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This paper presents and analyzes an incremental algorithm for the construction of Acyclic Non-deterministic Finite-state Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons.…
Alphabet size of auxiliary random variables in our canonical description is derived. Our analysis improves upon estimates known in special cases, and generalizes to an arbitrary multiterminal setup. The salient steps include decomposition…
The article continues our study of the genus of a regular language $L$, defined as the minimal genus among all genera of all finite deterministic automata recognizing $L$. Here we define and study two closely related tools on a directed…
In the last years there has been a growing interest in the study of learning problems associated with algebraic structures. The framework we use models the scenario in which a learner is given larger and larger fragments of a structure from…
Many of the numerous automaton models proposed in the literature can be regarded as a finite automaton equipped with an additional storage mechanism. In this thesis, we focus on two such models, namely the finite automata over groups and…
Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy.…
It is well known that the "store language" of every pushdown automaton -- the set of store configurations (state and stack contents) that can appear as an intermediate step in accepting computations -- is a regular language. Here many…
We propose DFAMiner, a passive learning tool for learning minimal separating deterministic finite automata (DFA) from a set of labelled samples. Separating automata are an interesting class of automata that occurs generally in regular model…
The minimum amount of resources to recognize a nonregular language is a fundamental research topic in theoretical computer science which has been examined for different kinds of resources and many different models. In this note, we focus on…
We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak $\log\log n$ space, (ii) $\log\log n$ is a…
Argumentation is a very active research field of Artificial Intelligence concerned with the representation and evaluation of arguments used in dialogues between humans and/or artificial agents. Acceptability semantics of formal…
We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
The powerset construction is a standard method for converting a nondeterministic automaton into a deterministic one recognizing the same language. In this paper, we lift the powerset construction from automata to the more general framework…
Bruyere and Carton lifted the notion of finite automata reading infinite words to finite automata reading words with shape an arbitrary linear order L. Automata on finite words can be used to represent infinite structures, the so-called…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
The emergent ability of Large Language Models to use a small number of examples to learn to perform in novel domains and tasks, also called in-context learning (ICL). In this work, we show that a much smaller model can be trained to perform…
Conversation designers continue to face significant obstacles when creating production quality task-oriented dialogue systems. The complexity and cost involved in schema development and data collection is often a major barrier for such…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
Matrix product operators allow efficient descriptions (or realizations) of states on a 1D lattice. We consider the task of learning a realization of minimal dimension from copies of an unknown state, such that the resulting operator is…