Learning Automata from Ordered Examples

Connectionist learning models have had considerable empirical success, but it is hard to characterize exactly what they learn. The learning of finite-state languages (FSL) from example strings is a domain which has been extensively studied and might provide an opportunity to help understand connectionist learning. A major problem is that traditional FSL learning assumes the storage of all examples and thus violates connectionist principles. This paper presents a provably correct algorithm for inferring any minimum-state deterministic finite-state automata (FSA) from a complete ordered sample using limited total storage and without storing example strings. The algorithm is an iterative strategy that uses at each stage a current encoding of the data considered so far, and one single sample string. One of the crucial advantages of our algorithm is that the total amount of space used in the course of learning for encoding any finite prefix of the sample is polynomial in the size of the inferred minimum state deterministic FSA. The algorithm is also relatively efficient in time and has been implemented. More importantly, there is a connectionist version of the algorithm that preserves these properties. The connectionist version requires much more structure than the usual models and has been implemented using the Rochester Connectionist Simulator. We also show that no machine with finite working storage can iteratively identify the FSL from arbitrary presentations.     

Online Induction of Probabilistic Real-Time Automata

The probabilistic real-time automaton （PRTA） is a representation of dynamic processes arising in the sciences and industry. Currently, the induction of automata is divided into two steps： the creation of the prefix tree acceptor （PTA） and the merge procedure based on clustering of the states. These two steps can be very time intensive when a PRTA is to be induced for massive or even unbounded datasets. The latter one can be efficiently processed, as there exist scalable online clustering algorithms. However, the creation of the PTA still can be very time consuming. To overcome this problem, we propose a genuine online PRTA induction approach that incorporates new instances by first collapsing them and then using a maximum frequent pattern based clustering. The approach is tested against a predefined synthetic automaton and real world datasets, for which the approach is scalable and stable. Moreover, we present a broad evaluation on a real world disease group dataset that shows the applicability of such a model to the analysis of medical processes.     

袋自动机

提出了袋自动机模型和袋语言的概念,并给出了袋自动机的状态转换图;分析了袋语言重复序列在状态转换图中的反映,并划分为不变重复序列、增重复序列、减重复序列和传递重复序列,给出了袋语言的结构特性;研究了袋语言类同Chomsky文法体系中各型语言的关系,证明了正规语言类是袋语言类的真子集,袋语言类是上下文有关语言类的真子集,而袋语言类同上下文无关语言类是两个相交但互不包含的语言类,即存在不是上下文无关语言的袋语言,也存在无法用袋自动机产生的上下文无关语言.     

基于超级自动机的语言识别及逻辑推理

该文根据自动机的定义,对超级自动机作了特定的定义,并给出了自动机对语言的识别功能的具体步骤。接着由超级自动机的定义,以一个特殊的例子给出了超级自动机的语言识别和逻辑推理功能。     

Exactly Learning Automata of Small Cover Time

We present algorithms for exactly learning unknown environments that can be described by deterministic finite automata. The learner performs a walk on the target automaton, where at each step it observes the output of the state it is at, and chooses a labeled edge to traverse to the next state. The learner has no means of a reset, and does not have access to a teacher that answers equivalence queries and gives the learner counterexamples to its hypotheses. We present two algorithms: The first is for the case in which the outputs observed by the learner are always correct, and the second is for the case in which the outputs might be corrupted by random noise. The running times of both algorithms are polynomial in the cover time of the underlying graph of the target automaton.     

基于混合自动机的随机噪声电路动态特性分析

在集成电路非线性随机噪声的分析中应用Petri网技术,需要对原有的Petri网从定义和变迁发射规则方面等进行统计特性与连续特性的拓展研究和补充.并且基于噪声的随机非线性特性分析目的需求,拓展了传统的Petri网,提出了混合随机Petri网(Hybrid Statistical Petri Net,HSPN)模型分析方法.通过分析非线性电路的混合自动机模型,增加Petri网随机参数变迁描述能力,针对电路噪声特点,确定适合HSPN的随机动态特性分析模型.通过实例电路说明验证HSPN的建模方法,并与SPICE仿真软件进行比较,验证了该方法的精度和可行性.     

