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A standard way to solve linear algebraic systems $Au=f,\,\,(*)$ with ill-conditioned matrices $A$ is to use variational regularization. This leads to solving the equation $(A^*A+aI)u=A^*f_\d$, where $a$ is a regularization parameter, and…
Asynchronous automata are a model of distributed finite state processes synchronising on shared actions. A celebrated result by Zielonka shows how a deterministic asynchronous automaton (AA) can be synthesised, starting from two inputs: a…
Symbolic Finite Automata and Register Automata are two orthogonal extensions of finite automata motivated by real-world problems where data may have unbounded domains. These automata address a demand for a model over large or infinite…
Several reachability problems in finite automata, such as completeness of NFAs and synchronisation of total DFAs, correspond to fundamental properties of sets of nonnegative matrices. In particular, the two mentioned properties correspond…
Foundation models have shown great success in natural language processing, computer vision, and multimodal tasks. FMs have a large number of model parameters, thus requiring a substantial amount of data to help optimize the model during the…
Finite-State Machines (FSMs) are critical for modeling the operational logic of network protocols, enabling verification, analysis, and vulnerability discovery. However, existing FSM extraction techniques face limitations such as…
Decoding speech from brain signals is a challenging research problem. Although existing technologies have made progress in reconstructing the mel spectrograms of auditory stimuli at the word or letter level, there remain core challenges in…
Forced alignment (FA) plays a key role in speech research through the automatic time alignment of speech signals with corresponding text transcriptions. Despite the move towards end-to-end architectures for speech technology, FA is still…
We consider Parallel Random Access Machine (PRAM) which has some processors and memory cells faulty. The faults considered are static, i.e., once the machine starts to operate, the operational/faulty status of PRAM components does not…
Automatic speech recognition enables a wide range of current and emerging applications such as automatic transcription, multimedia content analysis, and natural human-computer interfaces. This paper provides a glimpse of the opportunities…
We propose an automaton model which is a combination of symbolic and register automata, i.e., we enrich symbolic automata with memory. We call such automata Register Match Automata (RMA). RMA extend the expressive power of symbolic…
Regular expressions in an Automata Theory and Formal Languages course are mostly treated as a theoretical topic. That is, to some degree their mathematical properties and their role to describe languages is discussed. This approach fails to…
We present efficient algorithms to reduce the size of nondeterministic B\"uchi word automata (NBA) and nondeterministic finite word automata (NFA), while retaining their languages. Additionally, we describe methods to solve PSPACE-complete…
Recently, while large language models (LLMs) have demonstrated impressive results, they still suffer from hallucination, i.e., the generation of false information. Model editing is the task of fixing factual mistakes in LLMs; yet, most…
We present an algorithm for regular expression parsing and submatch extraction based on tagged deterministic finite automata. The algorithm works with different disambiguation policies. We give detailed pseudocode for the algorithm,…
Precise test oracles for reactive systems such as critical control systems and communication protocols can be modelled with deterministic finite state machines (FSMs). Among other roles, they serve in evaluating the correctness of systems…
Recurrent Neural Networks (RNNs) have achieved tremendous success in processing sequential data, yet understanding and analyzing their behaviours remains a significant challenge. To this end, many efforts have been made to extract finite…
We introduce a quantum-like classical computational model, called affine computation, as a generalization of probabilistic computation. After giving the basics of affine computation, we define affine finite automata (AfA) and compare it…
Many natural language processing systems operate over tokenizations of text to address the open-vocabulary problem. In this paper, we give and analyze an algorithm for the efficient construction of deterministic finite automata (DFA)…
Linear State-Space Models (SSMs) offer an efficient alternative to softmax Attention with constant memory and linear compute, but their lossy, fading summary of the past hurts recall-oriented tasks. We propose Gated KalmaNet (GKA,…