Related papers: Fuzzy Deterministic Top-down Tree Automata
We consider the memorization capabilities of multilayered \emph{sign} perceptrons neural networks (SPNNs). A recent rigorous upper-bounding capacity characterization, obtained in \cite{Stojnictcmspnncaprdt23} utilizing the Random Duality…
While language models (LMs) can sometimes generate factually correct text and estimate truth values of individual claims, these generally do not reflect a globally coherent, manipulable model of the world. As a consequence, current LMs also…
We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even if we allow epsilon-contractions and reachability predicates (with regular constraints) for pairs of configurations, the structures remain…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
We present a technique for the automated verification of abstract models of multithreaded programs providing fresh name generation, name mobility, and unbounded control. As high level specification language we adopt here an extension of…
Decision trees have been widely used in machine learning. However, due to some reasons, data collecting in real world contains a fuzzy and uncertain form. The decision tree should be able to handle such fuzzy data. This paper presents a…
We show that graphs generated by collapsible pushdown systems of level 2 are tree-automatic. Even when we allow $\epsilon$-contractions and add a reachability predicate (with regular constraints) for pairs of configurations, the structures…
The conversion of a given regular tree expression into a tree automaton has been widely studied. However, classical interpretations are based upon a Top-Down interpretation of tree automata. In this paper, we propose new constructions based…
We study whether a Large Language Model can learn the deterministic sequence of trees generated by the iterated prime factorization of the natural numbers. Each integer is mapped into a rooted planar tree and the resulting sequence $…
The determinisation problem for min-plus (tropical) weighted automata was recently shown to be decidable. However, the proof is purely existential, relying on several non-constructive arguments. Our contribution in this work is twofold:…
Temporal logics are widely used by the Formal Methods and AI communities. Linear Temporal Logic is a popular temporal logic and is valued for its ease of use as well as its balance between expressiveness and complexity. LTL is equivalent in…
Deep neural networks have been proven powerful at processing perceptual data, such as images and audio. However for tabular data, tree-based models are more popular. A nice property of tree-based models is their natural interpretability. In…
Tree-controlled grammars are context-free grammars where the derivation process is controlled in such a way that every word on a level of the derivation tree must belong to a certain control language. We investigate the generative capacity…
Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…
A locally testable language L is a language with the property that for some non negative integer k, called the order or the level of local testable, whether or not a word u in the language L depends on (1) the prefix and the suffix of the…
We study the expressiveness and succinctness of history-deterministic pushdown automata (HD-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of…
For some fixed alphabet A, a language L of A* is in the class L(1/2) of the Straubing-Therien hierarchy if and only if it can be expressed as a finite union of languages A*aA*bA*...A*cA*, where a,b,...,c are letters. The class L(1) is…
A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves,…
A word automaton recognizing a language $L$ is good for games (GFG) if its composition with any game with winning condition $L$ preserves the game's winner. While all deterministic automata are GFG, some nondeterministic automata are not.…
Originally proposed for handling time series data, Auto-regressive Decision Trees (ARDTs) have not yet been explored for language modeling. This paper delves into both the theoretical and practical applications of ARDTs in this new context.…