Orbits of Boolean Functions
نویسنده
چکیده
The group of congruences and permutations of the two-colored N-dimensional Boolean cube is considered. The total number of orbits generated by these automorphisms are shown to scale as 22”/(2y+‘N!) when N tends to infinity. The probability that a randomly chosen function will belong to an orbit containing the maximum possible number of elements, 2’v+’ N!, approaches one as N goes to infinity. Simulations for N <6 are in agreement with the scaling predictions.
منابع مشابه
ON THE FUZZY SET THEORY AND AGGREGATION FUNCTIONS: HISTORY AND SOME RECENT ADVANCES
Several fuzzy connectives, including those proposed by Lotfi Zadeh, can be seen as linear extensions of the Boolean connectives from the scale ${0,1}$ into the scale $[0,1]$. We discuss these extensions, in particular, we focus on the dualities arising from the Boolean dualities. These dualities allow to transfer the results from some particular class of extended Boolean functions, e.g., from c...
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 کاملOn Pivot Orbits of Boolean Functions
We derive a spectral interpretation of the pivot operation on a graph and generalise this operation to hypergraphs. We establish lower bounds on the number of flat spectra of a Boolean function, depending on internal structures, with respect to the {I,H}n and {I,H,N}n sets of transforms. We also construct a family of Boolean functions of degree higher than two with a large number of flat spectr...
متن کاملSymmetry in critical random Boolean network dynamics.
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at ...
متن کاملAlmost Enumeration of eight-variable Bent Functions
Bent functions are important cryptographic Boolean functions. In order to enumerate eight-variable bent functions, we solve the following three key problems. Firstly, under the action of AGL(7, 2), we almost completely classify R(4, 7)/R(2, 7). Secondly, we construct all seven-variable plateaued functions from the orbits of R(4, 7)/R(2, 7). Thirdly, we present a fast algorithm to expand plateau...
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:
- Discrete Applied Mathematics
دوره 75 شماره
صفحات -
تاریخ انتشار 1997