{"title":"A robust and verifiable cryptographically secure election scheme","authors":"Josh Benaloh, M. Fischer","doi":"10.1109/SFCS.1985.2","DOIUrl":"https://doi.org/10.1109/SFCS.1985.2","url":null,"abstract":"This paper describes a cryptographic scheme for holding a secure secret ballot election in which all communication is public. Voters cast their votes electronically, suitably encrypted, and a “government” releases a tally and a proof of its correctness which can be verified by all.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115754899","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}
{"title":"Fixed-point extensions of first-order logic","authors":"Y. Gurevich, S. Shelah","doi":"10.1109/SFCS.1985.27","DOIUrl":"https://doi.org/10.1109/SFCS.1985.27","url":null,"abstract":"We prove that the three extensions of first-order logic by means of positive inductions, monotone inductions, and so-called non-monotone (in our terminology, inflationary) inductions respectively, all have the same expressive power in the case of finite structures. As a by-product, the collapse of the corresponding fixed-point hierarchies can be deduced.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123770562","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}
{"title":"Slimming down search structures: A functional approach to algorithm design","authors":"B. Chazelle","doi":"10.1109/SFCS.1985.51","DOIUrl":"https://doi.org/10.1109/SFCS.1985.51","url":null,"abstract":"We establish new upper bounds on the complexity of several \"rectangle\" problems. Our results include, for instance, optimal algorithms for range counting and rectangle searching in two dimensions. These involve linear space implementations of range trees and segment trees. The algorithms we give are simple and practical; they can be dynamized and taken into higher dimensions. Also of interest is the nonstandard approach which we follow to obtain these results: it involves transforming data structures on the basis of functional specifications.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129627129","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}
{"title":"Collective coin flipping, robust voting schemes and minima of Banzhaf values","authors":"M. Ben-Or, N. Linial","doi":"10.1109/SFCS.1985.15","DOIUrl":"https://doi.org/10.1109/SFCS.1985.15","url":null,"abstract":"The power of players in a collective decision process is a central issue in Mathematical Economics and Game Theory. Similar issues arise in Computer Science in the study of distributed, fault tolerant computations when several processes, some perhaps faulty, have to reach agreement. In the present article we study voting schemes which are relatively immune to the presence of unfair players. In particular, we discuss how to perform collective coin flipping which is only slightly biased despite the presence of unfair players. Mathematically this corresponds to problems concerning the minima of Banzhaf values in certain n -person games. These are measures of power studied in Game Theory. It is quite remarkable that while dictatorial voting games are, of course, the most sensitive to the presence of unfair players, some voting schemes that we propose here are significantly more robust than majority voting. Coin flipping was selected as a study case because of its simplicity and because collective coin flipping is widely used in randomized algorithms for distributed computations. It is our feeling that Game Theory has much to contribute to Computer Science and we are sure that further applications will be found.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117091644","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}
{"title":"Unbiased bits from sources of weak randomness and probabilistic communication complexity","authors":"B. Chor, Oded Goldreich","doi":"10.1109/SFCS.1985.62","DOIUrl":"https://doi.org/10.1109/SFCS.1985.62","url":null,"abstract":"We introduce a general model for physical sources or weak randomness. Loosely speaking, we view physical sources as devices which output strings according to probability distributions in which no single string is too probable. The main question addressed is whether it is possible to extract alrnost unbiased random bits from such \"probability bounded\" sources. We show that most or the functions can be used to extract almost unbiased and independent bits from the output of any two independent \"probability-bounded\" sources. The number of extractable bits is within a constant factor of the information theoretic bound. We conclude this paper by establishing further connections between communication complexity and the problem discussed above. This allows us to show that most Boolean functions have linear communication complexity in a very strong sense.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127548927","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. Aggarwal, M. Klawe, David Lichtenstein, N. Linial, A. Wigderson
{"title":"Multi-layer grid embeddings","authors":"A. Aggarwal, M. Klawe, David Lichtenstein, N. Linial, A. Wigderson","doi":"10.1109/SFCS.1985.37","DOIUrl":"https://doi.org/10.1109/SFCS.1985.37","url":null,"abstract":"In this paper we propose two new multi-layer grid models for VLSI layout, both of which take into account the number of contact cuts used. For the first model in which nodes \"exist\" only on one layer, we prove a tight area x (number of contact cuts) = Θ(n2) trade-off for embedding any degree 4 n-node planar graph in two layers. For the second model in which nodes \"exist\" simultaneously on all layers, we prove a number of bounds on the area needed to embed graphs using no contact cuts. For example we prove that any n-node graph which is the union of two planar subgraphs can be embedded on two layers in O(n2) area without contact cuts. This bound is tight even if more layers and an unbounded number of contact cuts are allowed. We also show that planar graphs of bounded degree can be embedded on two layers in O(n1.6) area without contact cuts. These results use some interesting new results on embedding graphs in a single layer. In particular we give an O(n2) area embedding of planar graphs such that each edge makes a constant number of turns, and each exterior vertex has a path to the perimeter of the grid making a constant number of turns. We also prove a tight Ω(n3) lower bound on the area of grid n-permutation networks.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"5 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123628238","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}
