Related papers: Differential Tree Automata
This work considers weak deterministic B\"uchi automata reading encodings of non-negative reals in a fixed base. A Real Number Automaton is an automaton which recognizes all encoding of elements of a set of reals. It is explained how to…
Functional data analysis (FDA) and ensemble learning can be powerful tools for analyzing complex environmental time series. Recent literature has highlighted the key role of diversity in enhancing accuracy and reducing variance in ensemble…
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…
The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are…
We introduce heap automata, a formalism for automatic reasoning about robustness properties of the symbolic heap fragment of separation logic with user-defined inductive predicates. Robustness properties, such as satisfiability,…
We introduce (weighted) rational expressions to denote series over Cartesian products of monoids. To this end, we propose the operator $|$ to build multitape expressions such as $(a^+|x + b^+|y)^*$. We define expansions, which generalize…
We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…
Families of DFAs (FDFAs) provide an alternative formalism for recognizing $\omega$-regular languages. The motivation for introducing them was a desired correlation between the automaton states and right congruence relations, in a manner…
Anomaly detection in time series data is important for applications in finance, healthcare, sensor networks, and industrial monitoring. Traditional methods usually struggle with limited labeled data, high false-positive rates, and…
Standard Transformers excel at semantic modeling but struggle with rigid sequential logic and state tracking. Theoretical work establishes that self-attention is limited to $\AC^0$ (under hard attention) or $\TC^0$ (under soft attention),…
Deep Reinforcement Learning (DRL) has recently achieved significant advances in various domains. However, explaining the policy of RL agents still remains an open problem due to several factors, one being the complexity of explaining neural…
We give a simple, direct and reusable logical relations technique for languages with term and type recursion and partially defined differentiable functions. We demonstrate it by working out the case of Automatic Differentiation (AD)…
Weighted automata is a basic tool for specification in quantitative verification, which allows to express quantitative features of analysed systems such as resource consumption. Quantitative specification can be assisted by automata…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
In this work, we propose D3-Tree, a dynamic distributed deterministic structure for data management in decentralized networks. We present in brief the theoretical algorithmic analysis, in which our proposed structure is based on, and we…
We present probabilistic arithmetic automata (PAAs), a general model to describe chains of operations whose operands depend on chance, along with two different algorithms to exactly calculate the distribution of the results obtained by such…
Solving of regular equations via Arden's Lemma is folklore knowledge. We first give a concise algorithmic specification of all elementary solving steps. We then discuss a computational interpretation of solving in terms of coercions that…
We propose a conjecture for the exact expression of the dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer…
Out-Of-Distribution (OOD) generalization is an essential topic in machine learning. However, recent research is only focusing on the corresponding methods for neural networks. This paper introduces a novel and effective solution for OOD…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…