Inference of finite-state transducers from regular languages

Finite-state transducers are models that are being used in different areas of pattern recognition and computational linguistics. One of these areas is machine translation, where the approaches that are based on building models automatically from training examples are becoming more and more attractive. Finite-state transducers are very adequate to be used in constrained tasks where training samples of pairs of sentences are available. A technique to infer finite-state transducers is proposed in this work. This technique is based on formal relations between finite-state transducers and finite-state grammars. Given a training corpus of input-output pairs of sentences, the proposed approach uses statistical alignment methods to produce a set of conventional strings from which a stochastic finite-state grammar is inferred. This grammar is finally transformed into a resulting finite-state transducer. The proposed methods are assessed through series of machine translation experiments within the framework of the EUTRANS project.     

Strong separation of learning classes

Abstract

Suppose LC ₁ and LC ₂ are two machine learning classes each based on a criterion of success. Suppose, for every machine which learns a class of functions according to the LC ₂ criterion of success, there is a machine which learns this class according to the LC ₂ criterion. In the case where the converse does not hold LC, is said to be separated from LC ₂. It is shown that for many such separated learning classes from the literature a much stronger separation holds: (?𝒞∈LC ₁) (?𝒞' ∈LC ₂ - LC ₁(( [' ?𝒞] It is also shown that there is a pair of separated learning classes from the literature for which the stronger separation above does not hold. A philosophical heuristic toward the design of artificially intelligent learning programs is presented with each strong separation result.     

量子Mealy自动机和量子Moore自动机的等价

随着大数分解的量子算法和量子搜索算法的给出,量子计算进入了一个全新的迅速的发展时期.量子自动机是近十年来兴起的量子计算理论,是一个很活跃的研究领域,量子自动机的研究已经相当丰富.首先定义了字符集上的有限维Fock空间,给出基于有限维Fock空间的量子Mealy自动机和量子Moore自动机的定义,考虑在不受外界环境影响下的两种量子自动机构成的封闭的量子系统,详细地研究了量子Mealy自动机和量子Moore自动机的演化过程,利用量子力学中密度算子的基本理论给出量子Mealy自动机和量子Moore自动机生成的量子语言.最后,在考虑纯态的情形下证明了量子Mealy自动机与量子Moore自动机是等价的.     

Homomorphic characterizations of recursively enumerable languages with very small language classes

In this paper, we attempt to characterize the class of recursively enumerable languages with much smaller language classes than that of linear languages. Language classes, and , of (i,j) linear languages and (i,j) minimal linear languages are defined by posing restrictions on the form of production rules and the number of nonterminals. Then the homomorphic characterizations of the class of recursively enumerable languages are obtained using these classes and a class, , of minimal linear languages. That is, for any recursively enumerable language L over Σ, an alphabet Δ, a homomorphism h : Δ^*→Σ^* and two languages L₁ and L₂ over Δ in some classes mentioned above can be found such that L = h(L₁∩L₂). The membership relations of L₁ and L₂ of the main results are as follows:(I) For posing restrictions on the forms of production rules, the following result is obtained:(1) and .This result is the best one and cannot be improved using . However, with posing more restriction on L₂, this result can be improved and the follwing statement is obtained.(2) and .(II) For posing restrictions on the numbers of nonterminals, the follwing result is obtained.(3) and .We believe this result is also the best.     

处理图像语言的格点自动机与格点文法

Giammarresi与Restivo在一篇综述中总结出一个关于可识别的图像语言(即2维矩形语言)REC的等价性定理.对比1维字语言的相应结果,其中还缺少关于生成文法的相应一环.提出了一种(矩形的)格点文法,正好弥补了这一缺环.而取代2维on-line tesselation自动机,引入了格点自动机的概念.一方面,它与经典的2元树型自动机更相似,另一方面,它也是格点文法与等价性定理中关于REC的其他描述方式之间的一座桥梁.同时,标准的existential monadic二阶逻辑也被一种更弱的规范框架——positive monadic分划逻辑所取代.由此导出一个新的更完整的关于REC的等价性定理.     

Incremental Construction of Minimal Tree Automata

We describe an algorithm that allows the incremental addition or removal of unranked ordered trees to a minimal frontier-to-root deterministic finite-state tree automaton (DTA). The algorithm takes a tree t and a minimal DTA A as input; it outputs a minimal DTA A′ which accepts the language L(A) accepted by A incremented (or decremented) with the tree t. The algorithm can be used to efficiently maintain dictionaries which store large collections of trees or tree fragments.     

模糊有穷自动机与单体二阶Lukasiewicz逻辑

该文引入了单体二阶Lukasiewicz逻辑,进而给出了模糊有穷自动机识别语言的逻辑描述,证明了多值逻辑意义下的Bchi与Elgot基本定理.通过引入星-自由模糊语言与非周期模糊语言,刻画了可以用一阶Lukasiewicz逻辑定义的模糊语言.     

