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16
Pseudorandom generators for spacebounded computation
 Combinatorica
, 1992
"... Pseudorandom generators are constructed which convert O(SlogR) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). In particular, any randomized polynomial time algorithm that runs in space S can be simulated using only O(Slogn) random bits. An application of these ..."
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Cited by 192 (10 self)
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Pseudorandom generators are constructed which convert O(SlogR) truly random bits to R bits that appear random to any algorithm that runs in SPACE(S). In particular, any randomized polynomial time algorithm that runs in space S can be simulated using only O(Slogn) random bits. An application of these generators is an explicit construction of universal traversal sequences (for arbitrary graphs) of length n O(l~ The generators constructed are technically stronger than just appearing random to spacebounded machines, and have several other applications. In particular, applications are given for "deterministic amplification " (i.e. reducing the probability of error of randomized algorithms), as well as generalizations of it. 1.
On span programs
 In Proc. of the 8th Ann. Structures in Complexity Conference 102–111
, 1993
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Lower Bounds for Deterministic and Nondeterministic Branching Programs
 in Proceedings of the FCT'91, Lecture Notes in Computer Science
, 1991
"... We survey lower bounds established for the complexity of computing explicitly given Boolean functions by switchingandrectifier networks, branching programs and switching networks. We first consider the unrestricted case and then proceed to various restricted models. Among these are monotone networ ..."
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Cited by 57 (4 self)
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We survey lower bounds established for the complexity of computing explicitly given Boolean functions by switchingandrectifier networks, branching programs and switching networks. We first consider the unrestricted case and then proceed to various restricted models. Among these are monotone networks, boundedwidth devices , oblivious devices and readk times only devices. 1 Introduction The main goal of the Boolean complexity theory is to prove lower bounds on the complexity of computing "explicitly given" Boolean functions in interesting computational models. By "explicitly given" researchers usually mean "belonging to the class NP ". This is a very plausible interpretation since on the one hand this class contains the overwhelming majority of interesting Boolean functions and on the other hand it is small enough to prevent us from the necessity to take into account counting arguments. To illustrate the second point, let me remind the reader that already the class \Delta p 2 ,...
Undirected connectivity in O(log 1.5 (n)) space
 In Proceedings of the 33rd IEEE Symposium on Foundations of Computer Science
, 1992
"... We present a deterministic algorithm for the connectivity problem on undirected graphs that runs in O(log 1.5 n) space. Thus, the recursive doubling technique of Savich which requires Θ(log 2 n) space is not optimal for this problem. 1 ..."
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Cited by 51 (5 self)
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We present a deterministic algorithm for the connectivity problem on undirected graphs that runs in O(log 1.5 n) space. Thus, the recursive doubling technique of Savich which requires Θ(log 2 n) space is not optimal for this problem. 1
Randomization and Derandomization in SpaceBounded Computation
 In Proceedings of the 11th Annual IEEE Conference on Computational Complexity
, 1996
"... This is a survey of spacebounded probabilistic computation, summarizing the present state of knowledge about the relationships between the various complexity classes associated with such computation. The survey especially emphasizes recent progress in the construction of pseudorandom generators tha ..."
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Cited by 36 (0 self)
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This is a survey of spacebounded probabilistic computation, summarizing the present state of knowledge about the relationships between the various complexity classes associated with such computation. The survey especially emphasizes recent progress in the construction of pseudorandom generators that fool probabilistic spacebounded computations, and the application of such generators to obtain deterministic simulations.
Symmetric Logspace is Closed Under Complement
 CHICAGO JOURNAL OF THEORETICAL COMPUTER SCIENCE
, 1994
"... We present a Logspace, manyone reduction from the undirected stconnectivity problem to its complement. This shows that SL = co  SL. ..."
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Cited by 25 (1 self)
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We present a Logspace, manyone reduction from the undirected stconnectivity problem to its complement. This shows that SL = co  SL.
An Unambiguous Class Possessing a Complete Set
, 1996
"... In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a `promise' or `semantic' concept. These usually lead to classes apparently without complete problems. 1 Introduction One of the most central questions of complexity th ..."
