with generalized errorontrol odes Mark G. Karpovsky Lev B. Levitin Ari Tra htenberg fmarkkar,levi... more with generalized errorontrol odes Mark G. Karpovsky Lev B. Levitin Ari Tra htenberg fmarkkar,levitin,tra hteng bu.edu Reliable Computing Lab Boston University, Boston, MA 02215 The problem of re on iling data is inherent to appli ations that require onsisten y among distributed information. From the perspe tives of s alability and performan e, it is important that re on iliations o ur with minimum ommuni ation. When data are represented by sets this problem is known as the set re on iliation problem [1,2℄. The data re on iliation problem is a natural generalization in whi h data is represented by multi-sets rather than sets. data verification data reconciliation
International Symposium on Information Theory, Jan 17, 1993
Zipfs law is a famous empirical law that is observed in the behavior of many complex systems of s... more Zipfs law is a famous empirical law that is observed in the behavior of many complex systems of surprisingly different nature. Zipf [l] found a remarkable rank-frequency relationship in linguistics. If we consider a long text and assign ranks to all words that occur in the text in the order of decreasing frequencies, then the frequency f , of a word satisfies the empirical law: f, = cr-p , where c and p are constants and p -1. Zipfs law has been discovered independently in such diverse situations as distribution of biological species, distribution of income, distribution of city populations, etc.[2]
Proceedings of 1994 IEEE International Symposium on Information Theory
The traveling salesman problem in the space Z/sub 2//sup n/ of all n-dimensional binary vectors c... more The traveling salesman problem in the space Z/sub 2//sup n/ of all n-dimensional binary vectors can be formulated as follows. Given: a set C(n,M) of M n-dimensional vectors over GF(2) (M points in Z/sub 2//sup n/). Find: a Hamiltonian circuit for C(n,M) of minimum Hamming length, i.e., a cycle with minimum sum of Hamming distances between connected points (henceforth called minimal cycle). This problem is encountered in various situations related to the design and testing of computer hardware. In contrast with the "unrestricted" traveling salesman problem, the length of the minimal cycle in Z/sub 2//sup n/ is always upperbounded by that for the "worst" possible configuration of M points. Hence the authors come to the following variational problem. Problem: for any number M of points in Z/sub 2//sup n/ find the function L(n,M) defined as follows: M L(n,M)=max{C} min{P}/spl Sigma//sub i=1//sup M/ d(x/sub p(i)/,x/sub P(i+l(modM))/) where x/sub 1/, ..., x/sub M/ are the points comprising a binary code C(n,M), d(x,y) is the Hamming distance between points x and y, {P} is the set of all possible permutations of the codewords, and the maximum is taken over the set of all possible binary codes of size M and dimension n. The problem is still open, but partial results are presented.<<ETX>>
Quantum Communication, Computing, and Measurement 3
The main result of the paper can be summarized as follows. The number of distinguishable quantum ... more The main result of the paper can be summarized as follows. The number of distinguishable quantum states in a 2-dimensional Hilbert space is proportional to the square root of the number of identical copies of each state measured and to the total length of the angle intervals occupied by the state vectors. Surprisingly, it does not depend on the position of the arcs comprising the range on the unit circle. These results can be generalized for the N-dimensional Hilbert space of states of a quantum system.As in the 2-dimensional case, the unit sphere can be reduced to the non-negative orthant of the unit sphere in the real N-dimensional Euclidean space.It turns out [6] that the number of distinguishable states depends only on the area Ω of the domain on the unit sphere from which the states can be chosen, but does not depend on the shape and position of this domain. The optimal distribution is uniform over the domain in angular (polar) coordinates, and the number of distinguishable states is \( W(n,\Omega ) = \Omega (cn)^{\tfrac{{N - 1}} {2}} \) where c is a constant.
