieves its optimal value of unity.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127230267","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: 5
Testing flow graph reducibility 测试流图的可简化性
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804040
R. Tarjan
{"title":"Testing flow graph reducibility","authors":"R. Tarjan","doi":"10.1145/800125.804040","DOIUrl":"https://doi.org/10.1145/800125.804040","url":null,"abstract":"Many problems in program optimization have been solved by applying a technique called interval analysis to the flow graph of the program. A flow graph which is susceptible to this type of analysis is called reducible. This paper describes an algorithm for testing whether a flow graph is reducible. The algorithm uses depth-first search to reveal the structure of the flow graph and a good method for computing disjoint set unions to determine reducibility from the search information. When the algorithm is implemented on a random access computer, it requires O(E log* E) time to analyze a graph with E edges, where log* x = min{i/logix≤1}. The time bound compares favorably with the O(E log E) bound of a previously known algorithm.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130159408","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: 251
On the optimal evaluation of a set of bilinear forms 一类双线性形式的最优评价
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804039
D. Dobkin
{"title":"On the optimal evaluation of a set of bilinear forms","authors":"D. Dobkin","doi":"10.1145/800125.804039","DOIUrl":"https://doi.org/10.1145/800125.804039","url":null,"abstract":"Although general theories are beginning to emerge in the area of automata based complexity theory, there are very few general methods or even general problem formulations in the area of arithmetic complexity. In this paper we propose and defend a general model for studying bilinear multiplication in order to provide a common framework for discussing a wide class of problems. At the heart of a number of problems in minimizing the number of multiplications required to perform a calculation is a problem in matrix algebra relating to the expansion of a given set of matrices as linear combinations of rank one matrices. In this paper we make a systematic attack on this problem and derive some general results which unify and extend numerous known results. Among the new results given here to illustrate the strength of this approach is a new lower bound on the number of multiplications required for n by n matrix multiplication of 3n2-3n+1 which is independent of the subset of the reals with respect to which multiplication is regarded as free. An even sharper bound is obtained if this set is restricted to the integers.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131730124","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: 124
An observation on time-storage trade off 对时间存储权衡的观察
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804032
S. Cook
{"title":"An observation on time-storage trade off","authors":"S. Cook","doi":"10.1145/800125.804032","DOIUrl":"https://doi.org/10.1145/800125.804032","url":null,"abstract":"Recently there have been several attempts to prove that every set of strings in @@@@ (i.e., recognizable in deterministic polynomial time) can be recognized in deterministic storage (log n)2. The methods used in the attempts were based on that of [1], in which it is shown that every context free language can be accepted in storage (log n)2 Our thesis in the present paper is that these attempts must fail. We define a specific set SP of strings which is clearly in @@@@, but in a certain well-defined sense cannot be recognized in storage (log n)2 using the techniques in [1]. We conjecture that no Turing machine recognizes SP within storage (log n)2, and show that if this conjecture is false, then in fact every member of @@@@ can be recognized within storage (log n)2.","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129279332","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: 269
Attributed translations(Extended Abstract) 归因翻译(扩展摘要)
Proceedings of the fifth annual ACM symposium on Theory of computing Pub Date : 1973-04-30 DOI: 10.1145/800125.804047
P. M. Lewis, D. Rosenkrantz, R. Stearns
{"title":"Attributed translations(Extended Abstract)","authors":"P. M. Lewis, D. Rosenkrantz, R. Stearns","doi":"10.1145/800125.804047","DOIUrl":"https://doi.org/10.1145/800125.804047","url":null,"abstract":"Attributed translations are a means of specifying the input-output relation of a language processing device, such as for example the lexical or syntax box of a compiler. Considered as a mathematical object, an attributed translation is a mapping of certain strings of attributed “input symbols” into strings of attributed “action symbols”. Under the interpretation that action symbols represent the act of emitting an attributed output or the performing of some other “semantic actions”, and the attributes represent “semantic” information associated with the symbols, the model can be applied in depth to practical compiling problems. Theorems are proved giving conditions under which an attributed translation can be performed by an augmented pushdown machine while it is parsing top down or bottom up. Attributed translations are based on the ideas of attributed grammars [1] and syntax directed translations [2,3]. Other relevant concepts are property grammars and table machines [4], and attributed grammars with relations [5].","PeriodicalId":242946,"journal":{"name":"Proceedings of the fifth annual ACM symposium on Theory of computing","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1973-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132588004","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: 12
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