Related papers: Differential Tree Automata
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
In this paper, multivalued data or multiple values variables are defined. They are typical when there is some intrinsic uncertainty in data production, as the result of imprecise measuring instruments, such as in image recognition, in human…
We propose a new approach to heap analysis through an abstract domain of automata, called automatic shapes. The abstract domain uses a particular kind of automata, called quantified data automata on skinny trees (QSDAs), that allows to…
Algorithms for (nondeterministic) finite-state tree automata (FTAs) are often tested on random FTAs, in which all internal transitions are equiprobable. The run-time results obtained in this manner are usually overly optimistic as most such…
The class of tree-adjoining languages can be characterized by various two-level formalisms, consisting of a context-free grammar (CFG) or pushdown automaton (PDA) controlling another CFG or PDA. These four formalisms are equivalent to…
Reinforcement learning (RL) based post-training for large language models (LLMs) is computationally expensive, as it generates many rollout sequences that could frequently share long token prefixes. Existing RL frameworks usually process…
Partition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run…
The article defines and studies the genus of finite state deterministic automata (FSA) and regular languages. Indeed, a FSA can be seen as a graph for which the notion of genus arises. At the same time, a FSA has a semantics via its…
We present an algorithm to build an automaton from a rational expression. This approach introduces support for extended weighted expressions. Inspired by derived-term based algorithms, its core relies on a different construct, rational…
Discrete Differential Equations (DDEs) are functional equations that relate polynomially a power series $F(t,u)$ in $t$ with polynomial coefficients in a "catalytic" variable $u$ and the specializations, say at $u=1$, of $F(t,u)$ and of…
We generalize some of the central results in automata theory to the abstraction level of coalgebras and thus lay out the foundations of a universal theory of automata operating on infinite objects. Let F be any set functor that preserves…
We propose dynamical systems trees (DSTs) as a flexible class of models for describing multiple processes that interact via a hierarchy of aggregating parent chains. DSTs extend Kalman filters, hidden Markov models and nonlinear dynamical…
While one-dimensional cellular automata have been well studied, there are relatively few results about multidimensional cellular automata; the investigation of cellular automata defined on Cayley trees constitutes an intermediate class.…
Arc-standard derivations over projective dependency trees can be interpreted as the incremental construction of lexicalized ordered trees with contiguous yields. Each \textsc{shift}, \textsc{leftarc}, and \textsc{rightarc} transition…
The automatic generation of decision trees based on off-line reasoning on models of a domain is a reasonable compromise between the advantages of using a model-based approach in technical domains and the constraints imposed by embedded…
We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…
Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Formal languages over infinite alphabets serve as abstractions of structures and processes carrying data. Automata models over infinite alphabets, such as classical register automata or, equivalently, nominal orbit-finite automata, tend to…
Decision Trees (DTs) and Random Forests (RFs) are powerful discriminative learners and tools of central importance to the everyday machine learning practitioner and data scientist. Due to their discriminative nature, however, they lack…