Related papers: Weighted Automata over Vector Spaces
We present several new results and connections between various extensions of finite automata through the study of vector automata and homing vector automata. We show that homing vector automata outperform extended finite automata when both…
We examine inkdots placed on the input string as a way of providing advice to finite automata, and establish the relations between this model and the previously studied models of advised finite automata. The existence of an infinite…
Finding human-understandable circuits in language models is a central goal of the field of mechanistic interpretability. We train models to have more understandable circuits by constraining most of their weights to be zeros, so that each…
Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related…
Automated vehicles (AVs) are tested in diverse scenarios, typically specified by parameters such as velocities, distances, or curve radii. To describe scenarios uniformly independent of such parameters, this paper proposes a vectorized…
Based on multiple simulation trajectories, which started from dispersively selected initial conformations, the weighted ensemble dynamics method is designed to robustly and systematically explore the hierarchical structure of complex…
In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces…
A weight normalization procedure, commonly called pushing, is introduced for weighted tree automata (wta) over commutative semifields. The normalization preserves the recognized weighted tree language even for nondeterministic wta, but it…
We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vectorial (as well as Lineal) has been originally designed for quantum computing, as an extension to System F where linear combinations of lambda terms are also terms and…
For the optimum design of a driver-automation shared control system, an understanding of driver behavior based on measurements and modeling is crucial early in the development process. This paper presents a driver model through a weighting…
A recently introduced approach for the dynamical analysis and quantization of field theoretical models with second class constraints is ilustrated applied to linearized gravity in 3-D. The canonical structure of two different models of…
We show that the determinization problem for min-plus (tropical) weighted automata is decidable, thus resolving this long-standing open problem. In doing so, we develop a new toolbox for analyzing and reasoning about the run-structure of…
We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every…
Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…
We present a detailed description of our submission for the M4 forecasting competition, in which it ranked 3rd overall. Our solution utilizes several commonly used statistical models, which are weighted according to their performance on…
Congruences for stochastic automata are defined, the correspondin factor automata are constructed and investigated for automata ove analytic spaces. We study the behavior under finite and infinite streams. Congruences consist of multiple…
We determine all functional closure properties of finite $\mathbb{N}$-weighted automata, even all multivariate ones, and in particular all multivariate polynomials. We also determine all univariate closure properties in the promise setting,…
Compact representations of automata are important for efficiency. In this paper, we study methods to compute reduced automata, in which no two states accept the same language. We do this for finitary automata (FA), an abstract definition…
We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a…
In this paper we explore several approaches for sampling weight vectors in the context of weighted sum scalarisation approaches for solving multi-criteria decision making (MCDM) problems. This established method converts a multi-objective…