Essential arity gap of Boolean functions
نویسنده
چکیده
In this paper we investigate the Boolean functions with essential arity gap 2. We use Full Conjunctive Normal Forms instead of Zhegalkin’s polynomials, which allow us to simplify the proofs and to obtain several combinatorial results, concerning the Boolean functions with a given arity gap.
منابع مشابه
On the Arity Gap of Finite Functions: Results and Applications
Let A be a finite set and B an arbitrary set with at least two elements. The arity gap of a function f : An → B is the minimum decrease in the number of essential variables when essential variables of f are identified. A non-trivial fact is that the arity gap of such B-valued functions on A is at most |A|. Even less trivial to verify is the fact that the arity gap of B-valued functions on A wit...
متن کاملThe Arity Gap of Aggregation Functions and Further Extensions
The aim of this paper is to completely classify all aggregation functions based on the notion of arity gap. We first establish explicit descriptions of the arity gap of the Lovász extensions of pseudo-Boolean functions and, in particular, of the Choquet integrals. Then we consider the wider class of order-preserving functions between arbitrary, possibly different, posets, and show that similar ...
متن کاملThe arity gap of order-preserving functions and extensions of pseudo-Boolean functions
The aim of this paper is to classify order-preserving functions according to their arity gap. Noteworthy examples of order-preserving functions are the so-called aggregation functions.We first explicitly classify the Lovász extensions of pseudo-Boolean functions according to their arity gap. Then we consider the class of order-preserving functions between partially ordered sets, and establish a...
متن کاملEssential Arity Gap of k-Valued Functions
We investigate k−valued functions on a finite set of k elements with essential arity gap ≤ k. We describe the functions which have maximal arity gap. This description is based on the representation of the functions in their full conjunctive normal form. The combinatorial problem how many there are k−valued functions which have arity gap k is solved, also.
متن کاملOn the Discrete Functions with given Essential Arity Gap
In the paper the n−ary k−valued functions (k > 2) on a finite set of k elements with essential arity gap equal to p, p ≤ k are investigated. We give a formula (term-presentation of the functions which have given essential arity gap. This representation is based on the operation tables of the functions in their SC-forms as sums of conjunctions. The combinatorial problem how many there are k−valu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/0808.3892 شماره
صفحات -
تاریخ انتشار 2008