相关论文: Study of an identity
We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap…
A characterization is given of the subsets of a group that extend to the positive cone of a right order on the group and used to relate validity of equations in lattice-ordered groups (l-groups) to subsets of free groups that extend to…
We propound the thesis that there is a limitation to the number of possible structures which are axiomatically endowed with identities involving operations. In the case of algebras with a binary operation satisfying a formally reducible (to…
This paper proposes a simple test for compositionality (i.e., literal usage) of a word or phrase in a context-specific way. The test is computationally simple, relying on no external resources and only uses a set of trained word vectors.…
Let $x$ and $y$ be words. We consider the languages whose words $z$ are those for which the numbers of occurrences of $x$ and $y$, as subwords of $z$, are the same (resp., the number of $x$'s is less than the number of $y$'s, resp., is less…
This paper describes experiments on identifying the language of a single name in isolation or in a document written in a different language. A new corpus has been compiled and made available, matching names against languages. This corpus is…
The AZ identity is a generalization of the LYM-inequality. In this paper, we will give a generalization of the AZ identity.
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…
We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in…
Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects…
Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…
Social Network Analysis is a way of studying agents embedded in contexts. In about 1998, physicists discovered social networks as representations of complex systems. Small-world and scale-free networks are the paradigmatic models of this…
We describe a solution of the word problem in free fields (coming from non-commutative polynomials over a commutative field) using elementary linear algebra, provided that the elements are given by minimal linear representations. It relies…
In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful…
Let $R$ be an associative ring with identity and let $N$ be a nil ideal of $R$. It is shown that units of $R/N$ can be lifted to units in $R$. Under some mild conditions on the ring, a procedure is given to determine those lifted units in a…
In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure…
A family of general integral identities is derived and several applications of physical interest are presented
We consider decidability problems in self-similar semigroups, and in particular in semigroups of automatic transformations of $X^*$. We describe algorithms answering the word problem, and bound its complexity under some additional…
We study some aspects of reflexive modules. For example, we search conditions for which reflexive modules are free or being very close to free modules.