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On the Complexity of VLSI Implementations and Graph Representations of Boolean Functions with Application to Integer Multiplication
 IEEE Transactions on Computers
, 1998
"... This paper presents lower bound results on Boolean function complexity under two different models. The first is an abstraction of tradeoffs between chip area and speed in very large scale integrated (VLSI) circuits. The second is the ordered binary decision diagram (OBDD) representation used as a da ..."
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Cited by 233 (10 self)
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This paper presents lower bound results on Boolean function complexity under two different models. The first is an abstraction of tradeoffs between chip area and speed in very large scale integrated (VLSI) circuits. The second is the ordered binary decision diagram (OBDD) representation used as a data structure for symbolically representing and manipulating Boolean functions. These lower bounds demonstrate the fundamental limitations of VLSI as an implementation medium, and OBDDs as a data structure. They also lend insight into what properties of a Boolean function lead to high complexity under these models. Related techniques can be...
The NPcompleteness column: an ongoing guide
 Journal of Algorithms
, 1985
"... This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co ..."
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Cited by 188 (0 self)
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This is the nineteenth edition of a (usually) quarterly column that covers new developments in the theory of NPcompleteness. The presentation is modeled on that used by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NPCompleteness,’ ’ W. H. Freeman & Co., New York, 1979 (hereinafter referred to as ‘‘[G&J]’’; previous columns will be referred to by their dates). A background equivalent to that provided by [G&J] is assumed, and, when appropriate, crossreferences will be given to that book and the list of problems (NPcomplete and harder) presented there. Readers who have results they would like mentioned (NPhardness, PSPACEhardness, polynomialtimesolvability, etc.) or open problems they would like publicized, should
Special Purpose Parallel Computing
 Lectures on Parallel Computation
, 1993
"... A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing ..."
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Cited by 77 (5 self)
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A vast amount of work has been done in recent years on the design, analysis, implementation and verification of special purpose parallel computing systems. This paper presents a survey of various aspects of this work. A long, but by no means complete, bibliography is given. 1. Introduction Turing [365] demonstrated that, in principle, a single general purpose sequential machine could be designed which would be capable of efficiently performing any computation which could be performed by a special purpose sequential machine. The importance of this universality result for subsequent practical developments in computing cannot be overstated. It showed that, for a given computational problem, the additional efficiency advantages which could be gained by designing a special purpose sequential machine for that problem would not be great. Around 1944, von Neumann produced a proposal [66, 389] for a general purpose storedprogram sequential computer which captured the fundamental principles of...
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
On Randomized OneRound Communication Complexity
 Computational Complexity
, 1995
"... We present several results regarding randomized oneround communication complexity. Our results include a connection to the VCdimension, a study of the problem of computing the inner product of two real valued vectors, and a relation between \simultaneous" protocols and oneround protocols. Key wor ..."
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Cited by 56 (0 self)
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We present several results regarding randomized oneround communication complexity. Our results include a connection to the VCdimension, a study of the problem of computing the inner product of two real valued vectors, and a relation between \simultaneous" protocols and oneround protocols. Key words. Communication Complexity; Oneround and simultaneous protocols; VCdimension; Subject classications. 68Q25. 1.
Combining constraint solving and symbolic model checking for a class of systems with nonlinear constraints
 In Computer Aided Verification
, 1997
"... We extend the conventional BDDbased model checking algorithms to verify systems with nonlinear arithmetic constraints. We represent each constraint as a BDD variable, using the information from a constraint solver to prune the BDDs by removing paths that correspond to infeasible constraints. We il ..."
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Cited by 36 (3 self)
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We extend the conventional BDDbased model checking algorithms to verify systems with nonlinear arithmetic constraints. We represent each constraint as a BDD variable, using the information from a constraint solver to prune the BDDs by removing paths that correspond to infeasible constraints. We illustrate our technique with a simple example, which has been analyzed with our prototype implementation. 1
On the complexity of designing distributed protocols
 Information and Control
, 1982
"... The complexity of two problems of distributed computation and decisionmaking is studied. It is shown that deciding whether two distant agents can arrive at compatible decisions without any communication can be done in polynomial time if there are two possible decisions for each agent, but is NPcom ..."
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Cited by 17 (6 self)
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The complexity of two problems of distributed computation and decisionmaking is studied. It is shown that deciding whether two distant agents can arrive at compatible decisions without any communication can be done in polynomial time if there are two possible decisions for each agent, but is NPcomplete if one agent has three or more alternatives. It is also shown that minimizing the amount of communication necessary for the distributed computation of a function, when two distant computers receive each a part of the input, is NPcomplete. This proves a conjecture due to A. Yao. 1.
A Model of Computation for VLSI with Related Complexity Results
 Journal of the ACM
, 1985
"... Abstract. A new model of computation for VLSI, based on the assumption that time for propagating information is at least linear in the distance, is proposed. While accommodating for basic laws of physics, the model is designed to be general and technology independent. Thus, from a complexity viewpoi ..."
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Cited by 12 (0 self)
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Abstract. A new model of computation for VLSI, based on the assumption that time for propagating information is at least linear in the distance, is proposed. While accommodating for basic laws of physics, the model is designed to be general and technology independent. Thus, from a complexity viewpoint, it is especially suited for deriving lower bounds and tradeoffs. New results for a number of problems, including fanin, transitive functions, matrix multiplication, and sorting are presented. As regards upper bounds, it must be noted that, because of communication costs, the model clearly favors regular and pipelined architectures (e.g., systolic arrays).
Communicationspace tradeoffs for unrestricted protocols
 SIAM Journal on Computing
, 1994
"... This paper introduces communicating branching programs, and develops a general technique for demonstrating communicationspace tradeoffs for pairs of communicating branching programs. This technique is then used to prove communicationspace tradeoffs for any pair of communicating branching programs ..."
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Cited by 8 (0 self)
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This paper introduces communicating branching programs, and develops a general technique for demonstrating communicationspace tradeoffs for pairs of communicating branching programs. This technique is then used to prove communicationspace tradeoffs for any pair of communicating branching programs that hashes according to a universal family of hash functions. Other tradeoffs follow from this result. As an example, any pair of communicating Boolean branching programs that computes matrixvector products over GF(2) requires communicationspace product Ω(n 2), provided the space used is o(n / log n). These are the first examples of communicationspace tradeoffs on a completely general model of communicating processes.
The LinearArray Conjecture in Communication Complexity is False
, 1996
"... A linear array network consists of k + 1 processors P 0 ; P 1 ; : : : ; P k with links only between P i and P i+1 (0 i ! k). It is required to compute some boolean function f(x; y) in this network, where initially x is stored at P 0 and y is stored at P k . Let D k (f) be the (total) number of bi ..."
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Cited by 6 (1 self)
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A linear array network consists of k + 1 processors P 0 ; P 1 ; : : : ; P k with links only between P i and P i+1 (0 i ! k). It is required to compute some boolean function f(x; y) in this network, where initially x is stored at P 0 and y is stored at P k . Let D k (f) be the (total) number of bits that must be exchanged to compute f in worst case. Clearly, D k (f) k \Delta D(f ), where D(f) is the standard twoparty communication complexity of f . Tiwari proved that for almost all functions D k (f) k(D(f) \Gamma O(1)) and conjectured that this is true for all functions. In this paper we disprove Tiwari's conjecture, by exhibiting an infinite family of functions for which D k (f) is essentially at most 3 4 k \Delta D(f ). Our construction also leads to progress on another major problem in this area: It is easy to bound the twoparty communication complexity of any function, given the least number of monochromatic rectangles in any partition of the input space. How tight are suc...