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72
Quantum MerlinArthur proof systems: Are multiple . . .
, 2008
"... This paper introduces quantum “multipleMerlin”Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multiproof systems are obviously equivalent to classical singleproof systems (i.e., usual MerlinArthur proof systems), it ..."
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Cited by 24 (6 self)
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This paper introduces quantum “multipleMerlin”Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multiproof systems are obviously equivalent to classical singleproof systems (i.e., usual MerlinArthur proof systems), it is unclear whether or not quantum multiproof systems collapse to quantum singleproof systems (i.e., usual quantum MerlinArthur proof systems). This paper presents a necessary and sufficient condition under which the number of quantum proofs is reducible to two. It is also proved that, in the case of perfect soundness, using multiple quantum proofs
Completeness in the polynomialtime hierarchy: A compendium
 SIGACT News
"... We present a Garey/Johnsonstyle list of problems known to be complete for the second and higher levels of the polynomialtime Hierarchy (polynomial hierarchy, or PH for short). We also include the bestknown hardness of approximation results. The list will be updated as necessary. Updates The compe ..."
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Cited by 16 (2 self)
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We present a Garey/Johnsonstyle list of problems known to be complete for the second and higher levels of the polynomialtime Hierarchy (polynomial hierarchy, or PH for short). We also include the bestknown hardness of approximation results. The list will be updated as necessary. Updates The compendium currently lists more than 80 problems. Latest changes include: • added [GT26] SUCCINCT kKING, • added [GT25] SUCCINCT kDIAMETER, • added [GT4] SUCCINCT kRADIUS at third level, • added [GT24] MINIMUM VERTEX COLORING DEFINING SET, • added [GT23] GRAPH SANDWICH PROBLEM FOR Π, • added [L24] MINIMUM 3SAT DEFINING SET,
On the Noise Sensitivity of Monotone Functions
, 2003
"... It is known that for all monotone functions f: {0, 1} n → {0, 1}, if x ∈ {0, 1} n is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ɛ = n −α, then P[f(x) � = f(y)] < cn −α+1/2, for some c> 0. Previously, the best constructio ..."
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Cited by 9 (5 self)
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It is known that for all monotone functions f: {0, 1} n → {0, 1}, if x ∈ {0, 1} n is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ɛ = n −α, then P[f(x) � = f(y)] < cn −α+1/2, for some c> 0. Previously, the best construction of monotone functions satisfying P[fn(x) � = fn(y)] ≥ δ, where 0 < δ < 1/2, required ɛ ≥ c(δ)n −α, where α = 1 − ln 2 / ln 3 = 0.36907..., and c(δ)> 0. We improve this result by achieving for every 0 < δ < 1/2, P[fn(x) � = fn(y)] ≥ δ, with: • ɛ = c(δ)n−α for any α < 1/2, using the recursive majority function with arity k = k(α); π/2 =.3257..., using an explicit recursive majority • ɛ = c(δ)n −1/2 log t n for t = log 2 function with increasing arities; and, • ɛ = c(δ)n −1/2, nonconstructively, following a probabilistic CNF construction due to Talagrand. We also study the problem of achieving the best dependence on δ in the case that the noise rate ɛ is at least a small constant; the results we obtain are tight to within logarithmic factors.
On PublicKey Cryptosystems Based on Combinatorial Group Theory
, 2005
"... We analyze and critique the publickey cryptosystem, based on combinatorial group theory, that was proposed by Wagner and Magyarik in 1984. This idea is actually not based on the word problem but on another, generally easier, premise problem. Moreover, the idea of the WagnerMagyarik system is v ..."
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Cited by 9 (1 self)
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We analyze and critique the publickey cryptosystem, based on combinatorial group theory, that was proposed by Wagner and Magyarik in 1984. This idea is actually not based on the word problem but on another, generally easier, premise problem. Moreover, the idea of the WagnerMagyarik system is vague, and it is di#cult to find a secure realization of this idea. We describe a publickey cryptosystem inspired in part by the WagnerMagyarik idea, but we also use group actions on words.
An extended kernel for generalized multipleinstance learning
 16th IEEE International Conference on Tools with Artificial Intelligence (ICTAI 2004
, 2004
"... The multipleinstance learning (MIL) model has been successful in numerous application areas. Recently, a generalization of this model and an algorithm for it were introduced, showing significant advantages over the conventional MIL model on certain application areas. Unfortunately, that algorithm i ..."
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Cited by 8 (1 self)
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The multipleinstance learning (MIL) model has been successful in numerous application areas. Recently, a generalization of this model and an algorithm for it were introduced, showing significant advantages over the conventional MIL model on certain application areas. Unfortunately, that algorithm is not scalable to high dimensions. We adapt that algorithm to one using a support vector machine with our new kernel k∧. This reduces the time complexity from exponential in the dimension to polynomial. Computing our new kernel is equivalent to counting the number of boxes in a discrete, bounded space that contain at least one point from each of two multisets. We show that this problem is #Pcomplete, but then give a fully polynomial randomized approximation scheme (FPRAS) for it. We then extend k∧ by enriching its representation into a new kernel kmin, and also consider a normalized version of k∧ that we call k ∧/ ∨ (which may or may not not be a kernel, but whose approximation yielded positive semidefinite Gram matrices in practice). We then empirically evaluate all three measures on data from contentbased image retrieval, biological sequence analysis, and the Musk data sets. We found that our kernels performed well on all data sets relative to algorithms in the conventional MIL model. Index Terms kernels, support vector machines, generalized multipleinstance learning, contentbased image retrieval, biological sequence analysis, fully polynomial randomized approximation schemes I.