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Cited by 14 (3 self)
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In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a `promise' or `semantic' concept. These usually lead to classes apparently without complete problems. 1 Introduction One of the most central questions of complexity theory is to compare determinism with nondeterminism. Our inability to exhibit the precise relationship between these two features motivates the investigation of intermediate features such as symmetry or unambiguity. In this paper we will concentrate on the notion of unambiguity. Unfortunately, unambiguity of a device or of a language is in general an undecidable property. Unambiguous classes are not defined by a `syntactical' machine property but rather by a `semantical' restriction. A nasty consequence is the apparent lack of complete sets. In the case of time bounded computations there are relativizations of unambiguity which provably have no complete problem ([10]). For space bounded computations t...
An Optimal Randomized Logarithmic Time Connectivity Algorithm for the EREW PRAM
, 1996
"... Improving a long chain of works we obtain a randomised EREW PRAM algorithm for finding the connected components of a graph G = (V; E) with n vertices and m edges in O(logn) time using an optimal number of O((m + n)= log n) processors. The result returned by the algorithm is always correct. The pr ..."
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Cited by 12 (1 self)
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Improving a long chain of works we obtain a randomised EREW PRAM algorithm for finding the connected components of a graph G = (V; E) with n vertices and m edges in O(logn) time using an optimal number of O((m + n)= log n) processors. The result returned by the algorithm is always correct. The probability that the algorithm will not complete in O(log n) time is o(n \Gammac ) for any c ? 0. 1 Introduction Finding the connected components of an undirected graph is perhaps the most basic algorithmic graph problem. While the problem is trivial in the sequential setting, it seems that elaborate methods should be used to solve the problem efficiently in the parallel setting. A considerable number of researchers investigated the complexity of the problem in various parallel models including, in particular, various members of the PRAM family. In this work we consider the EREW PRAM model, the weakest member of this family, and obtain, for the first time, a parallel connectivity algorith...
Derandomizing Random Walks in Undirected Graphs Using Locally Fair Exploration Strategies
 In Proc. ICALP’09, LNCS
, 2009
"... Abstract We consider the problem of exploring an anonymous undirected graph using an oblivious robot. The studied exploration strategies are designed so that the next edge in the robot’s walk is chosen using only local information, and so that some local equity (fairness) criterion is satisfied for ..."
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Cited by 7 (3 self)
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Abstract We consider the problem of exploring an anonymous undirected graph using an oblivious robot. The studied exploration strategies are designed so that the next edge in the robot’s walk is chosen using only local information, and so that some local equity (fairness) criterion is satisfied for the adjacent undirected edges. Such strategies can be seen as an attempt to derandomize random walks, and are natural counterparts for undirected graphs of the rotorrouter model for symmetric directed graphs. The first of the studied strategies, known as OldestFirst (OF), always chooses the neighboring edge for which the most time has elapsed since its last traversal. Unlike in the case of symmetric directed graphs, we show that such a strategy in some cases leads to exponential cover time. We then consider another strategy called LeastUsedFirst (LUF) which always uses adjacent edges which have been traversed the smallest number of times. We show that any LeastUsedFirst exploration covers a graph G=(V,E) of diameter D within time O(DE), and in the long run traverses all edges of G with the same frequency. Keywords graph exploration · random walk · rotorrouter model · local knowledge · deterministic strategy 1
BPHSPACE(S) ` DSPACE(S3=2
 Preliminary version in 36th FOCS, 1995. BIBLIOGRAPHY 667 [197] W.J. Savitch. Relationships
, 1999
"... We prove that any language that can be recognized by a randomized algorithm (with possibly twosided error) that runs in space O(S) and always terminates can be recognized by a deterministic algorithm running in space O(S 3/2). This improves the best previously known result that such algorithms have ..."
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Cited by 6 (0 self)
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We prove that any language that can be recognized by a randomized algorithm (with possibly twosided error) that runs in space O(S) and always terminates can be recognized by a deterministic algorithm running in space O(S 3/2). This improves the best previously known result that such algorithms have deterministic space O(S 2) simulations which, for onesided error algorithms, follows from Savitch’s Theorem and for twosided error algorithms follows by reduction to recursive matrix powering. Our result includes as a special case the result due to Nisan, Szemerédi and Wigderson that undirected connectivity can be computed in space O(log 3/2 n). It is obtained via a new algorithm for repeated squaring of a matrix: we show how to approximate the 2 rth power of a d × d matrix in space O(r 1/2 log d), improving on the bound of O(r log d) that comes from the natural recursive algorithm. The algorithm employs Nisan’s pseudorandom generator for space bounded computation, together with some new techniques for reducing the number of random bits needed by an algorithm.