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On the Representational Capacity of Neural Language Models with Chain-of-Thought Reasoning 论具有思维链推理能力的神经语言模型的表征能力
Pub Date : 2024-06-20 DOI: arxiv-2406.14197
Franz Nowak, Anej Svete, Alexandra Butoi, Ryan Cotterell
The performance of modern language models (LMs) has been improved bychain-of-thought (CoT) reasoning, i.e., the process of generating intermediateresults that guide the model towards a final answer. A possible explanation forthis improvement is that CoT reasoning extends an LM's computational power, asRNNs and transformers with additional scratch space are known to be Turingcomplete. Comparing LMs to Turing machines, however, introduces a categoryerror - Turing machines decide language membership, whereas LMs definedistributions over strings. To bridge this gap, we formalize CoT reasoning in aprobabilistic setting. We present several results on the representationalcapacity of recurrent and transformer LMs with CoT reasoning, showing that theycan represent the same family of distributions over strings as probabilisticTuring machines.
现代语言模型(LM)的性能已通过思维链(CoT)推理(即生成中间结果以引导模型得出最终答案的过程)得到改善。对这种改进的一种可能解释是,CoT 推理扩展了 LM 的计算能力,因为已知具有额外划痕空间的 RNN 和变换器是图灵完备的。不过,将 LM 与图灵机进行比较会引入一个类别错误--图灵机决定语言成员资格,而 LM 则定义字符串的分布。为了弥合这一差距,我们将 CoT 推理形式化为robabilistic 环境。我们提出了几项关于具有 CoT 推理能力的递归 LM 和变换 LM 的表征能力的结果,表明它们可以表征与概率图灵机相同的字符串分布系列。
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引用次数: 0
Quantum automata and languages of finite index 量子自动机和有限指数语言
Pub Date : 2024-06-19 DOI: arxiv-2406.13797
Andrea Benso, Flavio D'Alessandro, Paolo Papi
This paper is a continuation of a previous study on the so-called measureonce finite quantum automata model introduced by Moore and Crutchfield in 2000.We investigate conditions assuring that, given a language recognized by such adevice and a language generated by a context-free grammar of finite index or bya matrix context-free grammar, it is recursively decidable whether or not theyhave a nonempty intersection.
本文是对摩尔和克拉奇菲尔德 2000 年提出的所谓 measureonce 有限量子自动机模型研究的延续。我们研究了一些条件,以确保在给定由这种设备识别的语言和由有限索引的无上下文语法或矩阵无上下文语法生成的语言的情况下,它们是否具有非空交集是可递归判定的。
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引用次数: 0
LLM-Oracle Machines LLM-Oracle 机器
Pub Date : 2024-06-18 DOI: arxiv-2406.12213
Jie Wang
Contemporary AI applications leverage large language models (LLMs) for theirknowledge and inference capabilities in natural language processing tasks. Thisapproach aligns with the concept of oracle Turing machines (OTMs). To capturethe essence of these computations, including those desired but not yet inpractice, we extend the notion of OTMs by employing a cluster of LLMs as theoracle. We present four variants: basic, augmented, fault-avoidance, and$epsilon$-fault. The first two variants are commonly observed, whereas thelatter two are specifically designed to ensure reliable outcomes by addressingLLM hallucinations, biases, and inconsistencies.
当代人工智能应用在自然语言处理任务中利用大型语言模型(LLM)的知识和推理能力。这种方法与甲骨文图灵机(OTM)的概念不谋而合。为了捕捉这些计算的本质,包括那些想要但尚未付诸实践的计算,我们扩展了 OTM 的概念,将 LLM 群集作为理论图灵机。我们提出了四种变体:基本变体、增强变体、故障规避变体和($epsilon$-fault)故障变体。前两种变体是常见的,而后两种变体则是专门设计的,目的是通过解决 LLM 的幻觉、偏差和不一致性来确保可靠的结果。
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引用次数: 0
Computing the Bandwidth of Meager Timed Automata 计算微小定时自动机的带宽
Pub Date : 2024-06-18 DOI: arxiv-2406.12694
Eugene Asarin, Aldric Degorre, Catalin Dima, Bernardo Jacobo Inclán
The bandwidth of timed automata characterizes the quantity of informationproduced/transmitted per time unit. We previously delimited 3 classes of TAaccording to the nature of their asymptotic bandwidth: meager, normal, andobese. In this paper, we propose a method, based on a finite-state simply-timedabstraction, to compute the actual value of the bandwidth of meager automata.The states of this abstraction correspond to barycenters of the faces of thesimplices in the region automaton. Then the bandwidth is $log 1/|z_0|$ where$z_0$ is the smallest root (in modulus) of the characteristic polynomial ofthis finite-state abstraction.
