This paper solves the two-sided version and provides a counterexample to general of 2003 conjecture by Hadwin Larson. Consider evaluations linear matrix pencils $L=T_0+x_1T_1+\cdots+x_mT_m$ on tuples as $L(X_1,\dots,X_m)=I\otimes T_0+X_1\otimes T_1+\cdots+X_m\otimes T_m$. It is shown that ranks constitute collection separating invariants for simultaneous similarity tuples. That is, $m$-tuples $...

The time complexity of algorithms establishing arc consistency for table constraints depends mainly on the number of involved tuples. Thus, several work have been carried out in order to decrease that number. Notably, Katsirelos and Walsh have proposed to compress the tuple set. They integrate their method into GAC-Schema and they showed how a set of f forbidden tuples may be represented by a s...

We enrich a curated resource of commonsense knowledge by formulating the problem as one of knowledge base completion (KBC). Most work in KBC focuses on knowledge bases like Freebase that relate entities drawn from a fixed set. However, the tuples in ConceptNet (Speer and Havasi, 2012) define relations between an unbounded set of phrases. We develop neural network models for scoring tuples on ar...

In this paper. we utilize intervals for unknown values in incomplete relational databases. We use tables to represent unknown relations. First, we define three partial tuple types in a table to specify incompleteness relationships among tuples of the same table. For tuples of different tables, we distinguish between the cases where incompleteness are introduced at the relation level, tuple leve...

We present an algorithm for compressing table constraints representing allowed or disallowed tuples. This type of constraint is used for example in configuration problems, where the satisfying tuples are read from a database. The arity of these constraints may be large. A generic GAC algorithm for such a constraint requires time exponential in the arity of the constraint to maintain GAC, but Be...

Disjoint NP-pairs are a well studied complexity-theoretic concept with important applications in cryptography and propositional proof complexity. In this paper we introduce a natural generalization of the notion of disjoint NP-pairs to disjoint k-tuples of NP-sets for k ≥ 2. We define subclasses of the class of all disjoint k-tuples of NP-sets. These subclasses are associated with a proposition...

A common problem in decision-making is to analyze a tuple of numerical values associated with options, such as the degree of satisfaction assigned by experts to alternatives or probability values for hypotheses computed from data. With no loss of generality, it is assumed that the tuple contains values in the unit interval. For post-processing of typical value(s), singular values that may arise...