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27
Parallel RAMs with Owned Global Memory and Deterministic ContextFree Language Recognition
, 1997
"... We identify and study a natural and frequently occurring subclass of ConcurrentRead, ExclusiveWrite Parallel Random Access Machines (CREWPRAMs). Called ConcurrentRead, OwnerWrite, or CROWPRAMs, these are machines in which each global memory location is assigned a unique "owner" processor, whi ..."
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Cited by 26 (0 self)
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We identify and study a natural and frequently occurring subclass of ConcurrentRead, ExclusiveWrite Parallel Random Access Machines (CREWPRAMs). Called ConcurrentRead, OwnerWrite, or CROWPRAMs, these are machines in which each global memory location is assigned a unique "owner" processor, which is the only processor allowed to write into it. Considering the difficulties that would be involved in physically realizing a full CREWPRAM model, it is interesting to observe that in fact, most known CREWPRAM algorithms satisfy the CROW restriction or can be easily modified to do so. This paper makes three main contributions. First, we formally define the CROWPRAM model and demonstrate its stability
The Computational Complexity of Generating Random Fractals
 J. Stat. Phys
, 1996
"... In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model ar ..."
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Cited by 16 (6 self)
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In this paper we examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation that can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics. Keywords: Cluster algorithms, computational complexity, diffusion limited aggregation, Ising model, Metropolis algorithm, Pcompleteness 1
Circuit and Decision Tree Complexity of Some Number Theoretic Problems
, 1998
"... We extend the area of applications of the Abstract Harmonic Analysis to lower bounds on the circuit and decision tree complexity of Boolean functions related to some number theoretic problems. In particular, we prove that deciding if a given integer is squarefree and testing coprimality of two int ..."
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Cited by 12 (10 self)
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We extend the area of applications of the Abstract Harmonic Analysis to lower bounds on the circuit and decision tree complexity of Boolean functions related to some number theoretic problems. In particular, we prove that deciding if a given integer is squarefree and testing coprimality of two integers by unbounded fanin circuits of bounded depth requires superpolynomial size. 1 Introduction In recent years spectral techniques based on the Abstract Harmonic Analysis on the hypercube have been shown to represent a very useful tool for obtaining lower complexity bounds. Various links between Fourier coefficients of Boolean functions and their complexity characteristics have been studied in a number of works, see [1, 2, 3, 4, 6, 8, 13, 19, 20, 22, 23]. In particular, these spectral techniques have been successfully applied to the parity function and to threshold functions. Institut fur Informatik, Technische Universitat Munchen, D80290 Munchen, Germany. bernasco@informatik.tumue...
The Parallel Complexity of Growth Models
 Journal of Statistical Physics
, 1994
"... This paper investigates the parallel complexity of several nonequilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solidonsolid growth are all seemingly highly sequential processes that yield selfsimilar or selfaffine random clusters. Nonetheless, we present f ..."
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Cited by 9 (6 self)
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This paper investigates the parallel complexity of several nonequilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solidonsolid growth are all seemingly highly sequential processes that yield selfsimilar or selfaffine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these clusters. The running times of the algorithms scale as O(log 2 N ), where N is the system size, and the number of processors required scale as a polynomial in N . The algorithms are based on fast parallel procedures for finding minimum weight paths; they illuminate the close connection between growth models and selfavoiding paths in random environments. In addition to their potential practical value, our algorithms serve to classify these growth models as less complex than other growth models, such as diffusionlimited aggregation, for which fast parallel algorithms probably do not exist. Keywords: Ballistic deposition, Computationa...
E.: Relationships between broadcast and shared memory in reliable anonymous distributed systems
 In: Proc. 18th International Symposium on Distributed Computing, LNCS
, 2004
"... the date of receipt and acceptance should be inserted later Abstract We study the power of reliable anonymous distributed systems, where processes do not fail, do not have identifiers, and run identical programmes. We are interested specifically in the relative powers of systems with different commu ..."
