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A central question in the theory of automata is which classes of automata can be minimized in polynomial time. We close the remaining gaps for deterministic and history-deterministic automata over infinite words by proving that…
Deterministic 2-head finite automata which are machines that process an input word from both ends are analyzed for their ability to perform reversible computations. This implies that the automata are backward deterministic, enabling unique…
Integrable systems have provided various insights into physical phenomena and mathematics. The way of constructing many-body integrable systems is limited to few ansatzes for the Lax pair, except for highly inventive findings of conserved…
Generalizations of numeration systems in which N is recognizable by a finite automaton are obtained by describing a lexicographically ordered infinite regular language L over a finite alphabet A. For these systems, we obtain a…
Systematic generalization refers to the capacity to understand and generate novel combinations from known components. Despite recent progress by large language models (LLMs) across various domains, these models often fail to extend their…
Generative models excel at mimicking real scenes, suggesting they might inherently encode important intrinsic scene properties. In this paper, we aim to explore the following key questions: (1) What intrinsic knowledge do generative models…
Machine learning is widely believed to be one of the most promising practical applications of quantum computing. Existing quantum machine learning schemes typically employ a quantum-classical hybrid approach that relies crucially on…
We present an algorithm for extraction of a probabilistic deterministic finite automaton (PDFA) from a given black-box language model, such as a recurrent neural network (RNN). The algorithm is a variant of the exact-learning algorithm L*,…
A DFA separates two disjoint languages $L_1$ and $L_2$ if it accepts every word in $L_1$ and rejects every word in $L_2$. Algorithms for active learning of small separating DFAs have many applications, e.g., for learning network invariants,…
We present the efficient implementations of probabilistic deterministic finite automaton learning methods available in FlexFringe. These implement well-known strategies for state-merging including several modifications to improve their…
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…
Humans understand a set of canonical geometric transformations (such as translation and rotation) that support generalization by being untethered to any specific object. We explore inductive biases that help a neural network model learn…
Predicate intuitionistic logic is a well established fragment of dependent types. According to the Curry-Howard isomorphism proof construction in the logic corresponds well to synthesis of a program the type of which is a given formula. We…
Native speakers can judge whether a sentence is an acceptable instance of their language. Acceptability provides a means of evaluating whether computational language models are processing language in a human-like manner. We test the ability…
Canonical Correlation Analysis (CCA) is a widely used statistical tool with both well established theory and favorable performance for a wide range of machine learning problems. However, computing CCA for huge datasets can be very slow…
We show that there are quantum devices that accept all regular languages and that are exponentially more concise than deterministic finite automata (DFA). For this purpose, we introduce a new computing model of {\it one-way quantum finite…
In this paper we revisit Safra's determinization constructions for automata on infinite words. We show how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions. Determinization is used in…
We consider the problem of explaining the temporal behavior of black-box systems using human-interpretable models. To this end, based on recent research trends, we rely on the fundamental yet interpretable models of deterministic finite…
Families of DFAs (FDFAs) have recently been introduced as a new representation of $\omega$-regular languages. They target ultimately periodic words, with acceptors revolving around accepting some representation $u\cdot v^\omega$. Three…
We study a model of one-way quantum automaton where only measurement operations are allowed (MOn-1qfa). We give an algebraic characterization of LMO, showing that the syntactic monoids of the languages in LMO are exactly the literal…