Combinatorial method of polynomial expansion of symmetric Boolean functions
نویسنده
چکیده
A novel polynomial expansion method of symmetric Boolean functions is described. The method is efficient for symmetric Boolean function with small set of valued numbers and has the linear complexity for elementary symmetric Boolean functions, while the complexity of the known methods for this class of functions is quadratic. The proposed method is based on the consequence of the combinatorial Lucas theorem.
منابع مشابه
A method to obtain the best uniform polynomial approximation for the family of rational function
In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...
متن کاملResults on rotation symmetric bent functions
In this paper we analyze the combinatorial properties related to the Walsh spectra of rotation symmetric Boolean functions on even number of variables. These results are then applied in studying rotation symmetric bent functions.
متن کاملMahler’s Expansion and Boolean Functions
The substitution of X by X2 in binomial polynomials generates sequences of integers by Mahler’s expansion. We give some properties of these integers and a combinatorial interpretation with covers by projection. We also give applications to the classification of boolean functions. This sequence arose from our previous research on classification and complexity of Binary Decision Diagrams (BDD) as...
متن کاملSynopsis: Dual Equivalence Graphs, Ribbon Tableaux and Macdonald Polynomials
The primary focus of this dissertation is symmetric function theory. The main objectives are to present a new combinatorial construction which may be used to establish the symmetry and Schur positivity of a function expressed in terms of monomials, and to use this method to find a combinatorial description of the Schur expansion for two important classes of symmetric functions, namely LLT and M...
متن کاملCOMBINATORIAL OPERATORS FOR KRONECKER POWERS OF REPRESENTATIONS OF Sn
We present combinatorial operators for the expansion of the Kronecker product of irreducible representations of the symmetric group Sn. These combinatorial operators are defined in the ring of symmetric functions and act on the Schur functions basis. This leads to a combinatorial description of the Kronecker powers of the irreducible representations indexed with the partition (n− 1, 1) which sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1306.5568 شماره
صفحات -
تاریخ انتشار 2013