Related papers: The language (and series) of Hammersley-type proce…
This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…
In order to obtain a stochastic model that accounts for the stochastic aspects of the dynamics of a business process, usually the following steps are taken. Given an event log, a process tree is obtained through a process discovery…
This paper describes an abstract machine for linguistic formalisms that are based on typed feature structures, such as HPSG. The core design of the abstract machine is given in detail, including the compilation process from a high-level…
We model the recursive production property of context-free grammars for natural and synthetic languages. To this end, we present a dynamic programming algorithm that marginalises over latent binary tree structures with $N$ leaves, allowing…
Quantitative languages are an extension of boolean languages that assign to each word a real number. Mean-payoff automata are finite automata with numerical weights on transitions that assign to each infinite path the long-run average of…
The article continues the study of the genus of regular languages that the authors introduced in a 2012 paper. Generalizing a previous result, we produce a new family of regular languages on a two-letter alphabet having arbitrary high…
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…
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…
Today's probabilistic language generators fall short when it comes to producing coherent and fluent text despite the fact that the underlying models perform well under standard metrics, e.g., perplexity. This discrepancy has puzzled the…
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
This paper describes a natural language parsing algorithm for unrestricted text which uses a probability-based scoring function to select the "best" parse of a sentence. The parser, Pearl, is a time-asynchronous bottom-up chart parser with…
This paper introduces derivation trees for general grammars. Within these trees, it defines context-dependent pairs of nodes, corresponding to rewriting two neighboring symbols using a non context-free rule. It proves that the language…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…
Large language models (LLM) have revolutionized the processing of natural language. Although first benchmarks of the process modeling abilities of LLM are promising, it is currently under debate to what extent an LLM can generate good…
We report some further developments regarding the language theory of higher-dimensional automata (HDAs). Regular languages of HDAs are sets of finite interval partially ordered multisets (pomsets) with interfaces. We show a pumping lemma…
The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…
We present a new approach to formal language theory using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. We first prove a strong version of a conjecture by Castiglione and…
Reasoning is a fundamentally algorithmic task. Yet current work on LLM-based reasoning relies on free-form generation whose theoretical guarantees (soundness, completeness, complexity, optimality) remain poorly understood. We argue that we…