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The Polynomial Time Function Hierarchy
, 1994
"... We study Krentel's polynomial time function hierarchy (PFH) which classifies and characterizes optimization functions using deterministic oracle transducers and NP sets as oracles. We introduce a quantifier syntax to describe PFH, and explicitly introduce the \Pi MM k levels of the hierarc ..."
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We study Krentel's polynomial time function hierarchy (PFH) which classifies and characterizes optimization functions using deterministic oracle transducers and NP sets as oracles. We introduce a quantifier syntax to describe PFH, and explicitly introduce the \Pi MM k levels
Polygraphic programs and polynomialtime functions
, 2008
"... We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of firstorder functional programs. We explain their semantics and prove that they form a Turingcomplete computational model. Their algebraic structure i ..."
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Cited by 6 (0 self)
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is used by analysis tools, called polygraphic interpretations, for complexity analysis. In particular, we delineate a subclass of polygraphic programs that compute exactly the functions that are Turingcomputable in polynomial time.
A New Characterization of Mehlhorn's Polynomial Time Functionals (Extended Abstract)
 PROCEEDINGS OF THE 32ND ANNUAL IEEE SYMPOSIUM FOUNDATIONS OF COMPUTER SCIENCE
, 1991
"... A type 1 function is a total mapping from N to N. We will denote the set of all such functions by N N. A type 2 functional is a total mapping from ( N N) k \Theta N l to N, for some k; l. More specifically, we will call a mapping of this sort a functional with rank (k; l). For type 1 fu ..."
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Cited by 4 (0 self)
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functions, there is a well established notion of computational feasibility. Namely a function is feasible if it is computable in polynomial time on a Turing machine. More specifically, a function f is poly time if there is a TM M and a polynomial p such that for all x, M with input x computes f(x) and runs
A Note on the Relation between Polynomial Time Functionals and Constable's Class K
 IN KLEINEBUNING, EDITOR, COMPUTER SCIENCE LOGIC. SPRINGER LECTURE NOTES IN COMPUTER SCIENCE
, 1996
"... . A result claimed without proof by R. Constable in a STOC73 paper is here corrected: a strictly increasing function f is presented for which Constable's class K(f) is properly contained in FP (f ), the collection of functions polynomial time computable in f . ..."
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Cited by 3 (1 self)
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. A result claimed without proof by R. Constable in a STOC73 paper is here corrected: a strictly increasing function f is presented for which Constable's class K(f) is properly contained in FP (f ), the collection of functions polynomial time computable in f .
Electronic Colloquium on Computational Complexity, Report No. 28 (2005) On the Lattice of Clones Below the Polynomial Time Functions
"... Abstract. A clone is a set of functions that is closed under generalized substitution. The set FP of functions being computable deterministically in polynomial time is such a clone. It is wellknown that the set of subclones of every clone forms a lattice. We study the lattice below FP, which contai ..."
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Abstract. A clone is a set of functions that is closed under generalized substitution. The set FP of functions being computable deterministically in polynomial time is such a clone. It is wellknown that the set of subclones of every clone forms a lattice. We study the lattice below FP, which
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 547 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
Large margin methods for structured and interdependent output variables
 JOURNAL OF MACHINE LEARNING RESEARCH
, 2005
"... Learning general functional dependencies between arbitrary input and output spaces is one of the key challenges in computational intelligence. While recent progress in machine learning has mainly focused on designing flexible and powerful input representations, this paper addresses the complementary ..."
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Cited by 624 (12 self)
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that solves the optimization problem in polynomial time for a large class of problems. The proposed method has important applications in areas such as computational biology, natural language processing, information retrieval/extraction, and optical character recognition. Experiments from various domains
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include
A hardcore predicate for all oneway functions
 In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing
, 1989
"... Abstract rity of f. In fact, for inputs (to f*) of practical size, the pieces effected by f are so small A central tool in constructing pseudorandom that f can be inverted (and the “hardcore” generators, secure encryption functions, and bit computed) by exhaustive search. in other areas are “hardc ..."
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Cited by 440 (5 self)
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(within a polynomial) 50) given only f(z). Both b, f are computable security. Namely, we prove a conjecture of in polynomial time. [Levin 87, sec. 5.6.21 that the sca1a.r product [Yao 821 transforms any oneway function of boolean vectors p, x is a hardcore of every f into a more complicated one, f
The Complexity of PolynomialTime Approximation
 TO APPEAR IN JOURNAL THEORY OF COMPUTING SYSTEMS
, 2006
"... In 1996, Khanna and Motwani [KM96] proposed three logicbased optimization problems constrained by planar structure, and offered the hypothesis that these putatively fundamental problems might provide insight into characterizing the class of optimization problems that admit a polynomialtime approxi ..."
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Cited by 6 (0 self)
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In 1996, Khanna and Motwani [KM96] proposed three logicbased optimization problems constrained by planar structure, and offered the hypothesis that these putatively fundamental problems might provide insight into characterizing the class of optimization problems that admit a polynomialtime
Results 1  10
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