The general theory of bivariate orthogonal polynomials goes back to the work of Jackson [12]. Special examples have arisen in studies related to symmetric groups [4, 16, 22]), as extensions of one variable polynomials [7, 15] and as eigenfunctions of partial differential equations [19, 14, 13, 21]. An updated account of the theory can be found in the books [5, 25]. A major difficulty encountere...

This note studies the learnability of ordered binary decision diagrams (obdds). We give a polynomial-time algorithm using membership and equivalence queries that nds the minimum obdd for the target respecting a given ordering. We also prove that both types of queries and the restriction to a given ordering are necessary if we want minimality in the output, unless P=NP. If learning has to occur ...

In this note we provide a concise report on the complexity of the causal ordering problem, originally introduced by Simon to reason about causal dependencies implicit in systems of mathematical equations. We show that Simon’s classical algorithm to infer causal ordering is NP-Hard—an intractability previously guessed but never proven. We present then a detailed account based on Nayak’s suggeste...

The internal structure of DNA-CTAB and DNA-DDAB is investigated by a Small Angel X- ray Scattering(SAXS) instrument. Hexagonal packing of DNA was observed for DNA complex with CTAB, and for DDABcomplex is observed lamellar structure. Variations in the internal spacing and degree of long-range ordering aredependent on both surfactant type and concentrations of added salt. When we increased the a...

C60 fullerides are uniquely flexible molecular materials that exhibit a rich variety of behaviour, including superconductivity and magnetism in bulk compounds, novel electronic and orientational phases in thin films and quantum transport in a single-C60 transistor. The complexity of fulleride properties stems from the existence of many competing interactions, such as electron-electron correlati...

After designing of Multi-Valued Logic Networks (MVLNs), the resulting circuits have to be veri ed to guarantee functional correctness. The most promising technique to cope with increasing device sizes are formal methods. Ordered Multi-Valued Decision Diagrams (OMDDs) have been proposed for formal veri cation of MVLNs. But OMDDs are very sensitive to the chosen variable ordering and several orde...

We consider in this paper the size of a Decomposable Negation Normal Form (DNNF) that respects a given vtree (known as structured DNNF). This representation of propositional knowledge bases was introduced recently and shown to include OBDD as a special case (an OBDD variable ordering is a special type of vtree). We provide a lower bound on the size of any structured DNNF and discuss three parti...

method to obtain the minimum number of nodes in Reduced Ordered Binary Decision Diagrams (ROBDD). The proposed method uses the graph topology to find the best variable ordering. Therefore the input Boolean function is converted to a unidirectional graph. Three levels of graph parameters are used to increase the probability of having a good variable ordering. The initial level uses the total num...

While affix ordering often reflects general syntactic or semantic principles, it can also be arbitrary or variable. This article develops a theory of morpheme ordering based on local morphotactic restrictions encoded as weighted bigram constraints. I examine the formal properties of morphotactic systems, including arbitrariness, nontransitivity, context-sensitivity, analogy, and variation. Seve...

In Bayesian Network Structure Learning (BNSL), we are given a variable set and parent scores for each aim to compute DAG, called network, that maximizes the sum of scores, possibly under some structural constraints. Even very restricted special cases BNSL computationally hard, and, thus, in practice heuristics such as local search used. typical algorithm, solution ask whether there is better wi...