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63
Expander Codes
 IEEE Transactions on Information Theory
, 1996
"... We present a new class of asymptotically good, linear errorcorrecting codes based upon expander graphs. These codes have linear time sequential decoding algorithms, logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both random ..."
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Cited by 280 (10 self)
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We present a new class of asymptotically good, linear errorcorrecting codes based upon expander graphs. These codes have linear time sequential decoding algorithms, logarithmic time parallel decoding algorithms with a linear number of processors, and are simple to understand. We present both randomized and explicit constructions for some of these codes. Experimental results demonstrate the extremely good performance of the randomly chosen codes. 1. Introduction We present a new class of error correcting codes derived from expander graphs. These codes have the advantage that they can be decoded very efficiently. That makes them particularly suitable for devices which must decode cheaply, such as compact disk players and remote satellite receivers. We hope that the connection we draw between expander graphs and error correcting codes will stimulate research in both fields. 1.1. Error correcting codes An error correcting code is a mapping from messages to codewords such that the mappi...
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 189 (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
A Regular Layout for Parallel Adders
, 1982
"... With VLSI architecture, the chip area and design regularity represent a better measure of cost than the conventional gate count. We show that addition of nbit binary numbers can be performed on a chip with a regular layout in time proportional to log n and with area proportional to n. ..."
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Cited by 181 (0 self)
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With VLSI architecture, the chip area and design regularity represent a better measure of cost than the conventional gate count. We show that addition of nbit binary numbers can be performed on a chip with a regular layout in time proportional to log n and with area proportional to n.
Analog Computation via Neural Networks
 THEORETICAL COMPUTER SCIENCE
, 1994
"... We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of "neurons". If allowed exponential time for computation, they turn out to ha ..."
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Cited by 87 (8 self)
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We pursue a particular approach to analog computation, based on dynamical systems of the type used in neural networks research. Our systems have a fixed structure, invariant in time, corresponding to an unchanging number of "neurons". If allowed exponential time for computation, they turn out to have unbounded power. However, under polynomialtime constraints there are limits on their capabilities, though being more powerful than Turing Machines. (A similar but more restricted model was shown to be polynomialtime equivalent to classical digital computation in the previous work [20].) Moreover, there is a precise correspondence between nets and standard nonuniform circuits with equivalent resources, and as a consequence one has lower bound constraints on what they can compute. This relationship is perhaps surprising since our analog devices do not change in any manner with input size. We note that these networks are not likely to solve polynomially NPhard problems, as the equality ...
Polynomial size proofs of the propositional pigeonhole principle
 Journal of Symbolic Logic
, 1987
"... Abstract. Cook and Reckhow defined a propositional formulation of the pigeonhole principle. This paper shows that there are Frege proofs of this propositional pigeonhole principle of polynomial size. This together with a result of Haken gives another proof of Urquhart's theorem that Frege systems ha ..."
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Cited by 72 (7 self)
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Abstract. Cook and Reckhow defined a propositional formulation of the pigeonhole principle. This paper shows that there are Frege proofs of this propositional pigeonhole principle of polynomial size. This together with a result of Haken gives another proof of Urquhart's theorem that Frege systems have an exponential speedup over resolution. We also discuss connections to provability in theories of bounded arithmetic. $1. Introduction. The motivation for this paper comes primarily from two sources. First, Cook and Reckhow [2] and Statman [7] discussed connections between lengths of proofs in propositional logic and open questions in computational complexity such as whether NP = coNP. Cook and Reckhow used the propositional pigeonhole principle as an example of a family of true formulae which
Issues in multiagent resource allocation
 INFORMATICA
, 2006
"... The allocation of resources within a system of autonomous agents, that not only have preferences over alternative allocations of resources but also actively participate in computing an allocation, is an exciting area of research at the interface of Computer Science and Economics. This paper is a sur ..."
