Related papers: A Myhill-Nerode Theorem for Register Automata and …
A \emph{data automaton} is a finite automaton equipped with variables (counters or registers) ranging over infinite data domains. A trace of a data automaton is an alternating sequence of alphabet symbols and values taken by the counters…
We introduce session automata, an automata model to process data words, i.e., words over an infinite alphabet. Session automata support the notion of fresh data values, which are well suited for modeling protocols in which sessions using…
This work studies the question of learning probabilistic deterministic automata from language models. For this purpose, it focuses on analyzing the relations defined on algebraic structures over strings by equivalences and similarities on…
Abstract numeration systems encode natural numbers using radix ordered words of an infinite regular language and linear recurrence sequences play a key role in their valuation. Sequence automata, which are deterministic finite automata with…
Saturation is a fundamental game-semantic property satisfied by strategies that interpret higher-order concurrent programs. It states that the strategy must be closed under certain rearrangements of moves, and corresponds to the intuition…
This paper deals with the problem of recognizability of functions l: Sigma* --> M that map words to values in the support set M of a monoid (M,.,1). These functions are called M-languages. M-languages are studied from the aspect of their…
Representation is a core issue in artificial intelligence. Humans use discrete language to communicate and learn from each other, while machines use continuous features (like vector, matrix, or tensor in deep neural networks) to represent…
Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework…
Hereditarily finite (HF) set theory provides a standard universe of sets, but with no infinite sets. Its utility is demonstrated through a formalisation of the theory of regular languages and finite automata, including the Myhill-Nerode…
Spatial reasoning based on natural language expressions is essential for everyday human tasks. This reasoning ability is also crucial for machines to interact with their environment in a human-like manner. However, recent research shows…
We study learning under regime variation, where the learner, its memory state, and the evaluative conditions may evolve over time. This paper is a foundational and structural contribution: its goal is to define the core learning-theoretic…
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…
Extensions of {\omega}-automata to infinite alphabets typically rely on symbolic guards to keep the transition relation finite, and on registers or memory cells to preserve information from past symbols. Symbolic transitions alone are…
The multilingual neural machine translation (MNMT) aims for arbitrary translations across multiple languages. Although MNMT-specific models trained on parallel data offer low costs in training and deployment, their performance consistently…
Nominal set plays a central role in a group-theoretic extension of finite automata to those over an infinite set of data values. Moerman et al. proposed an active learning algorithm for nominal word automata with the equality symmetry. In…
Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions/languages over finite words. In symbolic automata (or automata modulo…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
A Wheeler automaton is a finite state automaton whose states admit a total Wheeler order, reflecting the co-lexicographic order of the strings labeling source-to-node paths. A Wheeler language is a regular language admitting an accepting…
How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the Random…
A new model of symbol grounding is presented, in which the structures of natural language, logical semantics, perception and action are represented categorically, and symbol grounding is modeled via the composition of morphisms between the…