In this paper we extend fuzzy analytic hierarchy process into neutrosophic cubic environment. The neutrosophic cubic analytic hierarchy process can be used to manage more complex problems when the decision makers has a number of uncertainty, assigning preferences values to the considered object. We also define the concept of triangular neutrosophic cubic numbers and their operations laws. The a...

It is shown that products of eigenfunctions and (integrated) adjoint eigenfunctions associated with the (modiied) Kadomtsev-Petviashvili (KP) hierarchy form generators of a symmetry transformation. Linear integro-diierential representations for these symmetries are found. For special cases the corresponding nonlinear equations are the compatibility conditions of linear scattering problems of Lo...

We impose various oracle mechanisms on nondeterministic pushdown automata, which naturally induce nondeterministic reducibilities among formal languages in a theory of context-free languages. In particular, we examine a notion of nondeterministic many-one CFL reducibility and conduct a ground work to formulate a coherent framework for further expositions. Two more powerful reducibilities— bound...

We propose two admissible closures A(PTCA) and A(PHCA) of Ferreira’s system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) A(PTCA) is conservative over PTCA with respect to ∀∃Σ1 sentences, and (ii) A(PHCA) is conservative over full bounded arithmetic PHCA for ∀∃Σ∞ sentences. Th...

The ultimate goal we have is separating classes (or proving they are equal if they are). But our success so far seems to be limited: We know a (quite) tight time hierarchy, a tight space hierarchy, non-deterministic hierarchies, and some other (weaker) hierarchies. However, we are unable to even prove that LOG 6= P#P or that BPP 6= NEXP. In this lecture we seek some justification to this state ...

More and more modern computer applications, from business decision support to scientiic data analysis, utilize visualization techniques to support exploratory activities. Various tools have been proposed in the past decade to help users better interpret data using such display techniques. However, most do not scale well with regard to the size of the dataset upon which they operate. In particul...

In the early 1980s, Selman’s seminal work on positive Turing reductions showed that positive Turing reduction to NP yields no greater computational power than NP itself. Thus, positive Turing and Turing reducibility to NP differ sharply unless the polynomial hierarchy collapses. We show that the situation is quite different for DP, the next level of the boolean hierarchy. In particular, positiv...

We first define the classes in the polynomial-time hierarchy.

Hemaspaandra, Hempel, and Wechsung [HHW95] raised the following questions: If one is allowed one question to each of two different information sources, does the order in which one asks the questions affect the class of problems that one can solve with the given access? If so, which order yields the greater computational power? The answers to these questions have been learned—inasfar as they can...