相关论文: Free augmented LD-systems

Real world deployments of word alignment are almost certain to cover both high and low resource languages. However, the state-of-the-art for this task recommends a different model class depending on the availability of gold alignment…

In this paper, we observe the amalgamated free product structure of a Graph W*-probability space. In [16] and [17], we already observed the operator-valued freeness conditions on a graph W*-algebra. By using the conditions, we will consider…

In this work, we introduce a methodology for alignment designed to enhance the ability of large language models (LLMs) to articulate their reasoning (self-explanation) even in the absence of annotated rationale explanations. Our alignment…

A $d$-limited automaton is a Turing machine that may rewrite each input cell at most~$d$ times. Hibbard (1967) showed that for every $d \geq 2$ such automata recognize all context-free languages and that deterministic $d$-limited automata…

It is shown how to use a small finite state automaton in two variables in order to carry out part of the Knuth--Bendix process for rewriting words in a group. The main objective is to provide a substitute for the most space-demanding module…

We show that all balanced d-lattices must be complemented, answering a question of Chajda and Eigenthaler. (A bounded lattice is balanced if any two congruences agree on their 1-classes iff they agree on their 0-classes.) Our main tool is…

Bilinear systems emerge in a wide variety of fields as natural models for dynamical systems ranging from robotics to quantum dots. Analyzing controllability of such systems is of fundamental and practical importance, for example, for the…

We describe the groups of automorphisms of two generated free braided associative algebras with involutive diagonal braidings over a field of characteristic $\neq 2$. Depending on the form of the diagonal involutive braiding, five different…

We develop a new tool, namely polynomial and linear algebraic methods, for studying systems of word equations. We illustrate its usefulness by giving essentially simpler proofs of several hard problems. At the same time we prove extensions…

We introduce the class of MAT-free hyperplane arrangements which is based on the Multiple Addition Theorem by Abe, Barakat, Cuntz, Hoge, and Terao. We also investigate the closely related class of MAT2-free arrangements based on a recent…

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new…

We study the class of groups generated by automata that act essentially freely on the boundary of a rooted tree. In the process we establish and discuss some general tools for determining if a group belongs to this class, and explore the…

We introduce the notion of additive units, or `addits', of a pointed Arveson system, and demonstrate their usefulness through several applications. By a pointed Arveson system we mean a spatial Arveson system with a fixed normalised…

Let $\A$ be a free arrangement of $d$ lines in the complex projective plane, with exponents $d_1\leq d_2$. Let $m$ be the maximal multiplicity of points in $\A$. In this note, we describe first the simple cases $d_1 \leq m$. Then we study…

This paper studies Social Law Synthesis (SLS) in strategic multi-agent environments as a new multi-unit mechanism design problem. We model SLS as a Bayesian single-parameter procurement auction based on Alternating-time Temporal Logic (ATL)…

This study covers an analytical approach to calculate positively invariant sets of dynamical systems. Using Lyapunov techniques and quantifier elimination methods, an automatic procedure for determining bounds in the state space as an…

We prove the following result: Theorem. Every algebraic distributive lattice D with at most $\aleph\_1$ compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R. (By earlier results of the author, the $\aleph\_1$…

In the theory of hyperplane arrangements, the most important and difficult problem is the combinatorial dependency of several properties. In this atricle, we prove that Terao's celebrated addition-deletion theorem for free arrangements is…

We define a semidirect product groupoid of a system of partially defined local homeomorphisms $T=(T_{1},..., T_{r})$. We prove that this construction gives rise to amenable groupoids. The associated algebra is a Cuntz-like algebra. We use…

We consider group orders and right-orders which are discrete, meaning there is a least element which is greater than the identity. We note that free groups cannot be given discrete orders, although they do have right-orders which are…