S-equations are of the form E1(x1,..., xk) ⊇ E2 (X1,...,xk) where E1 and E2 are shuffle expressions having two types of symbols; variables and constants. E1⊇E2 is said to be S-satisfiable if the language expressed by E1(α1,...,αk) includes the language expressed by E2(α1,...,αk) where α1,...,αk are some strings of constants. A wide range of problems in string manipulation, data bases, etc., can be described in terms of S-equations. Major results include the solvability and complexity of several classes of S-satisfiability problems.
{"title":"On equations including string variables","authors":"K. Iwama","doi":"10.1109/SFCS.1982.77","DOIUrl":"https://doi.org/10.1109/SFCS.1982.77","url":null,"abstract":"S-equations are of the form E1(x1,..., xk) ⊇ E2 (X1,...,xk) where E1 and E2 are shuffle expressions having two types of symbols; variables and constants. E1⊇E2 is said to be S-satisfiable if the language expressed by E1(α1,...,αk) includes the language expressed by E2(α1,...,αk) where α1,...,αk are some strings of constants. A wide range of problems in string manipulation, data bases, etc., can be described in terms of S-equations. Major results include the solvability and complexity of several classes of S-satisfiability problems.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"60 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":"130012172","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}
An O(n2) space representation for permutation groups of degree n is presented. The representation can be constructed in time O(n5), and supports fast membership testing. Applications of the representation to the generation of systems of coset representatives, and of complete block systems, are discussed.
{"title":"A compact representation for permutation groups","authors":"M. Jerrum","doi":"10.1109/SFCS.1982.52","DOIUrl":"https://doi.org/10.1109/SFCS.1982.52","url":null,"abstract":"An O(n2) space representation for permutation groups of degree n is presented. The representation can be constructed in time O(n5), and supports fast membership testing. Applications of the representation to the generation of systems of coset representatives, and of complete block systems, are discussed.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"29 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":"127873493","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}
Linear-time for Linear Programming in R2 and R3 are presented. The methods used are applicable for some other problems. For example, a linear-time algorithm is given for the classical problem of finding the smallest circle enclosing n given points in the plane. This disproves a conjecture by Shamos and Hoey that this problem requires Ω(n log n) time. An immediate consequence of the main result is that the problem of linear separability is solvable in linear-time. This corrects an error in Shamos and Hoey's paper, namely, that their O(n log n) algorithm for this problem in the plane was optimal. Also, a linear-time algorithm is given for the problem of finding the weighted center of a tree and algorithms for other common location-theoretic problems are indicated. The results apply also to the problem of convex quadratic programming in three-dimensions. The results have already been extended to higher dimensions and we know that linear programming can be solved in linear-time when the dimension is fixed. This will be reported elsewhere; a preliminary report is available from the author.
{"title":"Linear-time algorithms for linear programming in R3 and related problems","authors":"N. Megiddo","doi":"10.1137/0212052","DOIUrl":"https://doi.org/10.1137/0212052","url":null,"abstract":"Linear-time for Linear Programming in R2 and R3 are presented. The methods used are applicable for some other problems. For example, a linear-time algorithm is given for the classical problem of finding the smallest circle enclosing n given points in the plane. This disproves a conjecture by Shamos and Hoey that this problem requires Ω(n log n) time. An immediate consequence of the main result is that the problem of linear separability is solvable in linear-time. This corrects an error in Shamos and Hoey's paper, namely, that their O(n log n) algorithm for this problem in the plane was optimal. Also, a linear-time algorithm is given for the problem of finding the weighted center of a tree and algorithms for other common location-theoretic problems are indicated. The results apply also to the problem of convex quadratic programming in three-dimensions. The results have already been extended to higher dimensions and we know that linear programming can be solved in linear-time when the dimension is fixed. This will be reported elsewhere; a preliminary report is available from the author.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"2 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":"129232502","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}
Polynomial algorithms are described that solve the MIN CUT LINEAR ARRANGEMENT problem on degree restricted trees. For example, the cutwidth or folding number of an arbitrary degree d tree can be found in O(n(logn)d-2) steps. This also yields an algorithm for determining the black/white pebble demand of degree three trees. A forbidden subgraph characterization is given for degree three trees having cutwidth k. This yields an interesting corollary: for degree three trees, cutwidth is identical to search number.