定时自动机的带宽表征了每个时间单位产生/传输的信息量。此前,我们曾根据定时自动机渐近带宽的性质将其分为三类:微弱带宽、正常带宽和大带宽。在本文中,我们提出了一种基于有限状态简单时间抽象的方法,来计算微小自动机带宽的实际值。这个抽象的状态对应于区域自动机中的简单面的边心。那么带宽就是 $log 1/|z_0|$,其中$z_0$是这个有限状态抽象的特征多项式的最小根(模)。
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引用次数: 0
Reversible Transducers over Infinite Words 无限词上的可逆变换器
Pub Date : 2024-06-17 DOI: arxiv-2406.11488
Luc Dartois, Paul Gastin, Loïc Germerie Guizouarn, R. Govind, Shankaranarayanan Krishna
Deterministic two-way transducers capture the class of regular functions. Theefficiency of composing two-way transducers has a direct implication inalgorithmic problems related to reactive synthesis, where transformationspecifications are converted into equivalent transducers. These specificationsare presented in a modular way, and composing the resultant machines simulatesthe full specification. An important result by Dartois et al. shows thatcomposition of two-way transducers enjoy a polynomial composition when theunderlying transducer is reversible, that is, if they are both deterministicand co-deterministic. This is a major improvement over general deterministictwo-way transducers, for which composition causes a doubly exponential blow-upin the size of the inputs in general. Moreover, they show that reversibletwo-way transducers have the same expressiveness as deterministic two-waytransducers. However, the question of expressiveness of reversible transducersover infinite words is still open. In this article, we introduce the class ofreversible two-way transducers over infinite words and show that they enjoy thesame expressive power as deterministic two-way transducers over infinite words.This is done through a non-trivial, effective construction inducing a singleexponential blow-up in the set of states. Further, we also prove that composingtwo reversible two-way transducers over infinite words incurs only a polynomialcomplexity, thereby providing foundations for efficient procedure forcomposition of transducers over infinite words.
确定性双向变换器捕捉了一类规则函数。组成双向变换器的高效性直接影响到与反应式合成相关的算法问题,在这些问题中,变换规范被转换为等价变换器。这些规范以模块化的方式呈现,组合后的机器可以模拟完整的规范。Dartois 等人的一项重要研究结果表明,当底层转换器是可逆的,也就是说,如果它们既是确定性的,又是共同确定性的,那么双向转换器的组合就可以享受多项式组合。与一般的确定性双向变换器相比,这是一个重大改进,因为一般情况下,双向变换器的组成会导致输入大小的双倍指数膨胀。此外,他们还证明了可逆双向变换器与确定性双向变换器具有相同的表现力。然而,在无穷字之上的可逆变换器的表达能力问题仍然悬而未决。在本文中,我们介绍了无限词上的可逆双向变换器,并证明它们与无限词上的确定性双向变换器具有相同的表达力。此外,我们还证明了在无限词上组合两个可逆双向变换器只产生多项式复杂性,从而为在无限词上组合变换器的高效程序奠定了基础。
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引用次数: 0
$ω$-regular Expression Synthesis from Transition-Based Büchi Automata 基于转换的布基自动机的ω$$正则表达式合成
Pub Date : 2024-06-12 DOI: arxiv-2406.08136
Charles Pert, Dalal Alrajeh, Alessandra Russo
A popular method for modelling reactive systems is to use $omega$-regularlanguages. These languages can be represented as nondeterministic B"uchiautomata (NBAs) or $omega$-regular expressions. Existing methods synthesiseexpressions from state-based NBAs. Synthesis from transition-based NBAs istraditionally done by transforming transition-based NBAs into state-based NBAs.This transformation, however, can increase the complexity of the synthesisedexpressions. This paper proposes a novel method for directly synthesising$omega$-regular expressions from transition-based NBAs. We prove that themethod is sound and complete. Our empirical results show that the$omega$-regular expressions synthesised from transition-based NBAs are morecompact than those synthesised from state-based NBAs. This is particularly thecase for NBAs computed from obligation, reactivity, safety and recurrence-typeLTL formulas, reporting in the latter case an average reduction of over 50%. Wealso show that our method successfully synthesises $omega$-regular expressionsfrom more LTL formulas when using a transition-based instead of a state-basedNBA.