Digest of Papers 1991 VLSI Test Symposium 'Chip-to-System Test Concerns for the 90's
An analysis and design of a pseudorandom pattern generator, (PRPG), based on a linear recurrence,... more An analysis and design of a pseudorandom pattern generator, (PRPG), based on a linear recurrence, for built-in self-test (BIST) boundary scan design is presented. The authors present for the case when r&amp;amp;amp;amp;ges;s, a design of an s-stage PRPG capable of producing 2s-1 distinct r-bit patterns within 2s-1 clock pulses independent of the hardware realization of the PRPG. For the case
A novel approach to the identification of a faulty processing element, based on an analysis of th... more A novel approach to the identification of a faulty processing element, based on an analysis of the compressed response of the system, is proposed. The test response is compressed first in space and then in time, and a faulty processing element is identified by a hard-decision decoding of the corresponding space-time signature. The overhead analysis and the solution for the
Proceedings of the 2nd conference on Computing frontiers, 2005
Specific ergodicity asks, for an invertible cellular automaton, lattice gas, or similar indefinit... more Specific ergodicity asks, for an invertible cellular automaton, lattice gas, or similar indefinitely-extended computational medium, what fraction of the information needed to specify an individual state is still missing after one is told the computational trajectory to which that state belongs. While the well-known distinction between "ergodic" and "nonergodic" for a dynamical system is an all-or-nothing classification, specific ergodicity---with range in the [0,1] interval---provides a continuous parameter which may be interpreted as "degree of ergodicity." Moreover, while the property of a system's being ergodic can only refer to the system as a whole, specific ergodicity is an intensive quantity (ie it factors out the size of the system); thus, for a spatially-distributed, homogeneous computational system such as a cellular automaton or a lattice gas, in the limit of infinite system size this quantity reflects an intrinsic property of the material that makes up the computational medium, abstracting from its specific size or shapeWe provide the conceptual background, present theoretical and numerical results, and discuss the relevance of specific ergodicity to a number of concrete research questions.Values of specific ergodicity for a variety of systems of actual interest turn out to be well distributed over its entire range; in this sense, this quantity is an informative indicator. Indeed, besides representing a useful parameter in the classification of distributed computational media, specific ergodicity provides a "sense of direction" in issues such as protection from noise, design of self-organizing media, necessary conditions for the emergence and persistence of life, effectiveness of a parallel architecture as a "programmable medium," and a number of topics in nanotechnology
International Journal of Theoretical Physics, 1996
Ranking procedures are widely used in the description of many different types of complex systems.... more Ranking procedures are widely used in the description of many different types of complex systems. Zipf&amp;#x27;s law is one of the most remarkable frequency-rank relationships and has been observed independently in physics, linguistics, biology, demography, etc. We show that ranking plays a crucial role in making it possible to detect empirical relationships in systems that exist in one realization only,
A simple network model with torus topology and the virtual cut-through routing has been considere... more A simple network model with torus topology and the virtual cut-through routing has been considered in order to find out and analyze certain relationships between network parameters, load and performance. An expression for the saturation point (message generation rate at which network saturates) and approximate expressions for the latency as a function of the message generation rate have been obtained. Simulation experiments for various values of network parameters (mesh size, message path length, and message length) have been performed. It is found that if the mesh linear dimension is at least twice as large as the message path length (the distance from source to destination) the network behavior (latency and saturation point) does not depend on the mesh size. Both theoretical and empirical results show that the saturation point is inversely proportional to the message length. If the network is in the steady state, a good agreement with Little’s theorem has been observed.Accepted ma...
with generalized errorontrol odes Mark G. Karpovsky Lev B. Levitin Ari Tra htenberg fmarkkar,levi... more with generalized errorontrol odes Mark G. Karpovsky Lev B. Levitin Ari Tra htenberg fmarkkar,levitin,tra hteng bu.edu Reliable Computing Lab Boston University, Boston, MA 02215 The problem of re on iling data is inherent to appli ations that require onsisten y among distributed information. From the perspe tives of s alability and performan e, it is important that re on iliations o ur with minimum ommuni ation. When data are represented by sets this problem is known as the set re on iliation problem [1,2℄. The data re on iliation problem is a natural generalization in whi h data is represented by multi-sets rather than sets. data verification data reconciliation
International Symposium on Information Theory, Jan 17, 1993
Zipfs law is a famous empirical law that is observed in the behavior of many complex systems of s... more Zipfs law is a famous empirical law that is observed in the behavior of many complex systems of surprisingly different nature. Zipf [l] found a remarkable rank-frequency relationship in linguistics. If we consider a long text and assign ranks to all words that occur in the text in the order of decreasing frequencies, then the frequency f , of a word satisfies the empirical law: f, = cr-p , where c and p are constants and p -1. Zipfs law has been discovered independently in such diverse situations as distribution of biological species, distribution of income, distribution of city populations, etc.[2]
Proceedings of 1994 IEEE International Symposium on Information Theory
The traveling salesman problem in the space Z/sub 2//sup n/ of all n-dimensional binary vectors c... more The traveling salesman problem in the space Z/sub 2//sup n/ of all n-dimensional binary vectors can be formulated as follows. Given: a set C(n,M) of M n-dimensional vectors over GF(2) (M points in Z/sub 2//sup n/). Find: a Hamiltonian circuit for C(n,M) of minimum Hamming length, i.e., a cycle with minimum sum of Hamming distances between connected points (henceforth called minimal cycle). This problem is encountered in various situations related to the design and testing of computer hardware. In contrast with the "unrestricted" traveling salesman problem, the length of the minimal cycle in Z/sub 2//sup n/ is always upperbounded by that for the "worst" possible configuration of M points. Hence the authors come to the following variational problem. Problem: for any number M of points in Z/sub 2//sup n/ find the function L(n,M) defined as follows: M L(n,M)=max{C} min{P}/spl Sigma//sub i=1//sup M/ d(x/sub p(i)/,x/sub P(i+l(modM))/) where x/sub 1/, ..., x/sub M/ are the points comprising a binary code C(n,M), d(x,y) is the Hamming distance between points x and y, {P} is the set of all possible permutations of the codewords, and the maximum is taken over the set of all possible binary codes of size M and dimension n. The problem is still open, but partial results are presented.<<ETX>>
Quantum Communication, Computing, and Measurement 3
The main result of the paper can be summarized as follows. The number of distinguishable quantum ... more The main result of the paper can be summarized as follows. The number of distinguishable quantum states in a 2-dimensional Hilbert space is proportional to the square root of the number of identical copies of each state measured and to the total length of the angle intervals occupied by the state vectors. Surprisingly, it does not depend on the position of the arcs comprising the range on the unit circle. These results can be generalized for the N-dimensional Hilbert space of states of a quantum system.As in the 2-dimensional case, the unit sphere can be reduced to the non-negative orthant of the unit sphere in the real N-dimensional Euclidean space.It turns out [6] that the number of distinguishable states depends only on the area Ω of the domain on the unit sphere from which the states can be chosen, but does not depend on the shape and position of this domain. The optimal distribution is uniform over the domain in angular (polar) coordinates, and the number of distinguishable states is \( W(n,\Omega ) = \Omega (cn)^{\tfrac{{N - 1}} {2}} \) where c is a constant.
