Related papers: The language (and series) of Hammersley-type proce…
We investigate a signed version of the Hammersley process, a discrete process on words related to a property of integer sequences called heapability (Byers et al., ANALCO 2011). The specific version that we investigate corresponds to a…
Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed…
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 introduce a family of synthetic languages with hierarchical structure -- generated by a broadcast process on trees -- for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart…
While systems designed for solving planning tasks vastly outperform Large Language Models (LLMs) in this domain, they usually discard the rich semantic information embedded within task descriptions. In contrast, LLMs possess parametrised…
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends…
Large language models (LLMs) achieve astonishing results on a wide range of tasks. However, their formal reasoning ability still lags behind. A promising approach is Neurosymbolic LLM reasoning. It works by using LLMs as translators from…
We present a novel parsing algorithm for all context-free languages, based on computing the relation between configurations and reaching transitions in a recursive transition network. Parsing complexity w.r.t. input length matches the state…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
A classical theorem states that the set of languages given by a pushdown automaton coincides with the set of languages given by a context-free grammar. In previous work, we proved the pendant of this theorem in a setting with interaction:…
In this paper we have defined the language theoretical properties of Parallel languages and series parallel languages. Parallel languages and Series parallel languages play vital roles in parallel processing and many applications in…
This paper solves an open problem concerning the generative power of nonerasing context-free rewriting systems using a simple mechanism for checking for context dependencies, in the literature known as semi-conditional grammars of degree…
The HOM problem, which asks whether the image of a regular tree language under a given tree homomorphism is again regular, is known to be decidable [Godoy & Gim\'enez: The HOM problem is decidable. JACM 60(4), 2013]. However, the problem…
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…
In this paper, we study a series of algorithmic problems related to the subsequences occurring in the strings of a given language, under the assumption that this language is succinctly represented by a grammar generating it, or an automaton…
Large language models (LLMs) achieve astonishing results on a wide range of tasks. However, their formal reasoning ability still lags behind. A promising approach is Neurosymbolic LLM reasoning. It works by using LLMs as translators from…
Large Language Models (LLMs) have transformed text generation through inherently probabilistic context-aware mechanisms, mimicking human natural language. In this paper, we systematically investigate the performance of various LLMs when…
Language models (LMs) are often expected to generate strings in some formal language; for example, structured data, API calls, or code snippets. Although LMs can be tuned to improve their adherence to formal syntax, this does not guarantee…