Generalized Statistical Equivalence of Automata

The notion of generalized statistical equivalence of automata is introduced, and this equivalence is demonstrated to be weaker than the usual equivalence but stronger than the statistical equivalence of automata.     

赋权型自动机的不同模型研究

自动机理论是理论计算机科学的基础理论之一,在很多领域自动机有着广泛的应用,有穷状态自动机是正则语言的识别机器,通常分为确定型与非确定型两种模型,其识别语言的能力是等价的。赋权自动机是另一类重要的自动机模型,自动机的每条转移规则和状态可以赋以某一代数结构上的某一数值,从而可以计算输入字符串的权值。任何有穷状态自动机都可以视为一特殊赋权自动机,因此赋权自动机功能更强大,应用更为广泛。     

The Power of Amnesia: Learning Probabilistic Automata with Variable Memory Length

We propose and analyze a distribution learning algorithm for variable memory length Markov processes. These processes can be described by a subclass of probabilistic finite automata which we name Probabilistic Suffix Automata (PSA). Though hardness results are known for learning distributions generated by general probabilistic automata, we prove that the algorithm we present can efficiently learn distributions generated by PSAs. In particular, we show that for any target PSA, the KL-divergence between the distribution generated by the target and the distribution generated by the hypothesis the learning algorithm outputs, can be made small with high confidence in polynomial time and sample complexity. The learning algorithm is motivated by applications in human-machine interaction. Here we present two applications of the algorithm. In the first one we apply the algorithm in order to construct a model of the English language, and use this model to correct corrupted text. In the second application we construct a simple stochastic model for E.coli DNA.     

基于元胞自动机的人工金融市场及其仿真研究

该文通过对金融市场复杂性的分析,并基于元胞自动机和争当少数者模型提出了一个开放的金融预测模型。模型中的投资者相当于争当少数者模型里的agent,每个投资者都必须从初始时各自定义的策略集合中选择最成功的作为每一步的预测策略。同样,投资者也相仿于元胞自动机中的元胞,而选定的预测策略就作为元胞的局部规则,每个元胞都根据局部信息和局部规则做出估价。模型的最终预测值就是由数千个这样的投资者决定的。此模型是开放性的,因为可以通过扩充或重构其预测策略库来获得更精确的预测结果。数值实验显示,虽然策略库比较简单,但其预测的平均相对误差仅为1．73％。     

Finding Minimum Vertex Covering in Stochastic Graphs: A Learning Automata Approach

Structural and behavioral parameters of many real networks such as social networks are unpredictable, uncertain, and have time-varying parameters, and for these reasons, deterministic graphs for modeling such networks are too restrictive to solve most of the real-network problems. It seems that stochastic graphs, in which weights associated to the vertices are random variables, might be better graph models for real-world networks. Once we use a stochastic graph as the model for a network, every feature of the graph such as path, spanning tree, clique, dominating set, and cover set should be treated as a stochastic feature. For example, choosing a stochastic graph as a graph model of an online social network and defining community structure in terms of clique, the concept of a stochastic clique may be used to study community structures’ properties or define spreading of influence according to the coverage of influential users; the concept of stochastic vertex covering may be used to study spread of influence. In this article, minimum vertex covering in stochastic graphs is first defined, and then four learning, automata-based algorithms are proposed for solving a minimum vertex-covering problem in stochastic graphs where the probability distribution functions of the weights associated with the vertices of the graph are unknown. It is shown that through a proper choice of the parameters of the proposed algorithms, one can make the probability of finding minimum vertex cover in a stochastic graph as close to unity as possible. Experimental results on synthetic stochastic graphs reveal that at a certain confidence level the proposed algorithms significantly outperform the standard sampling method in terms of the number of samples needed to be taken from the vertices of the stochastic graph.     

Bounded Model Checking with SNF,Alternating Automata,and Büchi Automata

Model checking of LTL formulæis traditionally carried out by a conversion to Büchi automata, and there is therefore a large body of research in this area including some recent studies on the use of alternating automata as an intermediate representation.Bounded model checking has until recently been apart from this, typically using a direct conversion from LTL to propositional logic. In this paper we give a new bounded model checking encoding using alternating automata and focus on the relationship between alternating automata and SNF. We also explore the differences in the way SNF, alternating, and Büchi automata are used from both a theoretical and an experimental perspective.