Related papers: Ogden's Lemma for Regular Tree Languages
Automated interpretability aims to translate large language model (LLM) features into human understandable descriptions. However, natural language feature descriptions can be vague, inconsistent, and require manual relabeling. In response,…
Large language models (LLMs) provide powerful means to leverage prior knowledge for predictive modeling when data is limited. In this work, we demonstrate how LLMs can use their compressed world knowledge to generate intrinsically…
Suppose that some polynomial $f$ with rational coefficients takes only natural values at natural numbers, i.e., $L=\{f(n)\mid n\in \mathbb N\}\subset\mathbb N$. We show that the base-$q$ representation of $L$ is a context-free language if…
Large language models (LLMs) have displayed an impressive ability to harness natural language to perform complex tasks. In this work, we explore whether we can leverage this learned ability to find and explain patterns in data.…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
We consider forkable regular expressions, which enrich regular expressions with a fork operator, to establish a formal basis for static and dynamic analysis of the communication behavior of concurrent programs. We define a novel…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
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…
Large transformer-based language models (LMs) trained on huge text corpora have shown unparalleled generation capabilities. However, controlling attributes of the generated language (e.g. switching topic or sentiment) is difficult without…
We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by \emph{game…
Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas…
Lecture notes on tree language theory, in particular recognizable tree languages and finite state tree transformations.
In the following paper, we present a simple method for sampling trees with or without replacement from BCFLs. A BCFL is a context-free language (CFL) corresponding to an incomplete string with holes, which can be completed by valid…
We study the dynamic membership problem for regular tree languages under relabeling updates: we fix an alphabet $\Sigma$ and a regular tree language $L$ over $\Sigma$ (expressed, e.g., as a tree automaton), we are given a tree $T$ with…
Natural language reasoning plays an increasingly important role in improving language models' ability to solve complex language understanding tasks. An interesting use case for reasoning is the resolution of context-dependent ambiguity. But…
Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for…
We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.
Pumping lemma has been a very difficult topic for students to understand in a theoretical computer science course due to a lack of tool support. In this paper, we present an active learning tool called MInimum PUmping length (MIPU)…
We present a new framework for compositional distributional semantics in which the distributional contexts of lexemes are expressed in terms of anchored packed dependency trees. We show that these structures have the potential to capture…
This work studies the general principles of improving the learning of language models (LMs), which aims at reducing the necessary training steps for achieving superior performance. Specifically, we present a theory for the optimal learning…