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We present an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata (DFTAs). Unlike string automata, tree automata operate over hierarchical structures, posing unique challenges for…
Much of human knowledge sits in large databases of unstructured text. Leveraging this knowledge requires algorithms that extract and record metadata on unstructured text documents. Assigning topics to documents will enable intelligent…
Tagging is nowadays the most prevalent and practical way to make images searchable. However, in reality many manually-assigned tags are irrelevant to image content and hence are not reliable for applications. A lot of recent efforts have…
This article deals with the computation of guaranteed lower bounds of the error in the framework of finite element (FE) and domain decomposition (DD) methods. In addition to a fully parallel computation, the proposed lower bounds separate…
We present DMax, a new paradigm for efficient diffusion language models (dLLMs). It mitigates error accumulation in parallel decoding, enabling aggressive decoding parallelism while preserving generation quality. Unlike conventional masked…
This paper considers the existence of short synchronizing words in deterministic finite automata (DFAs). We define two general strategies for generating synchronizing words, and we show that each of these strategies can be applied if and…
Modern societies have developed insatiable demands for more computation capabilities. Exploiting implicit parallelism to provide automatic performance improvement remains a central goal in engineering future general-purpose computing…
Augmenting algorithms with learned predictions is a promising approach for going beyond worst-case bounds. Dinitz, Im, Lavastida, Moseley, and Vassilvitskii~(2021) have demonstrated that a warm start with learned dual solutions can improve…
While tensor-based methods excel at Direction-of-Arrival (DOA) estimation, their performance degrades severely with faulty or sparse arrays that violate the required manifold structure. To address this challenge, we propose Tensor…
Large language models (LLMs) often benefit from verbalized reasoning at inference time, but it remains unclear which aspects of task difficulty these extra reasoning tokens address. To investigate this question, we formalize a framework…
The rapid growth of symbolic data in areas like internet, biological, and financial data has increased the demand for efficient pattern matching and regular expression processing. Non-deterministic Finite Automata (NFA) are used for these…
Lexers and parsers are typically defined separately and connected by a token stream. This separate definition is important for modularity and reduces the potential for parsing ambiguity. However, materializing tokens as data structures and…
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…
Traffic of Industrial Control System (ICS) between the Human Machine Interface (HMI) and the Programmable Logic Controller (PLC) is known to be highly periodic. However, it is sometimes multiplexed, due to asynchronous scheduling. Modeling…
This paper introduces the retrieval-augmented large language model with Definite Finite Automaton (DFA-RAG), a novel framework designed to enhance the capabilities of conversational agents using large language models (LLMs). Traditional…
The communication matrix for two-way deterministic finite automata (2DFA) with $n$ states is defined for an automaton over a full alphabet of all $(2n+1)^n$ possible symbols: its rows and columns are indexed by strings, and the entry $(u,…
Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics, psychometrics and econometrics. In this paper, we revisit the classical rank-constrained FA problem, which…
Automata play important roles in wide area of computing and the growth of multicores calls for their efficient parallel implementation. Though it is known in theory that we can perform the computation of a finite automaton in parallel by…
Decentralized federated learning (DFL), a serverless variant of federated learning, poses unique challenges for parameter-efficient fine-tuning due to the factorized structure of low-rank adaptation (LoRA). Unlike linear parameters,…
The class of Unambiguous Star-Free Regular Languages (UL) was defined by Schutzenberger as the class of languages defined by Unambiguous Polynomials. UL has been variously characterized (over finite words) by logics such as TL[X_a,Y_a],…