{"title":"Polynomial time algorithms for the MIN CUT problem on degree restricted trees","authors":"M. Chung, F. Makedon, I. H. Sudborough, J. Turner","doi":"10.1137/0214013","DOIUrl":"https://doi.org/10.1137/0214013","url":null,"abstract":"Polynomial algorithms are described that solve the MIN CUT LINEAR ARRANGEMENT problem on degree restricted trees. For example, the cutwidth or folding number of an arbitrary degree d tree can be found in O(n(logn)d-2) steps. This also yields an algorithm for determining the black/white pebble demand of degree three trees. A forbidden subgraph characterization is given for degree three trees having cutwidth k. This yields an interesting corollary: for degree three trees, cutwidth is identical to search number.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"34 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":"121309872","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 assume that long wires represent large capacitive loads, and investigate the effect on the area of a VLSI layout when drivers are introduced along many long wires in the layout. We present a layout for which the introduction of drivers along long wires squares the area of the layout; we show, however, that the increase in area is never greater than this, if the driver can be laid out in a square region. We also show an area-time trade-off for a single long wire by which we can reduce the area of its driver to Θ(lq), q ≪ 1, from Θ(l), if we can tolerate a delay of Θ(l1-q) rather than Θ(log l); and we obtain tight bounds on the worst-case area increase in general lay-outs having these drivers, using the Brouwer fixed-point theorem. We also derive results for the case when drivers are embedded in rectangles that are not square. Finally, we extend the use of our upper-bound technique to other layout, problems.
{"title":"On driving many long lines in a VLSI layout","authors":"V. Ramachandran","doi":"10.1145/6490.6784","DOIUrl":"https://doi.org/10.1145/6490.6784","url":null,"abstract":"We assume that long wires represent large capacitive loads, and investigate the effect on the area of a VLSI layout when drivers are introduced along many long wires in the layout. We present a layout for which the introduction of drivers along long wires squares the area of the layout; we show, however, that the increase in area is never greater than this, if the driver can be laid out in a square region. We also show an area-time trade-off for a single long wire by which we can reduce the area of its driver to Θ(lq), q ≪ 1, from Θ(l), if we can tolerate a delay of Θ(l1-q) rather than Θ(log l); and we obtain tight bounds on the worst-case area increase in general lay-outs having these drivers, using the Brouwer fixed-point theorem. We also derive results for the case when drivers are embedded in rectangles that are not square. Finally, we extend the use of our upper-bound technique to other layout, problems.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"113 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":"114956946","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}
A high-resolution raster-graphics display is usually combined with processing power and a memory organization that facilitates basic graphics operations. For many applications, including interactive text processing, the ability to quickly move or copy small rectangles of pixels is essential. This paper proposes a novel organization of raster-graphics memory that permits all small rectangles to be moved efficiently. The memory organization is based on a doubly periodic assignment of pixels to M memory chips according to a "Fibonacci" lattice. The memory organization guarantees that if a rectilinearly oriented rectangle contains fewer than M/√5 pixels, then all pixels will reside in different memory chips, and thus can be accessed simultaneously. We also define a continuous amdogue of the problem which can be posed as, "What is the maximum density of a set of points in the plane such that no two points are contained in the interior of a rectilinearly oriented rectangle of area N." We give a lower bound of 1/2N on the density of such a set, and show that 1/√5N can be achieved.
{"title":"An application of number theory to the organization of raster-graphics memory","authors":"B. Chor, C. Leiserson, R. Rivest","doi":"10.1145/4904.4800","DOIUrl":"https://doi.org/10.1145/4904.4800","url":null,"abstract":"A high-resolution raster-graphics display is usually combined with processing power and a memory organization that facilitates basic graphics operations. For many applications, including interactive text processing, the ability to quickly move or copy small rectangles of pixels is essential. This paper proposes a novel organization of raster-graphics memory that permits all small rectangles to be moved efficiently. The memory organization is based on a doubly periodic assignment of pixels to M memory chips according to a \"Fibonacci\" lattice. The memory organization guarantees that if a rectilinearly oriented rectangle contains fewer than M/√5 pixels, then all pixels will reside in different memory chips, and thus can be accessed simultaneously. We also define a continuous amdogue of the problem which can be posed as, \"What is the maximum density of a set of points in the plane such that no two points are contained in the interior of a rectilinearly oriented rectangle of area N.\" We give a lower bound of 1/2N on the density of such a set, and show that 1/√5N can be achieved.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"31 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":"128593518","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 this paper is to introduce a new information theory and explore its appplications. Using modern computational complexity, we study the notion of information that can be accessed through a feasible computation. In Part 1 of this paper, we lay the foundation of the theory and set up a framework for cryptography and pseudorandom number generation. In Part 2, we study the concept of trapdoor functions and examine applications of such functions in cryptography, pseudorandom number generation, and abstract complexity theory.
