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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 ,...
Models of Computation  Exploring the Power of Computing
"... Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and oper ..."
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Cited by 57 (7 self)
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Theoretical computer science treats any computational subject for which a good model can be created. Research on formal models of computation was initiated in the 1930s and 1940s by Turing, Post, Kleene, Church, and others. In the 1950s and 1960s programming languages, language translators, and operating systems were under development and therefore became both the subject and basis for a great deal of theoretical work. The power of computers of this period was limited by slow processors and small amounts of memory, and thus theories (models, algorithms, and analysis) were developed to explore the efficient use of computers as well as the inherent complexity of problems. The former subject is known today as algorithms and data structures, the latter computational complexity. The focus of theoretical computer scientists in the 1960s on languages is reflected in the first textbook on the subject, Formal Languages and Their Relation to Automata by John Hopcroft and Jeffrey Ullman. This influential book led to the creation of many languagecentered theoretical computer science courses; many introductory theory courses today continue to reflect the content of this book and the interests of theoreticians of the 1960s and early 1970s. Although
A nonlinear time lower bound for boolean branching programs
 In Proc. of 40th FOCS
, 1999
"... Abstract: We give an exponential lower bound for the size of any lineartime Boolean branching program computing an explicitly given function. More precisely, we prove that for all positive integers k and for all sufficiently small ε> 0, if n is sufficiently large then there is no Boolean (or 2way) ..."
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Cited by 55 (0 self)
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Abstract: We give an exponential lower bound for the size of any lineartime Boolean branching program computing an explicitly given function. More precisely, we prove that for all positive integers k and for all sufficiently small ε> 0, if n is sufficiently large then there is no Boolean (or 2way) branching program of size less than 2 εn which, for all inputs X ⊆ {0,1,...,n − 1}, computes in time kn the parity of the number of elements of the set of all pairs 〈x,y 〉 with the property x ∈ X, y ∈ X, x < y, x + y ∈ X. For the proof of this fact we show that if A = (ai, j) n i=0, j=0 is a random n by n matrix over the field with 2 elements with the condition that “A is constant on each minor diagonal,” then with high probability the rank of each δn by δn submatrix of A is at least cδlogδ  −2n, where c> 0 is an absolute constant and n is sufficiently large with respect to δ.
TimeSpace Tradeoffs for Branching Programs
, 1999
"... We obtain the first nontrivial timespace tradeoff lower bound for functions f : {0, 1}^n → {0, 1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε)n, for some constant ε > 0 ..."
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Cited by 44 (2 self)
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We obtain the first nontrivial timespace tradeoff lower bound for functions f : {0, 1}^n → {0, 1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length (1 + ε)n, for some constant ε > 0. We also give the first separation result between the syntactic and semantic readk models [BRS93] for k > 1 by showing that polynomialsize semantic readtwice branching programs can compute functions that require exponential size on any syntactic readk branching program. We also show...
Readonce branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus
 in: Proceedings of the 29th ACM Symposium on Theory of Computing
, 1997
"... We investigate readonce branching programs for the following search problem: given a Boolean m n matrix with m>n, nd either an allzero row, or two 1's in some column. Our primary motivation is that this models regular resolution proofs of the pigeonhole principle PHP m n, and that for m>n 2 no low ..."
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Cited by 34 (9 self)
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We investigate readonce branching programs for the following search problem: given a Boolean m n matrix with m>n, nd either an allzero row, or two 1's in some column. Our primary motivation is that this models regular resolution proofs of the pigeonhole principle PHP m n, and that for m>n 2 no lower bounds are known for the length of such proofs. We prove exponential lower bounds (for arbitrarily large m!) if we further restrict this model by requiring the branching program either
TimeSpace Tradeoff Lower Bounds for Randomized Computation of Decision Problems
 In Proc. of 41st FOCS
, 2000
"... We prove the first timespace lower bound tradeoffs for randomized computation of decision problems. ..."
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Cited by 28 (2 self)
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We prove the first timespace lower bound tradeoffs for randomized computation of decision problems.
Optimal and Efficient Clock Synchronization Under Drifting Clocks (Extended Abstract)
 IN PROCEEDINGS OF THE 18TH ANNUAL ACM SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 1999
"... We consider the classical problem of clock synchronization in distributed systems. Previously, this problem was solved optimally and efficiently only in the case when all individual clocks are nondrifting, i.e., only for systems where all clocks advance at the rate of real time. In this paper, we ..."
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Cited by 28 (1 self)
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We consider the classical problem of clock synchronization in distributed systems. Previously, this problem was solved optimally and efficiently only in the case when all individual clocks are nondrifting, i.e., only for systems where all clocks advance at the rate of real time. In this paper, we present a new algorithm for systems with drifting clocks, which is the first optimal algorithm to solve the problem efficiently: clock drift bounds and message latency bounds may be arbitrary; the computational complexity depends on the communication pattern of the system in a way which is bounded by a polynomial in the network size for most systems. More specifically, the complexity is polynomial in the maximal number of messages known to be sent but not received, the relative system speed, and timestamp s...
A General Sequential TimeSpace Tradeoff for Finding Unique Elements
 SIAM Journal on Computing
, 1991
"... An optimal R(n2) lower bound is shown for the timespace product of any Rway branching program that determines those values which occur exactly once in a list of n integers in the range [l, R] where R 1 n. This Q(n2) tradeoff also applies to the sorting problem and thus improves the previous times ..."
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Cited by 27 (2 self)
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An optimal R(n2) lower bound is shown for the timespace product of any Rway branching program that determines those values which occur exactly once in a list of n integers in the range [l, R] where R 1 n. This Q(n2) tradeoff also applies to the sorting problem and thus improves the previous timespace tradeoffs for sorting. Because the Rway branching program is a such a powerful model these timespace product tradeoffs also apply to all models of sequential computation that have a fair measure of space such as offline multitape Turing machines and offline logcost RAMS. 1
Parallel Sorting With Limited Bandwidth
 in Proc. 7th ACM Symp. on Parallel Algorithms and Architectures
, 1995
"... We study the problem of sorting on a parallel computer with limited communication bandwidth. By using the recently proposed PRAM(m) model, where p processors communicate through a small, globally shared memory consisting of m bits, we focus on the tradeoff between the amount of local computation an ..."
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Cited by 26 (5 self)
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We study the problem of sorting on a parallel computer with limited communication bandwidth. By using the recently proposed PRAM(m) model, where p processors communicate through a small, globally shared memory consisting of m bits, we focus on the tradeoff between the amount of local computation and the amount of interprocessor communication required for parallel sorting algorithms. We prove a lower bound of \Omega\Gamma n log m m ) on the time to sort n numbers in an exclusiveread variant of the PRAM(m) model. We show that Leighton's Columnsort can be used to give an asymptotically matching upper bound in the case where m grows as a fractional power of n. The bounds are of a surprising form, in that they have little dependence on the parameter p. This implies that attempting to distribute the workload across more processors while holding the problem size and the size of the shared memory fixed will not improve the optimal running time of sorting in this model. We also show that bot...
A TimeSpace Tradeoff for Sorting on NonOblivious Machines
, 1981
"... This paper adopts the latter strategy in order to pursue the complexity of sorting ..."
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Cited by 24 (2 self)
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This paper adopts the latter strategy in order to pursue the complexity of sorting