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Large language models (LLMs) have achieved remarkable results on tasks framed as reasoning problems, yet their true ability to perform procedural reasoning, executing multi-step, rule-based computations remains unclear. Unlike algorithmic…
Finite-state transducers (FSTs) are frequently used in speech recognition. Transducer composition is an essential operation for combining different sources of information at different granularities. However, composition is also one of the…
Text normalization (TN) systems in production are largely rule-based using weighted finite-state transducers (WFST). However, WFST-based systems struggle with ambiguous input when the normalized form is context-dependent. On the other hand,…
Large Language Models (LLMs) have become increasingly important in natural language processing, enabling advanced data analytics through natural language queries. However, these models often generate "hallucinations"-inaccurate or…
We present techniques to parallelize membership tests for Deterministic Finite Automata (DFAs). Our method searches arbitrary regular expressions by matching multiple bytes in parallel using speculation. We partition the input string into…
The problem of k-minimisation for a DFA M is the computation of a smallest DFA N (where the size |M| of a DFA M is the size of the domain of the transition function) such that their recognized languages differ only on words of length less…
In order to learn complex grammars, recurrent neural networks (RNNs) require sufficient computational resources to ensure correct grammar recognition. A widely-used approach to expand model capacity would be to couple an RNN to an external…
To tackle the exponentiality associated with NP-hard problems, two paradigms have been proposed. First, Branch & Bound, like Dynamic Programming, achieve efficient exact inference but requires extensive information and analysis about the…
State statistics of linear systems satisfy certain structural constraints that arise from the underlying dynamics and the directionality of input disturbances. In the present paper we study the problem of completing partially known state…
Complementation of finite automata is a basic operation used in numerous applications. The standard way to complement a nondeterministic finite automaton (NFA) is to transform it into an equivalent deterministic finite automaton (DFA) and…
We introduce a new complexity measure for finite strings using probabilistic finite-state automata (PFAs), in the same spirit as existing notions employing DFAs and NFAs, and explore its properties. The PFA complexity $A_P(x)$ is the least…
State-space models (SSMs) face a fundamental trade-off between efficiency and expressivity that is mainly dictated by the structure of the model's transition matrix. Unstructured transition matrices enable maximal expressivity, as measured…
We propose the Neural Functional Alignment Space (NFAS), a brain-referenced representational framework for characterizing artificial neural networks on equal functional grounds. NFAS departs from conventional alignment approaches that rely…
Formal languages over infinite alphabets serve as abstractions of structures and processes carrying data. Automata models over infinite alphabets, such as classical register automata or, equivalently, nominal orbit-finite automata, tend to…
It was conjectured by \v{C}ern\'y in 1964, that a synchronizing DFA on $n$ states always has a synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all…
In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language…
Distributed Transactional Memory (DTM) is an emerging approach to distributed synchronization based on the application of the transaction abstraction to distributed computation. DTM comes in several system models, but the control flow model…
We introduce Symbolic Alternating Finite Automata (s-AFA) as an expressive, succinct, and decidable model for describing sets of finite sequences over arbitrary alphabets. Boolean operations over s-AFAs have linear complexity, which is in…
We propose a query learning algorithm for residual symbolic finite automata (RSFAs). Symbolic finite automata (SFAs) are finite automata whose transitions are labeled by predicates over a Boolean algebra, in which a big collection of…
Continual Federated Learning (CFL) allows distributed devices to collaboratively learn novel concepts from continuously shifting training data while avoiding knowledge forgetting of previously seen tasks. To tackle this challenge, most…