{"title":"Theory and application of trapdoor functions","authors":"A. Yao","doi":"10.1109/SFCS.1982.95","DOIUrl":"https://doi.org/10.1109/SFCS.1982.95","url":null,"abstract":"The purpose of this paper is to introduce a new information theory and explore its appplications. Using modern computational complexity, we study the notion of information that can be accessed through a feasible computation. In Part 1 of this paper, we lay the foundation of the theory and set up a framework for cryptography and pseudorandom number generation. In Part 2, we study the concept of trapdoor functions and examine applications of such functions in cryptography, pseudorandom number generation, and abstract complexity theory.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"6 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":"134462752","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 present several polynomial-time approximation algorithms for the one-dimensional bin-packing problem. using a subroutine to solve a certain linear programming relaxation of the problem. Our main results are as follows: There is a polynomial-time algorithm A such that A(I) ≤ OPT(I) + O(log2 OPT(I)). There is a polynomial-time algorithm A such that, if m(I) denotes the number of distinct sizes of pieces occurring in instance I, then A(I) ≤ OPT(I) + O(log2 m(I)). There is an approximation scheme which accepts as input an instance I and a positive real number ε, and produces as output a packing using as most (1 + ε) OPT(I) + O(ε-2) bins. Its execution time is O(ε-c n log n), where c is a constant. These are the best asymptotic performance bounds that have been achieved to date for polynomial-time bin-packing. Each of our algorithms makes at most O(log n) calls on the LP relaxation subroutine and takes at most O(n log n) time for other operations. The LP relaxation of bin packing was solved efficiently in practice by Gilmore and Gomory. We prove its membership in P, despite the fact that it has an astronomically large number of variables.
{"title":"An efficient approximation scheme for the one-dimensional bin-packing problem","authors":"N. Karmarkar, R. Karp","doi":"10.1109/SFCS.1982.61","DOIUrl":"https://doi.org/10.1109/SFCS.1982.61","url":null,"abstract":"We present several polynomial-time approximation algorithms for the one-dimensional bin-packing problem. using a subroutine to solve a certain linear programming relaxation of the problem. Our main results are as follows: There is a polynomial-time algorithm A such that A(I) ≤ OPT(I) + O(log2 OPT(I)). There is a polynomial-time algorithm A such that, if m(I) denotes the number of distinct sizes of pieces occurring in instance I, then A(I) ≤ OPT(I) + O(log2 m(I)). There is an approximation scheme which accepts as input an instance I and a positive real number ε, and produces as output a packing using as most (1 + ε) OPT(I) + O(ε-2) bins. Its execution time is O(ε-c n log n), where c is a constant. These are the best asymptotic performance bounds that have been achieved to date for polynomial-time bin-packing. Each of our algorithms makes at most O(log n) calls on the LP relaxation subroutine and takes at most O(n log n) time for other operations. The LP relaxation of bin packing was solved efficiently in practice by Gilmore and Gomory. We prove its membership in P, despite the fact that it has an astronomically large number of variables.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"41 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":"115799488","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}
Simultaneous Diophantine approximation in d dimensions deals with the approximation of a vector α = (α1, ..., αd) of d real numbers by vectors of rational numbers all having the same denominator. This paper considers the computational complexity of algorithms to find good simultaneous approximations to a given vector α of d rational numbers. We measure the goodness of an approximation using the sup norm. We show that a result of H. W. Lenstra, Jr. produces polynomial-time algorithms to find sup norm best approximations to a given vector α when the dimension d is fixed. We show that a recent algorithm of A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovasz to find short vectors in an integral lattice can be used to find a good approximation to a given vector α in d dimensions with a denominator Q satisfying 1 ≤ Q ≤ 2d/2 N which is within a factor √5d 2d+1/2 of the best approximation with denominator Q* with 1 ≤ Q* ≤ N. This algorithm runs in time polynomial in the input size, independent of the dimension d. We prove results complementing these, showing certain natural simultaneous Diophantine approximation problems are NP-hard. We show that the problem of deciding whether a given vector α of rational numbers has a simultaneous approximation of specified accuracy with respect to the sup norm with denominator Q in a given interval 1 ≤ Q ≤ N is NP-complete. (Here the dimension d is allowed to vary.) We prove two other complexity results, which suggest that the problem of locating best (sup norm) simultaneous approximations is harder than this NP-complete problem.