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Cited by 9 (0 self)
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the date of receipt and acceptance should be inserted later Abstract We study the power of reliable anonymous distributed systems, where processes do not fail, do not have identifiers, and run identical programmes. We are interested specifically in the relative powers of systems with different communication mechanisms: anonymous broadcast, readwrite registers, or readwrite registers plus additional sharedmemory objects. We show that a system with anonymous broadcast can simulate a system of sharedmemory objects if and only if the objects satisfy a property we call idemdicence; this result holds regardless of whether either system is synchronous or asynchronous. Conversely, the key to simulating anonymous broadcast in anonymous shared memory is the ability to count: broadcast can be simulated by an asynchronous sharedmemory system that uses only counters, but readwrite registers by themselves are not enough. We further examine the relative power of different types and sizes of bounded counters and conclude with a nonrobustness result.
MODULAR EXPONENTIATION VIA THE EXPLICIT CHINESE REMAINDER THEOREM
"... Abstract. Fix pairwise coprime positive integers p1, p2,..., ps. We propose representing integers u modulo m, where m is any positive integer up to roughly √ p1p2 · · · ps, as vectors (u mod p1, u mod p2,..., u mod ps). We use this representation to obtain a new result on the parallel complexity o ..."
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Cited by 8 (2 self)
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Abstract. Fix pairwise coprime positive integers p1, p2,..., ps. We propose representing integers u modulo m, where m is any positive integer up to roughly √ p1p2 · · · ps, as vectors (u mod p1, u mod p2,..., u mod ps). We use this representation to obtain a new result on the parallel complexity of modular exponentiation: there is an algorithm for the Common CRCW PRAM that, given positive integers x, e, and m in binary, of total bit length n, computes x e mod m in time O(n/lg lg n) using n O(1) processors. 1.
On the average sensitivity of testing squarefree numbers
 in "Proc. 5th Intern. Computing and Combin. Conf.", Lect. Notes in Comp. Sci
, 1627
"... Abstract We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain a linear lower bound on the average sensitivity of the Boolean function deciding whether a given integer is squarefree. This result allows us to de ..."
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Cited by 7 (7 self)
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Abstract We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain a linear lower bound on the average sensitivity of the Boolean function deciding whether a given integer is squarefree. This result allows us to derive a quadratic lower bound for the formula size complexity of testing squarefree numbers and a linear lower bound on the average decision tree depth. We also obtain lower bounds on the degrees of exact and approximative polynomial representations of this function. \Lambda Supported by DFG grant Me 1077/141.
On polynomial representations of Boolean functions related to some number theoretic problems
 Electronic Colloq. on Comp. Compl
, 1998
"... Abstract. We say a polynomial P over ZM strongly Mrepresents a Boolean function F if F(x) ≡ P(x) (mod M) for all x ∈ {0, 1} n. Similarly, P onesidedly Mrepresents F if F(x) = 0 ⇐ ⇒ P(x) ≡ 0 (mod M) for all x ∈ {0, 1} n. Lower bounds are obtained on the degree and the number of monomials of pol ..."
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Cited by 6 (4 self)
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Abstract. We say a polynomial P over ZM strongly Mrepresents a Boolean function F if F(x) ≡ P(x) (mod M) for all x ∈ {0, 1} n. Similarly, P onesidedly Mrepresents F if F(x) = 0 ⇐ ⇒ P(x) ≡ 0 (mod M) for all x ∈ {0, 1} n. Lower bounds are obtained on the degree and the number of monomials of polynomials over Z M, which strongly or onesidedly Mrepresent the Boolean function deciding if a given nbit integer is squarefree. Similar lower bounds are also obtained for polynomials over the reals which provide a threshold representation of the above Boolean function. 1
The average sensitivity of squarefreeness
 Comp. Compl
, 1999
"... Abstract We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain an asymtotic formula, having a linear main term, for the average sensitivity of the Boolean function deciding whether a given integer is squarefree ..."
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Cited by 5 (3 self)
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Abstract We study combinatorial complexity characteristics of a Boolean function related to a natural number theoretic problem. In particular we obtain an asymtotic formula, having a linear main term, for the average sensitivity of the Boolean function deciding whether a given integer is squarefree. This result allows us to derive a quadratic lower bound for the formula size complexity of testing squarefree numbers and a linear lower bound on the average decision tree depth. We also obtain lower bounds on the degrees of exact and approximative polynomial representations of this function. *Supported by DFG grant Me 1077/141.#