اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPartial clones containing all Boolean monotone self-dual partial functions
126
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The study of partial clones on $mathbf{2}:={0,1}$ 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 $mathbf{2}$. Several papers dealing with intersections of maximal partial clones on $mathbf{2}$ have appeared after Freivald work. It is known that there are infinitely many partial clones that contain the set of all monotone self-dual partial functions on $mathbf{2}$, and the problem of describing them all was posed by some authors. In this paper we show that the set of partial clones that contain all monotone self-dual partial functions is of continuum cardinality on $mathbf{2}$.
قيم البحث
اقرأ أيضاً
For a class C of operations on a nonempty base set A, an operation f is called a C-subfunction of an operation g, if f = g(h_1, ..., h_n), where all the inner functions h_i are members of C. Two operations are C-equivalent if they are C-subfunctions
of each other. The C-subfunction relation is a quasiorder if and only if the defining class C is a clone. The C-subfunction relations defined by clones that contain all unary operations on a finite base set are examined. For each such clone it is determined whether the corresponding partial order satisfies the descending chain condition and whether it contains infinite antichains.
We provide two sufficient and necessary conditions to characterize any $n$-bit partial Boolean function with exact quantum 1-query complexity. Using the first characterization, we present all $n$-bit partial Boolean functions that depend on $n$ bits
and have exact quantum 1-query complexity. Due to the second characterization, we construct a function $F$ that maps any $n$-bit partial Boolean function to some integer, and if an $n$-bit partial Boolean function $f$ depends on $k$ bits and has exact quantum 1-query complexity, then $F(f)$ is non-positive. In addition, we show that the number of all $n$-bit partial Boolean functions that depend on $k$ bits and have exact quantum 1-query complexity is not bigger than $n^{2}2^{2^{n-1}(1+2^{2-k})+2n^{2}}$ for all $ngeq 3$ and $kgeq 2$.
Let A be a finite non-singleton set. For |A|=2 we show that the partial clone consisting of all selfdual monotone partial functions on A is not finitely generated, while it is the intersection of two finitely generated maximal partial clones on A. Mo
reover for |A| >= 3 we show that there are pairs of finitely generated maximal partial clones whose intersection is a non-finitely generated partial clone on A.
In this paper we set up a bivariate representation of partial theta functions which not only unifies some famous identities for partial theta functions due to Andrews and Warnaar, et al. but also unveils a new characteristic of such identities. As fu
rther applications, we establish a general form of Warnaars identity and a general $q$--series transformation associated with Bailey pairs via the use of the power series expansion of partial theta functions.
We define toric partial orders, corresponding to regions of graphic toric hyperplane arrangements, just as ordinary partial orders correspond to regions of graphic hyperplane arrangements. Combinatorially, toric posets correspond to finite posets und
er the equivalence relation generated by converting minimal elements into maximal elements, or sources into sinks. We derive toric analogues for several features of ordinary partial orders, such as chains, antichains, transitivity, Hasse diagrams, linear extensions, and total orders.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
