Related papers: Why the equivalence problem for unambiguous gramma…
A complete deterministic finite (semi)automaton (DFA) with a set of states $Q$ is \emph{completely reachable} if every nonempty subset of $Q$ is the image of the action of some word applied to $Q$. The concept of completely reachable…
Every formal grammar defines a language and can in principle be used in three ways: to generate strings (production), to recognize them (parsing), or -- given only examples -- to infer the grammar itself (grammar induction). Generation and…
Given two weighted automata, we consider the problem of whether one is big-O of the other, i.e., if the weight of every finite word in the first is not greater than some constant multiple of the weight in the second. We show that the…
A notion of alternating timed automata is proposed. It is shown that such automata with only one clock have decidable emptiness problem over finite words. This gives a new class of timed languages which is closed under boolean operations…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
Solving an open problem stated by Shvachko, it is shown that a language which is not real-time recognizable by some variants of pointer machines can be accepted by a Kolmogorov-Uspensky machine in real-time.
This paper presents a new model for word sense disambiguation formulated in terms of evolutionary game theory, where each word to be disambiguated is represented as a node on a graph whose edges represent word relations and senses are…
Entity disambiguation, or mapping a phrase to its canonical representation in a knowledge base, is a fundamental step in many natural language processing applications. Existing techniques based on global ranking models fail to capture the…
**Context** Context-free grammars are widely used for language prototyping and implementation. They allow formalizing the syntax of domain-specific or general-purpose programming languages concisely and declaratively. However, the natural…
GF(2)-grammars are a recently introduced grammar family with some unusual algebraic properties. They are closely connected to unambiguous grammars. By using the method of formal power series, we establish strong conditions that are…
In 1991 H\'ebrard introduced a factorization of words that turned out to be a powerful tool for the investigation of a word's scattered factors (also known as (scattered) subwords or subsequences). Based on this, first Karandikar and…
As large language models (LLMs) are increasingly deployed in real-world applications, ensuring their fair responses across demographics has become crucial. Despite many efforts, an ongoing challenge is hidden bias: LLMs appear fair under…
The idea of Universal Grammar (UG) as the hypothetical linguistic structure shared by all human languages harkens back at least to the 13th century. The best known modern elaborations of the idea are due to Chomsky. Following a devastating…
In this paper, we look at an unambiguous version of Simon's forest factorization theorem, a very deep result which has wide connections in algebra, logic and automata. Given a morphism $\varphi$ from $\Sigma^+$ to a finite semigroup $S$, we…
Recently researchers working in the LFG framework have proposed algorithms for taking advantage of the implicit context-free components of a unification grammar [Maxwell 96]. This paper clarifies the mathematical foundations of these…
Part of the theory of logic programming and nonmonotonic reasoning concerns the study of fixed-point semantics for these paradigms. Several different semantics have been proposed during the last two decades, and some have been more…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
Analogous to regular string and tree languages, regular languages of directed acyclic graphs (DAGs) are defined in the literature. Although called regular, those DAG-languages are more powerful and, consequently, standard problems have a…
We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in…