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Cited by 70 (17 self)
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The allocation of resources within a system of autonomous agents, that not only have preferences over alternative allocations of resources but also actively participate in computing an allocation, is an exciting area of research at the interface of Computer Science and Economics. This paper is a survey of some of the most salient issues in Multiagent Resource Allocation. In particular, we review various languages to represent the preferences of agents over alternative allocations of resources as well as different measures of social welfare to assess the overall quality of an allocation. We also discuss pertinent issues regarding allocation procedures and present important complexity results. Our presentation of theoretical issues is complemented by a discussion of software packages for the simulation of agentbased market places. We also introduce four major application areas for Multiagent Resource Allocation, namely industrial procurement, sharing of satellite resources, manufacturing control, and grid computing.
The Boolean formula value problem is in ALOGTIME
 in Proceedings of the 19th Annual ACM Symposium on Theory of Computing
, 1987
"... The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value ..."
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Cited by 68 (7 self)
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The Boolean formula value problem is in alternating log time and, more generally, parenthesis contextfree languages are in alternating log time. The evaluation of reverse Polish notation Boolean formulas is also in alternating log time. These results are optimal since the Boolean formula value problem is complete for alternating log time under deterministic log time reductions. Consequently, it is also complete for alternating log time under AC reductions.
The Computational Power and Complexity of Constraint Handling Rules
 In Second Workshop on Constraint Handling Rules, at ICLP05
, 2005
"... Constraint Handling Rules (CHR) is a highlevel rulebased programming language which is increasingly used for general purposes. We introduce the CHR machine, a model of computation based on the operational semantics of CHR. Its computational power and time complexity properties are compared to thos ..."
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Cited by 50 (21 self)
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Constraint Handling Rules (CHR) is a highlevel rulebased programming language which is increasingly used for general purposes. We introduce the CHR machine, a model of computation based on the operational semantics of CHR. Its computational power and time complexity properties are compared to those of the wellunderstood Turing machine and Random Access Memory machine. This allows us to prove the interesting result that every algorithm can be implemented in CHR with the best known time and space complexity. We also investigate the practical relevance of this result and the constant factors involved. Finally we expand the scope of the discussion to other (declarative) programming languages.
Space Bounds for Resolution
, 1999
"... We introduce a new way to measure the space needed in resolution refutations of CNF formulas in propositional logic. With the former definition [11] the space required for the resolution of any unsatisfiable formula in CNF is linear in the number of clauses. The new definition allows a much finer ..."
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Cited by 50 (3 self)
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We introduce a new way to measure the space needed in resolution refutations of CNF formulas in propositional logic. With the former definition [11] the space required for the resolution of any unsatisfiable formula in CNF is linear in the number of clauses. The new definition allows a much finer analysis of the space in the refutation, ranging from constant to linear space. Moreover, the new definition allows to relate the space needed in a resolution proof of a formula to other well studied complexity measures. It coincides with the complexity of a pebble game in the resolution graphs of a formula, and as we show, has relationships to the size of the refutation. We also give upper and lower bounds on the space needed for the resolution of unsatisfiable formulas. We show that Tseitin formulas associated to a certain kind of expander graphs of n nodes need resolution space n \Gamma c for some constant c. Measured on the number of clauses, this result is the best possible. We also show that the formulas expressing the general Pigeonhole Principle with n holes and more than n pigeons, need space n + 1 independently of the number of pigeons. Since a matching space upper bound of n + 1 for these formulas exist, the obtained bound is exact. We also point to a possible connection between resolution space and resolution width, another measure for the complexity of resolution refutations. 3 1
An Optimal Parallel Algorithm for Formula Evaluation
, 1992
"... A new approach to Buss’s NC¹ algorithm [Proc. 19thACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1987, pp. 123131] for evaluation of Boolean formulas is presented. This problem is shown to be complete for NC¹ over AC¬ reductions. This approach is then used to s ..."
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Cited by 45 (6 self)
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A new approach to Buss’s NC¹ algorithm [Proc. 19thACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1987, pp. 123131] for evaluation of Boolean formulas is presented. This problem is shown to be complete for NC¹ over AC¬ reductions. This approach is then used to solve the more general problem of evaluating arithmetic formulas by using arithmetic circuits.