In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finall...

In this paper, we prove that any BL-general fuzzy automaton (BL-GFA) and its quotient have the same behavior. In addition, we obtain the minimal quotient BL-GFA and minimal quotient transformation of the BL-GFA, considering the notion of maximal admissible partition. Furthermore, we show that the number of input symbols and time complexity of the minimal quotient transformation of a BL-GFA are ...

We discuss coloring and partitioning questions related to Sperner’s Lemma, originally motivated by an application in hardness of approximation. Informally, we call a partitioning of the (k − 1)-dimensional simplex into k parts, or a labeling of a lattice inside the simplex by k colors, “Sperner-admissible” if color i avoids the face opposite to vertex i. The questions we study are of the follow...

We propose a type of admissible-region analysis for track initiation in multisatellite problems when angles are the primary observable. For a specified rectangular partition in the space of orbital elements, we present explicit upper and lower bounds, and other constraints, for the values of range and range rate that will lead to initial orbit hypotheses (data association hypotheses) associated...

The aim of this paper is the study of a covering of a max-mingeneral fuzzy automaton by another, admissible relations, admissiblepartitions of a max-min general fuzzy automaton,$tilde{delta}$-orthogonality of admissible partitions, irreduciblemax-min general fuzzy automata. Then we obtain the relationshipsbetween them.  

We explore a method for computing admissible heuristic evaluation functions for search problems. It utilizes pattern databases (Culberson & Schaeffer, 1998), which are precomputed tables of the exact cost of solving various subproblems of an existing problem. Unlike standard pattern database heuristics, however, we partition our problems into disjoint subproblems, so that the costs of solving t...

We prove generalizations of some partition theorems of Farkas and Kra. 1. The Farkas and Kra partition theorem and its generalization In a recent talk given at the University of Melbourne, Hershel Farkas asked for a(nother) proof of the following elegant partition theorem. Theorem 1.1 (Farkas and Kra [2],[3, Chapter 7]). Consider the positive integers such that multiples of 7 occur in two copie...

We study the surface defect in $\mathcal{N}=2^*$ $U(N)$ gauge theory four dimensions and its relation to quantum Hall states two dimensions. first prove that partition function becomes Jack polynomial of variables describing brane positions by imposing Higgsing condition taking bulk decoupling limit. Further tuning adjoint mass parameter, we may obtain various fractional states, including Laugh...

A perfectly one-factorable (P1F) regular graph G is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. We consider the case in which G is a cubic graph. The existence of a P1F cubic graph is guaranteed for each admissible value of the number of vertices. We give conditions for determining P1F graphs within a subfamily of...