Minimum self-dual decompositions of positive dual-minor Boolean functions
نویسندگان
چکیده
منابع مشابه
Minimum Self-dual Decompositions of Positive Dual-minor Boolean Functions
In this paper we consider decompositions of a positive dual-minor Boolean function $f$ into $f=$ $f_{1}f_{2}\ldots\ldots.f_{k}$ , where all $f_{j}$ are positive and self-dual. It is shown that the minimum $k$ having such a decomposition equals the chromatic number of a graph associated with $f$ , and the problem of deciding whether a decomposition of size $k$ exists is
متن کاملDual Subimplicants of Positive Boolean Functions∗
Given a positive Boolean function f and a subset ∆ of its variables, we give a combinatorial condition characterizing the existence of a prime implicant D̂ of the Boolean dual fd of f , having the property that every variable in ∆ appears in D̂. We show that the recognition of this property is an NP-complete problem, suggesting an inherent computational difficulty of Boolean dualization, independ...
متن کاملPartial Clones Containing all Boolean Monotone Self-dual Partial Functions
The study of partial clones on 2 := {0, 1} was initiated by R. V. Freivald. In his fundamental paper published in 1966, Freivald showed, among other things, that the set of all monotone partial functions and the set of all self-dual partial functions are both maximal partial clones on 2. Several papers dealing with intersections of maximal partial clones on 2 have appeared after Freivald work. ...
متن کاملOn Self-Dual Quantum Codes, Graphs, and Boolean Functions
A short introduction to quantum error correction is given, and it is shown that zero-dimensional quantum codes can be represented as self-dual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes with high minimum distance can be described as nested regular graphs having minimum regular vertex degree and containing long cycles. Two graphs correspond ...
متن کاملSelf-dual bent functions
A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterization in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1999
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00096-7