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An incomplete set of shortest descriptions
 The Journal of Symbolic logic
"... The truthtable degree of the set of shortest programs remains an outstanding problem in recursion theory. We examine two related sets, the set of shortest descriptions and the set of domainrandom strings, and show that the truthtable degrees of these sets depend on the underlying acceptable numb ..."
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Cited by 2 (2 self)
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numbering. We achieve some additional properties for the truthtable incomplete versions of these sets, namely retraceability and approximability. We give priorityfree constructions of bounded truthtable chains and bounded truthtable antichains inside the truthtable complete degree by identifying
Slowly synchronizing automata with zero and incomplete sets
, 2009
"... Using combinatorial properties of incomplete sets in a free monoid we construct a series of nstate deterministic automata with zero whose shortest synchronizing word has length n2 n ..."
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Cited by 5 (2 self)
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Using combinatorial properties of incomplete sets in a free monoid we construct a series of nstate deterministic automata with zero whose shortest synchronizing word has length n2 n
Stable signal recovery from incomplete and inaccurate measurements,”
 Comm. Pure Appl. Math.,
, 2006
"... Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y? To r ..."
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Cited by 1397 (38 self)
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Abstract Suppose we wish to recover a vector x 0 ∈ R m (e.g., a digital signal or image) from incomplete and contaminated observations y = Ax 0 + e; A is an n × m matrix with far fewer rows than columns (n m) and e is an error term. Is it possible to recover x 0 accurately based on the data y
STRUCTURE OF LARGE INCOMPLETE SETS IN ABELIAN GROUPS
, 2006
"... Abstract. Let G be a finite abelian group and A be a subset of G. We say that A is complete if every element of G can be represented as a sum of different elements of A. In this paper, we study the following question: What is the structure of a large incomplete set? The typical answer is that such a ..."
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Cited by 2 (1 self)
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Abstract. Let G be a finite abelian group and A be a subset of G. We say that A is complete if every element of G can be represented as a sum of different elements of A. In this paper, we study the following question: What is the structure of a large incomplete set? The typical answer
FARSITE: Federated, Available, and Reliable Storage for an Incompletely Trusted Environment
 IN PROCEEDINGS OF THE 5TH SYMPOSIUM ON OPERATING SYSTEMS DESIGN AND IMPLEMENTATION (OSDI
, 2002
"... Farsite is a secure, scalable file system that logically functions as a centralized file server but is physically distributed among a set of untrusted computers. Farsite provides file availability and reliability through randomized replicated storage; it ensures the secrecy of file contents with cry ..."
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Cited by 487 (13 self)
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Farsite is a secure, scalable file system that logically functions as a centralized file server but is physically distributed among a set of untrusted computers. Farsite provides file availability and reliability through randomized replicated storage; it ensures the secrecy of file contents
Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information
, 2006
"... This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result of this pa ..."
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Cited by 2632 (50 self)
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This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discretetime signal and a randomly chosen set of frequencies. Is it possible to reconstruct from the partial knowledge of its Fourier coefficients on the set? A typical result
Exact Matrix Completion via Convex Optimization
, 2008
"... We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can perfe ..."
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Cited by 873 (26 self)
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perfectly recover most lowrank matrices from what appears to be an incomplete set of entries. We prove that if the number m of sampled entries obeys m ≥ C n 1.2 r log n for some positive numerical constant C, then with very high probability, most n × n matrices of rank r can be perfectly recovered
BISS: Building Secure Routing out of an Incomplete Set of Security Associations
, 2003
"... We investigate secure routing in ad hoc networks in which security associations exist only between a subset of all pairs of nodes. We focus on source routing protocols. We show that to establish secure routes, it is in general not necessary that security associations exist between all pairs of nodes ..."
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Cited by 32 (2 self)
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of nodes; a fraction of security associations is su#cient. We analyze the performance of existing proposals for secure routing in such conditions. We also propose a new protocol, designed specifically for ad hoc networks with an incomplete set of security associations between the nodes. We call
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