d维的同时丢番图近似处理向量α = (α1，…(d)用有理数的向量表示d个实数，它们的分母相同。本文考虑了d有理数向量α的同时逼近算法的计算复杂度。我们用sup范数来衡量一个近似的优度。我们证明了H. W. Lenstra, Jr.的结果产生了多项式时间算法，以在维数d固定时找到给定向量α的sup范数最佳逼近。我们表明,最近的算法a . k . Lenstra h·w·Lenstra, Jr .)和l . Lovasz找到短向量积分格可以用来找到一个好的近似给定向量α与分母d维Q Q满足1≤≤2 d / 2 N等于√5 d 2 d + 1/2倍以内最好的近似与分母Q * 1≤Q *≤N这个算法的运行时间在多项式输入大小,独立的维d。我们证明结果补充这些,表明某些自然同时的丢番图近似问题是np困难的。我们证明了在给定区间1≤Q≤N内判定给定有序数向量α对分母为Q的sup范数是否具有指定精度的同时逼近的问题是np完全的。(这里的维度d是允许变化的。)我们证明了另外两个复杂性结果，这表明定位最佳(sup范数)同时逼近的问题比这个np完全问题更难。
{"title":"The computational complexity of simultaneous Diophantine approximation problems","authors":"J. Lagarias","doi":"10.1137/0214016","DOIUrl":"https://doi.org/10.1137/0214016","url":null,"abstract":"Simultaneous Diophantine approximation in d dimensions deals with the approximation of a vector α = (α1, ..., αd) of d real numbers by vectors of rational numbers all having the same denominator. This paper considers the computational complexity of algorithms to find good simultaneous approximations to a given vector α of d rational numbers. We measure the goodness of an approximation using the sup norm. We show that a result of H. W. Lenstra, Jr. produces polynomial-time algorithms to find sup norm best approximations to a given vector α when the dimension d is fixed. We show that a recent algorithm of A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovasz to find short vectors in an integral lattice can be used to find a good approximation to a given vector α in d dimensions with a denominator Q satisfying 1 ≤ Q ≤ 2d/2 N which is within a factor √5d 2d+1/2 of the best approximation with denominator Q* with 1 ≤ Q* ≤ N. This algorithm runs in time polynomial in the input size, independent of the dimension d. We prove results complementing these, showing certain natural simultaneous Diophantine approximation problems are NP-hard. We show that the problem of deciding whether a given vector α of rational numbers has a simultaneous approximation of specified accuracy with respect to the sup norm with denominator Q in a given interval 1 ≤ Q ≤ N is NP-complete. (Here the dimension d is allowed to vary.) We prove two other complexity results, which suggest that the problem of locating best (sup norm) simultaneous approximations is harder than this NP-complete problem.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"2 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":"125735550","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}
An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factoring a univariate integer polynomial. Together with A. Lenstra's, H. Lenstra's and L. Lovasz' polynomial-time factorization algorithm for univariate integer polynomials and the author's multivariate to bivariate reduction the new algorithm implies the following theorem. Factoring a polynomial with a fixed number of variables into irreducibles, except for the constant factors, can be accomplished in time polynomial in the total degree and the size of its coefficients. The new algorithm can be generalized to reducing multivariate factorization directly to univariate factorization and to factoring multivariate polynomials with coefficients in algebraic number fields and finite fields in polynomial time.
提出了一种算法，将总度和系数长度为多项式时间的二元整数多项式的不可约因子求解问题简化为一元整数多项式的因式分解问题。与A. Lenstra, H. Lenstra和L. Lovasz的单变量整数多项式的多项式时间分解算法和作者的多元到二元化简算法一起，新算法隐含了以下定理。将一个变量数固定的多项式分解为除常数因子外的不可约因子，可以在时间多项式的总度和系数大小上完成。该算法可推广到将多元因子分解直接分解为单变量因子分解，也可推广到在多项式时间内分解代数数域和有限域的带系数的多元多项式。
{"title":"A polynomial-time reduction from bivariate to univariate integral polynomial factorization","authors":"E. Kaltofen","doi":"10.1145/1089310.1089311","DOIUrl":"https://doi.org/10.1145/1089310.1089311","url":null,"abstract":"An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factoring a univariate integer polynomial. Together with A. Lenstra's, H. Lenstra's and L. Lovasz' polynomial-time factorization algorithm for univariate integer polynomials and the author's multivariate to bivariate reduction the new algorithm implies the following theorem. Factoring a polynomial with a fixed number of variables into irreducibles, except for the constant factors, can be accomplished in time polynomial in the total degree and the size of its coefficients. The new algorithm can be generalized to reducing multivariate factorization directly to univariate factorization and to factoring multivariate polynomials with coefficients in algebraic number fields and finite fields in polynomial time.","PeriodicalId":127919,"journal":{"name":"23rd Annual Symposium on Foundations of Computer Science (sfcs 1982)","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1982-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128955419","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}
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