{"title":"Improved processor bounds for algebraic and combinatorial problems in RNC","authors":"Z. Galil, V. Pan","doi":"10.1109/SFCS.1985.33","DOIUrl":"https://doi.org/10.1109/SFCS.1985.33","url":null,"abstract":"of Results Our two main results improve the processor bounds of two important problems: Problem 1: Computing the exact inverse and the determinant of an n x n matrix whose entries are L-bit integers, L =nO(l). The improved solutions maintain the best running time (O(log2 n), O(log3 n), resp.) for the two problems. A solution to Problem 1 is used in a number of parallel algorithms for algebraic problems as··well as for solving Problem 2. A solution for Problem 2 is used in parallel algorithms for severai combinatorial problems. Consequently, the new algorithms lead to improved solutions to several algebraic and combinatorial problems. We state the bounds in the arithmetic circuit model (0A (f(n))) in which each arithmetic operation is performed in one unit of time and in the (more realistic) Boolean circuit model (OB (g(n))) in which each Boolean operation takes one unit of time: New Algorithms Previous best bound Problem 1 OA(n 2 .","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131310919","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}
{"title":"On minima of function, intersection patterns of curves, and davenport-schinzel sequences","authors":"M. Sharir, R. Livne","doi":"10.1109/SFCS.1985.40","DOIUrl":"https://doi.org/10.1109/SFCS.1985.40","url":null,"abstract":"We present several results related to the problem of estimating the complexity M(f1, ..., fn) of the pointwise minimum of n continuous univariate or bivariate functions f1, ..., fn under the assumption that no pair (resp. triple) of these functions intersect in more than some fixed number s of points. Our main result is that in the one-dimensional case M(f1, ..., fn) - O(nα(n)O(α(n)s-3)) (α(n) is the functional inverse of Ackermann's function). In the twodimensional case the problem is substantially harder, and we have only some initial estimates on M, including a tight bound Θ(n2) if s = 2, and a worst-case lower bound Ω(n2α(n)) for s ≥ 6. The treatment of the twodimensional problem is based on certain properties of the intersection patterns of a collection of planar Jordan curves, which we also develop and prove here.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128372579","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}
{"title":"Nondeterministic versus probabilistic linear search algorithms","authors":"F. Heide","doi":"10.1109/SFCS.1985.38","DOIUrl":"https://doi.org/10.1109/SFCS.1985.38","url":null,"abstract":"The \"component counting lower bound\" known for deterministic linear search algorithms (LSA's) also holds for their probabilistic versions (PLSA's) for many problems, even if two-sided error is allowed, and if one does not charge for probabilistic choice. This implies lower bounds on PLSA's for e.g. the element distinctness problem (n log n) or the knapsack problem (n2). These results yield the first separations between probabilistic and non-deterministic LSA's, because the above problems are non-deterministically much easier. Previous lower bounds for PLSA's either only worked for one-sided error \"on the nice side\", i.e. on the side where the problems are even non-deterministically hard, or only for probabilistic comparison trees. The proof of the lower bound differs fundamentally from all known lower bounds for LSA's or PLSA's, because it does not reduce the problem to a combinatorial one but argues extensively about e.g. a non-discrete measure for similarity of sets in Rn. This lower bound result solves an open problem posed by Manber and Tompa as well as by Snir. Furthermore, a PLSA for n input variables with two-sided error and expected runtime T can be simulated by a (deterministic) LSA in T2n steps. This proves that the gaps between probabilistic and deterministic LSA's shown by Snir cannot be too large. As this simulation even holds for algebraic computation trees we show that probabilistic and deterministic versions of this model are polynomially related. This is a weaker version of a result due to the author which shows that in case of LSA's, even the non-deterministic and deterministic versions are polynomially related.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132876595","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}
{"title":"Geometrical realization of set systems and probabilistic communication complexity","authors":"N. Alon, P. Frankl, V. Rödl","doi":"10.1109/SFCS.1985.30","DOIUrl":"https://doi.org/10.1109/SFCS.1985.30","url":null,"abstract":"Let d = d(n) be the minimum d such that for every sequence of n subsets F1, F2, . . . , Fn of {1, 2, . . . , n} there exist n points P1, P2, . . . , Pn and n hyperplanes H1, H2 .... , Hn in Rd such that Pj lies in the positive side of Hi iff j ∈ Fi. Then n/32 ≤ d(n) ≤ (1/2 + 0(1)) ¿ n. This implies that the probabilistic unbounded-error 2-way complexity of almost all the Boolean functions of 2p variables is between p-5 and p, thus solving a problem of Yao and another problem of Paturi and Simon. The proof of (1) combines some known geometric facts with certain probabilistic arguments and a theorem of Milnor from real algebraic geometry.","PeriodicalId":296739,"journal":{"name":"26th Annual Symposium on Foundations of Computer Science (sfcs 1985)","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1985-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114427365","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}