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Combinatorial characterization of readonce formulae
, 2002
"... We give an alternative proof to a characterization theorem of Gurvich for Boolean functions whose formula size is exactly the number of variables. Those functions are called ReadOnce. We use methods of combinatorial optimization and give as a corollary an alternative proof for some results of Seymo ..."
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Cited by 25 (0 self)
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We give an alternative proof to a characterization theorem of Gurvich for Boolean functions whose formula size is exactly the number of variables. Those functions are called ReadOnce. We use methods of combinatorial optimization and give as a corollary an alternative proof for some results
Building above readonce polynomials: identity testing and hardness of representation
"... Abstract. Polynomial Identity Testing (PIT) algorithms have focussed on polynomials computed either by small alternationdepth arithmetic circuits, or by readrestricted formulas. Readonce polynomials (ROPs) are computed by readonce formulas (ROFs) and are the simplest of readrestricted polynomia ..."
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Abstract. Polynomial Identity Testing (PIT) algorithms have focussed on polynomials computed either by small alternationdepth arithmetic circuits, or by readrestricted formulas. Readonce polynomials (ROPs) are computed by readonce formulas (ROFs) and are the simplest of read
Optimal Ordered Binary Decision Diagrams for ReadOnce Formulas
, 1999
"... In many applications like verification or combinatorial optimization, OBDDs (ordered binary decision diagrams) are used as a representation or data structure for Boolean functions. Efficient algorithms exist for the important operations on OBDDs, and many functions can be represented in reasonable s ..."
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Cited by 2 (0 self)
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by fanin 2 readonce formulas the structure of optimal variable orderings is described, leading to a linear time algorithm for the construction of optimal variable orderings and the size of the corresponding OBDD. Moreover, it is proved that the hardest readonce formula has an OBDD size of order n
A Recursion and a Combinatorial Formula for Jack Polynomials
 Invent. Math
, 1997
"... this paper is to add to the existing characterizations of Jack polynomials two further ones: c) a recursion formula among the F together with two formulas to obtain J from them. d) combinatorial formulas of both J and F in terms of certain generalized tableaux ..."
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Cited by 100 (5 self)
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this paper is to add to the existing characterizations of Jack polynomials two further ones: c) a recursion formula among the F together with two formulas to obtain J from them. d) combinatorial formulas of both J and F in terms of certain generalized tableaux
A Combinatorial Characterization of Resolution Width
 In 18th IEEE Conference on Computational Complexity
, 2002
"... We provide a characterization of the resolution width introduced in the context of propositional proof complexity in terms of the existential pebble game introduced in the context of finite model theory. The characterization is tight and purely combinatorial. Our first application of this result i ..."
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Cited by 52 (6 self)
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We provide a characterization of the resolution width introduced in the context of propositional proof complexity in terms of the existential pebble game introduced in the context of finite model theory. The characterization is tight and purely combinatorial. Our first application of this result
A COMBINATORIAL FORMULA FOR NONSYMMETRIC MACDONALD POLYNOMIALS
"... Abstract. We give a combinatorial formula for the nonsymmetric Macdonald polynomials Eµ(x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials Jµ(x; q, t). We prove the new formula by verifying that it satisfies a recurrence, ..."
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Cited by 31 (4 self)
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Abstract. We give a combinatorial formula for the nonsymmetric Macdonald polynomials Eµ(x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials Jµ(x; q, t). We prove the new formula by verifying that it satisfies a recurrence
Results 1  10
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99,945