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A natural language (or ordinary language) is a language that is spoken, written, or signed by humans for general-purpose communication, as distinguished from formal languages (such as computer-programming languages or the "languages" used…
A leaf path language is a Boolean combination of sets of the form $\mathsf{{}^mE}^k L$, with $k \ge 1$ and $L$ a regular word language, which consist of those forests where the node labels in at least $k$ leaf-to-root paths make up a word…
Language models can produce fluent, grammatical text. Nonetheless, some maintain that language models don't really learn language and also that, even if they did, that would not be informative for the study of human learning and processing.…
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
Why do some languages like Czech permit free word order, while others like English do not? We address this question by pretraining transformer language models on a spectrum of synthetic word-order variants of natural languages. We observe…
Floyd languages (FL), alias Operator Precedence Languages, have recently received renewed attention thanks to their closure properties and local parsability which allow one to apply automatic verification techniques (e.g. model checking)…
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by lambda terms of second order lambda…
An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
A prefix normal word is a binary word with the property that no substring has more 1s than the prefix of the same length. This class of words is important in the context of binary jumbled pattern matching. In this paper we present an…
This paper presents a new system of logic, LF, that is intended to be used as the foundation of the formalization of science. That is, deductive validity according to LF is to be used as the criterion for assessing what follows from the…
We introduce a new formalisation of languages, called keyboards. We consider a set of elementary operations (writing/erasing a letter, going to the right or to the left,...) and we define a keyboard as a set of finite sequences of such…
We develop a formal grammatical system called a link grammar, show how English grammar can be encoded in such a system, and give algorithms for efficiently parsing with a link grammar. Although the expressive power of link grammars is…
Prompted models have demonstrated impressive few-shot learning abilities. Repeated interactions at test-time with a single model, or the composition of multiple models together, further expands capabilities. These compositions are…
We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean…
It is well-known that: (i) every context-free language over a singleton terminal alphabet is regular, and (ii) the class of languages that satisfy the Pumping Lemma is a proper super-class of the context-free languages. We show that any…
Language Generation Models produce words based on the previous context. Although existing methods offer input attributions as explanations for a model's prediction, it is still unclear how prior words affect the model's decision throughout…
Language models (LMs) are sentence-completion engines trained on massive corpora. LMs have emerged as a significant breakthrough in natural-language processing, providing capabilities that go far beyond sentence completion including…
We consider the language consisting of all words such that it is possible to obtain the empty word by iteratively deleting powers. It turns out that in the case of deleting squares in binary words this language is regular, and in the case…
Translating formal language into natural language is a foundational challenge in NLP, driving various downstream applications in semantic parsing, theorem validation, and question answering. In this study, we introduce First-Order Logic to…
A generate and test algorithm is described which parses a surface form into one or more lexical entries using linearly ordered phonological rules. This algorithm avoids the exponential expansion of search space which a naive parsing…