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A two-dimensional finite automaton has a read-only input head that moves in four directions on a finite array of cells labelled by symbols of the input alphabet. A three-way two-dimensional automaton is prohibited from making upward moves,…

Let $L_{>\lambda}(\mathcal{A})$ and $L_{\geq\lambda}(\mathcal{A})$ be the languages recognized by {\em measure many 1-way quantum finite automata (MM-QFA)} (or,{\em enhanced 1-way quantum finite automata(EQFA)}) $\mathcal{A}$ with strict…

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…

Watson-Crick (WK) finite automata work on a Watson-Crick tape representing a DNA molecule. They have two reading heads. In 5'->3' WK automata, the heads move and read the input in opposite physical directions. In this paper, we consider…

Every language recognized by a non-deterministic finite automaton can be recognized by a deterministic automaton, at the cost of a potential increase of the number of states, which in the worst case can go from $n$ states to $2^n$ states.…

Low-frequency word prediction remains a challenge in modern neural machine translation (NMT) systems. Recent adaptive training methods promote the output of infrequent words by emphasizing their weights in the overall training objectives.…

Nature language inference (NLI) task is a predictive task of determining the inference relationship of a pair of natural language sentences. With the increasing popularity of NLI, many state-of-the-art predictive models have been proposed…

Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language $L$ it is shown that there exists a…

The purpose of this paper is to use reinforcement learning to model learning agents which can recognize formal languages. Agents are modeled as simple multi-head automaton, a new model of finite automaton that uses multiple heads, and six…

In this note, we introduce a new algorithm to deal with finite dimensional clustering with errors in variables. The design of this algorithm is based on recent theoretical advances (see Loustau (2013a,b)) in statistical learning with errors…

Large Language Models (LLMs) exhibit high inference latency due to their autoregressive decoding nature. While the draft head in speculative decoding mitigates this issue, its full potential remains unexplored. In this paper, we introduce…

#NFA refers to the problem of counting the words of length $n$ accepted by a non-deterministic finite automaton. #NFA is #P-hard, and although fully-polynomial-time randomized approximation schemes (FPRAS) exist, they are all impractical.…

{\it Two-way finite automata with quantum and classical states} (2QCFA) were introduced by Ambainis and Watrous, and {\it two-way two-tape deterministic finite automata} (2TFA) were introduced by Rabin and Scott. In this paper we study 2TFA…

A classical result (often credited to Y. Medvedev) states that every language recognized by a finite automaton is the homomorphic image of a local language, over a much larger so-called local alphabet, namely the alphabet of the edges of…

We propose a computing model, the Two-Way Optical Interference Automata (2OIA), that makes use of the phenomenon of optical interference. We introduce this model to investigate the increase in power, in terms of language recognition, of a…

Machine-translated text plays an important role in modern life by smoothing communication from various communities using different languages. However, unnatural translation may lead to misunderstanding, a detector is thus needed to avoid…

Traditional recurrent neural networks (RNNs) have a fixed, finite number of memory cells. In theory (assuming bounded range and precision), this limits their formal language recognition power to regular languages, and in practice, RNNs have…

The main purpose of this paper is to show that we can exploit the difference ($l_1$-norm and $l_2$-norm) in the probability calculation between quantum and probabilistic computations to claim the difference in their space efficiencies. It…

We consider the random $k$-SAT problem with $n$ variables, $m=m(n)$ clauses, and clause density $\alpha=\lim_{n\to\infty}m/n$ for $k=2,3$. It is known that if $\alpha$ is small enough, then the random $k$-SAT problem admits a solution with…

While Vision Language Models (VLMs) show advancing reasoning capabilities, their application in meteorology is constrained by a domain gap and a reasoning faithfulness gap. Specifically, mainstream Reinforcement Fine-Tuning (RFT) can induce…