Related papers: Asymptotic Approximation by Regular Languages
Controlling the output of Large Language Models (LLMs) through context-sensitive constraints has emerged as a promising approach to overcome the limitations of Context-Free Grammars (CFGs) in guaranteeing generation validity. However, such…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
We give a universal kernel that renders all the regular languages linearly separable. We are not able to compute this kernel efficiently and conjecture that it is intractable, but we do have an efficient $\eps$-approximation.
We survey recent results on the topological complexity of context-free omega-languages which form the second level of the Chomsky hierarchy of languages of infinite words. In particular, we consider the Borel hierarchy and the Wadge…
Most recent research in trainable part of speech taggers has explored stochastic tagging. While these taggers obtain high accuracy, linguistic information is captured indirectly, typically in tens of thousands of lexical and contextual…
We consider the set of infinite real traces, over a dependence alphabet (Gamma, D) with no isolated letter, equipped with the topology induced by the prefix metric. We then prove that all rational languages of infinite real traces are…
In this paper, homological methods together with the theory of formal languages of theoretical computer science are proved to be effective tools to determine the growth and the Hilbert series of an associative algebra. Namely, we construct…
We investigate the proof theory of regular expressions with fixed points, construed as a notation for (omega-)context-free grammars. Starting with a hypersequential system for regular expressions due to Das and Pous, we define its extension…
Compositional generalization is the ability of a model to generalize to complex, previously unseen types of combinations of entities from just having seen the primitives. This type of generalization is particularly relevant to the semantic…
A regular language has the zero-one law if its asymptotic density converges to either zero or one. We prove that the class of all zero-one languages is closed under Boolean operations and quotients. Moreover, we prove that a regular…
We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…
Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the…
Most scripting languages nowadays use regex pattern-matching libraries. These regex libraries borrow the syntax of regular expressions, but have an informal semantics that is different from the semantics of regular expressions, removing the…
Pumping lemmas are created to prove that given languages are not belong to certain language classes. There are several known pumping lemmas for the whole class and some special classes of the context-free languages. In this paper we prove…
Retrieval-Augmented Generation (RAG) enhances factual grounding in large language models (LLMs) by incorporating retrieved evidence, but LLM accuracy declines when long or noisy contexts exceed the model's effective attention span. Existing…
Recently we proposed relative observability for supervisory control of discrete-event systems under partial observation. Relative observability is closed under set unions and hence there exists the supremal relatively observable sublanguage…
Despite significant research effort in the development of automatic dialogue evaluation metrics, little thought is given to evaluating dialogues other than in English. At the same time, ensuring metrics are invariant to semantically similar…
Language Confusion is a phenomenon where Large Language Models (LLMs) generate text that is neither in the desired language, nor in a contextually appropriate language. This phenomenon presents a critical challenge in text generation by…
Are large language models (LLMs) sensitive to the distinction between humanly possible and impossible languages? This question was recently used in a broader debate on whether LLMs and humans share the same innate learning biases. Previous…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…