Solving Regular Path Queries
 In Proceedings of the 6th International Conference on Mathematics of Program Construction
, 2002
"... Regular path queries are a way of declaratively specifying program analyses as a kind of regular expressions that are matched against paths in graph representations of programs. This paper describes the precise specication, derivation, and analysis of a complete algorithm and data structures for ..."
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Cited by 5 (4 self)
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Regular path queries are a way of declaratively specifying program analyses as a kind of regular expressions that are matched against paths in graph representations of programs. This paper describes the precise specication, derivation, and analysis of a complete algorithm and data structures for solving regular path queries. The time and space complexity of the algorithm is linear in the size of the graph. We rst show two ways of specifying the problem and deriving a highlevel algorithmic solution, using predicate logic and language inclusion, respectively.
Mathematical definition of “intelligence” (and consequences)
, 2006
"... In §9 we propose an abstract mathematical definition of, and practical way to measure, “intelligence.” Before that is much motivating discussion and arguments why it is a good definition, and after it we deduce several important consequences – fundamental theorems about intelligence. The most impo ..."
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Cited by 5 (0 self)
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In §9 we propose an abstract mathematical definition of, and practical way to measure, “intelligence.” Before that is much motivating discussion and arguments why it is a good definition, and after it we deduce several important consequences – fundamental theorems about intelligence. The most important (theorem 5 of §12) is our construction of an algorithm that implements an “asymptotically uniformly competitive intelligence” (UACI). Although our definition of intelligence initially seems “multidimensional”– two entities would seem capable of being relatively more or less intelligent independently in each of an infinite number of “dimensions” of intelligence – the UACI is an intelligent entity that is simultaneously as intelligent as any other entity (asymptotically) in every dimension simultaneously. This in a considerable sense
Theory of one tape linear time Turing machines
 Proc. 30th SOFSEM Conference on Current Trends in Theory and Practice of Computer Science, Lecture Notes in Computer Science, Vol.2932, pp.335–348
, 2004
"... Abstract. A theory of onetape lineartime Turing machines is quite different from its polynomialtime counterpart. This paper discusses the computational complexity of onetape Turing machines of various machine types (deterministic, nondeterministic, reversible, alternating, probabilistic, countin ..."
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Cited by 5 (3 self)
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Abstract. A theory of onetape lineartime Turing machines is quite different from its polynomialtime counterpart. This paper discusses the computational complexity of onetape Turing machines of various machine types (deterministic, nondeterministic, reversible, alternating, probabilistic, counting, and quantum Turing machines) that halt in time O(n), where the running time of a machine is defined as the height of its computation tree. We also address a close connection between onetape lineartime Turing machines and finite state automata. §1. Model of Computation: Turing Machines. We use a standard definition of an offline Turing machine. Of special interest is a onetape Turing machine (abbreviated 1TM) M = (Q, Σ, Γ, δ, q0, qacc, qrej), where Q is a finite set of (internal) states, Σ is a nonempty finite input alphabet 3, Γ is a finite tape alphabet including Σ, q0 in Q is an initial state, qacc and qrej in Q are an accepting state and a rejecting state, respectively, and δ is a transition function. Different transition functions δ give rise to various types of 1TMs described in
Resource Management for AdHoc Wireless Networks with Cluster Organization
 Journal of Cluster Computing in the Internet, Kluwer Academic Publishers
, 2004
"... Boosted by technology advancements, government and commercial interest, adhoc wireless networks are emerging as a serious platform for distributed missioncritical applications. Guaranteeing QoS in this environment is a hard problem because several applications may share the same resources in the n ..."
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Cited by 5 (1 self)
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Boosted by technology advancements, government and commercial interest, adhoc wireless networks are emerging as a serious platform for distributed missioncritical applications. Guaranteeing QoS in this environment is a hard problem because several applications may share the same resources in the network, and mobile adhoc wireless networks (MANETs) typically exhibit high variability in network topology and communication quality. In this paper we introduce DYNAMIQUE, a resource management infrastructure for MANETs. We present a resource model for multiapplication admission control that optimizes the application admission utility, defined as a combination of the QoS satisfaction ratio. A method based on external adaptation (shrinking QoS for existing applications and later QoS expansion) is introduced as a way to reduce computation complexity by reducing the search space. We designed an application admission protocol that uses a greedy heuristic to improve application utility. For this, the admission control considers network topology information from the routing layer. Specifically, the admission protocol takes benefit from a cluster network organization, as defined by adhoc routing protocols such as CBRP and LANMAR. Information on cluster membership and cluster head elections allows the admission protocol to minimize control signaling and to improve application quality by localizing task mapping.