对反应式系统进行建模的一种流行方法是使用$omega$正则表达式语言。这些语言可以表示为非确定性正则表达式(NBAs)或$omega$-正则表达式。现有的方法是从基于状态的 NBA 合成表达式。然而,这种转换会增加合成表达式的复杂性。本文提出了一种从基于转换的 NBA 直接合成$omega$正则表达式的新方法。我们证明了该方法的合理性和完整性。我们的实证结果表明,从基于过渡的 NBA 合成的$omega$正则表达式比从基于状态的 NBA 合成的表达式更紧凑。尤其是根据义务、反应性、安全性和递推型 LTL 公式计算出的 NBA,在后一种情况下平均减少了 50% 以上。我们还表明,当使用基于转换的 NBA 而不是基于状态的 NBA 时,我们的方法成功地从更多的 LTL 公式中合成了 $omega$-正则表达式。
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引用次数: 0
Analyzing constrained LLM through PDFA-learning 通过 PDFA 学习分析受限 LLM
Pub Date : 2024-06-12 DOI: arxiv-2406.08269
Matías Carrasco, Franz Mayr, Sergio Yovine, Johny Kidd, Martín Iturbide, Juan Pedro da Silva, Alejo Garat
We define a congruence that copes with null next-symbol probabilities thatarise when the output of a language model is constrained by some means duringtext generation. We develop an algorithm for efficiently learning the quotientwith respect to this congruence and evaluate it on case studies for analyzingstatistical properties of LLM.
当语言模型的输出在文本生成过程中受到某种限制时,就会出现下一符号概率为空的情况。我们开发了一种算法,用于高效地学习与该一致性相关的商,并在分析 LLM 统计属性的案例研究中对其进行了评估。
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引用次数: 0
Database-assisted automata learning 数据库辅助自动学习
Pub Date : 2024-06-11 DOI: arxiv-2406.07208
Hielke Walinga, Robert Baumgartner, Sicco Verwer
This paper presents DAALder (Database-Assisted Automata Learning, with Dutchsuffix from leerder), a new algorithm for learning state machines, or automata,specifically deterministic finite-state automata (DFA). When learning statemachines from log data originating from software systems, the large amount oflog data can pose a challenge. Conventional state merging algorithms cannotefficiently deal with this, as they require a large amount of memory. To solvethis, we utilized database technologies to efficiently query a big tracedataset and construct a state machine from it, as databases allow to save largeamounts of data on disk while still being able to query it efficiently.Building on research in both active learning and passive learning, the proposedalgorithm is a combination of the two. It can quickly find a characteristic setof traces from a database using heuristics from a state merging algorithm.Experiments show that our algorithm has similar performance to conventionalstate merging algorithms on large datasets, but requires far less memory.
本文介绍了 DAALder(数据库辅助自动机学习,荷兰语后缀为 leerder),这是一种用于学习状态机或自动机的新算法,特别是确定性有限状态自动机(DFA)。从软件系统的日志数据中学习状态机时,大量的日志数据可能会带来挑战。传统的状态合并算法需要占用大量内存,因此无法有效处理这一问题。为了解决这个问题,我们利用数据库技术来有效地查询大型跟踪数据集,并从中构建状态机,因为数据库可以将大量数据保存在磁盘上,同时还能有效地进行查询。实验表明,我们的算法在大型数据集上的性能与传统的状态合并算法相似,但所需内存要少得多。
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引用次数: 0
Learning EFSM Models with Registers in Guards 学习带有寄存器的 EFSM 模型
Pub Date : 2024-06-11 DOI: arxiv-2406.07040
Germán Vega, Roland Groz, Catherine Oriat, Michael Foster, Neil Walkinshaw, Adenilso Simão
This paper presents an active inference method for Extended Finite StateMachines, where inputs and outputs are parametrized, and transitions can beconditioned by guards involving input parameters and internal variables calledregisters. The method applies to (software) systems that cannot be reset, so itlearns an EFSM model of the system on a single trace.
本文提出了一种用于扩展有限状态机的主动推理方法,在这种推理方法中,输入和输出都是参数化的,转换可以通过涉及输入参数和称为寄存器的内部变量的守护来进行。该方法适用于无法重置的(软件)系统,因此它能在单条轨迹上识别系统的扩展有限状态机模型。
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引用次数: 0
Attributed Tree Transducers for Partial Functions 部分函数的归属树变换器
Pub Date : 2024-06-10 DOI: arxiv-2406.06141
Sebastian Maneth, Martin Vu
Attributed tree transducers (atts) have been equipped with regularlook-around (i.e., a preprocessing via an attributed relabeling) in order toobtain a more robust class of translations. Here we give further evidence ofthis robustness: we show that if the class of translations realized bynondeterministic atts with regular look-around is restricted to partialfunctions, then we obtain exactly the class of translations realized bydeterministic atts with regular look-around.
归属树转换器(atts)已经配备了正则环顾(即通过归属重标注进行预处理),以获得一类更稳健的转换。在这里,我们进一步证明了这一稳健性:我们证明,如果将带有正则环顾的非定域性 atts 所实现的译码类别限制为部分函数,那么我们得到的正是带有正则环顾的非定域性 atts 所实现的译码类别。
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引用次数: 0
期刊
arXiv - CS - Formal Languages and Automata Theory
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