Digest of Papers 1991 VLSI Test Symposium 'Chip-to-System Test Concerns for the 90's
An analysis and design of a pseudorandom pattern generator, (PRPG), based on a linear recurrence,... more An analysis and design of a pseudorandom pattern generator, (PRPG), based on a linear recurrence, for built-in self-test (BIST) boundary scan design is presented. The authors present for the case when r&amp;amp;amp;amp;ges;s, a design of an s-stage PRPG capable of producing 2s-1 distinct r-bit patterns within 2s-1 clock pulses independent of the hardware realization of the PRPG. For the case
A novel approach to the identification of a faulty processing element, based on an analysis of th... more A novel approach to the identification of a faulty processing element, based on an analysis of the compressed response of the system, is proposed. The test response is compressed first in space and then in time, and a faulty processing element is identified by a hard-decision decoding of the corresponding space-time signature. The overhead analysis and the solution for the
Proceedings of the 2nd conference on Computing frontiers, 2005
Specific ergodicity asks, for an invertible cellular automaton, lattice gas, or similar indefinit... more Specific ergodicity asks, for an invertible cellular automaton, lattice gas, or similar indefinitely-extended computational medium, what fraction of the information needed to specify an individual state is still missing after one is told the computational trajectory to which that state belongs. While the well-known distinction between "ergodic" and "nonergodic" for a dynamical system is an all-or-nothing classification, specific ergodicity---with range in the [0,1] interval---provides a continuous parameter which may be interpreted as "degree of ergodicity." Moreover, while the property of a system's being ergodic can only refer to the system as a whole, specific ergodicity is an intensive quantity (ie it factors out the size of the system); thus, for a spatially-distributed, homogeneous computational system such as a cellular automaton or a lattice gas, in the limit of infinite system size this quantity reflects an intrinsic property of the material that makes up the computational medium, abstracting from its specific size or shapeWe provide the conceptual background, present theoretical and numerical results, and discuss the relevance of specific ergodicity to a number of concrete research questions.Values of specific ergodicity for a variety of systems of actual interest turn out to be well distributed over its entire range; in this sense, this quantity is an informative indicator. Indeed, besides representing a useful parameter in the classification of distributed computational media, specific ergodicity provides a "sense of direction" in issues such as protection from noise, design of self-organizing media, necessary conditions for the emergence and persistence of life, effectiveness of a parallel architecture as a "programmable medium," and a number of topics in nanotechnology
International Journal of Theoretical Physics, 1996
Ranking procedures are widely used in the description of many different types of complex systems.... more Ranking procedures are widely used in the description of many different types of complex systems. Zipf&amp;#x27;s law is one of the most remarkable frequency-rank relationships and has been observed independently in physics, linguistics, biology, demography, etc. We show that ranking plays a crucial role in making it possible to detect empirical relationships in systems that exist in one realization only,
A simple network model with torus topology and the virtual cut-through routing has been considere... more A simple network model with torus topology and the virtual cut-through routing has been considered in order to find out and analyze certain relationships between network parameters, load and performance. An expression for the saturation point (message generation rate at which network saturates) and approximate expressions for the latency as a function of the message generation rate have been obtained. Simulation experiments for various values of network parameters (mesh size, message path length, and message length) have been performed. It is found that if the mesh linear dimension is at least twice as large as the message path length (the distance from source to destination) the network behavior (latency and saturation point) does not depend on the mesh size. Both theoretical and empirical results show that the saturation point is inversely proportional to the message length. If the network is in the steady state, a good agreement with Little’s theorem has been observed.Accepted ma...
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