An improved algorithm for determinization of weighted and fuzzy automata

For a given weighted finite automaton over a strong bimonoid we construct its reduced Nerode automaton, which is crisp-deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics. We show that the reduced Nerode automaton is even smaller than the Nerode automaton, which was previously used in determinization related to this semantics. We determine necessary and sufficient conditions under which the reduced Nerode automaton is finite and provide an efficient algorithm which computes the reduced Nerode automaton whenever it is finite. In determinization of weighted finite automata over semirings and fuzzy finite automata over lattice-ordered monoids this algorithm gives smaller crisp-deterministic automata than any other known determinization algorithm.     

Temporal determinization of mutating finite automata: Reconstructing or restructuring

A mutating finite automaton (MFA) is a nondeterministic finite automaton (NFA) that changes its morphology over discrete time by a sequence of mutations. This results in a sequence of NFAs, the initial NFA, and one mutated NFA for each mutation. Some application domains, including model-based diagnosis of discrete-event systems in artificial intelligence and model-based testing in software engineering, require temporal determinization of MFAs. Determinizing an MFA temporally means generating a deterministic finite automaton (DFA) that is equivalent to the mutated NFA as soon as a mutation occurs. Since, in computation time, the classical Subset Construction determinization algorithm may be less than optimal when applied to MFAs, a conservative algorithm is proposed, called Subset Restructuring, which, instead of constructing the new DFA from scratch based on the mutated NFA, generates the new DFA by updating the previous DFA based on the mutation occurred. Subset Restructuring is sound and complete, thereby yielding the same DFA generated by Subset Construction. Results from massive experimentation indicate the viability of Subset Restructuring, especially so when large MFAs change by small mutations.     

A tighter analysis of Piterman's Büchi determinization

Determinization and complementation are two fundamental problems in automata theory. Very recently, Piterman improved Safra's determinization and, presented a new construction which produces parity automata with a smaller size. We give a tighter analysis on that determinization construction and show that the number of states of the resulting deterministic automaton is bounded by 2n²(n!) instead of 2n!nn.     

An Approximate Determinization Algorithm for Weighted Finite-State Automata

Nondeterministic weighted finite-state automata are a key abstraction in automatic speech recognition systems. The efficiency of automatic speech recognition depends directly on the sizes of these automata and the degree of nondeterminism present, so recent research has studied ways to determinize and minimize them, using analogues of classical automata determinization and minimization. Although, as we describe here, determinization can in the worst case cause poly-exponential blowup in the number of states of a weighted finite-state automaton, in practice it is remarkably successful. In extensive experiments in automatic speech recognition systems, deterministic weighted finite-state automata tend to be smaller than the corresponding nondeterministic inputs. Our observations show that these size reductions depend critically on the interplay between weights and topology in nondeterministic weighted finite-state automata. We exploit these observations to design a new approximate determinization algorithm, which produces a deterministic weighted finite-state automaton that preserves the strings of a weighted language but not necessarily their weights. We apply our algorithm to two different types of weighted finite-state automata that occur in automatic speech recognition systems and in each case provide extensive experimental results showing that, compared with current techniques, we achieve significant size reductions without affecting performance. In particular, for a standard test bed, we can reduce automatic speech recognition memory requirements by 25—35\percent with negligible effects on recognition time and accuracy. Received March 31, 1998; revised January 29, 1999.     

Improving the bit-parallel NFA of Baeza-Yates and Navarro for approximate string matching

We propose a new variant of the bit-parallel NFA of Baeza-Yates and Navarro (BPD) for approximate string matching [R. Baeza-Yates, G. Navarro, Faster approximate string matching, Algorithmica 23 (1999) 127-158]. BPD is one of the most practical approximate string matching algorithms under moderate pattern lengths and error levels [G. Myers, A fast bit-vector algorithm for approximate string matching based on dynamic programming, J. ACM 46 (3) 1989 395-415; G. Navarro, M. Raffinot, Flexible Pattern Matching in Strings—Practical On-line Search Algorithms for Texts and Biological Sequences, Cambridge University Press, Cambridge, UK, 2002]. Given a length-m pattern and an error threshold k, the original BPD requires (m−k)(k+2) bits of space to represent an NFA with (m−k)(k+1) states. In this paper we remove redundancy from the original NFA representation. Our variant requires (m−k)(k+1) bits of space, which is optimal in the sense that exactly one bit per state is used. The space efficiency is achieved by using an alternative, but equally or even more efficient, simulation algorithm for the bit-parallel NFA. We also present experimental results to compare our modified NFA against the original BPD and its main competitors. Our new variant is more efficient than the original BPD, and it hence takes over/extends the role of the original BPD as one of the most practical approximate string matching algorithms under moderate values of k and m.     

A memory-based NFA regular expression match engine for signature-based intrusion detection

Signature-based intrusion detection is required to inspect network traffic at wire-speed. Matching packet payloads against patterns specified with regular expression is a computation intensive task. Hence, the design of hardware accelerator to speed up regular expression matching has been an active research area. A systematic approach to detect regular expression is based on finite automaton. The space-time trade-off between deterministic finite automaton (DFA) and non-deterministic finite automaton (NFA) is well-known. DFA can offer constant throughput but it may suffer from the state explosion problem. Hence, implementation of DFA for large pattern sets on embedded device with limited on-chip memory may not be viable. NFA requires linear space but the throughput can be very low. Implementations of NFA with hardwired circuits can overcome the speed deficiency by exploiting the massive parallelism offered by dedicated hardware circuitries, but this approach does not support efficient dynamic updates. In this paper, we shall present a memory-based architecture for the implementation of NFA to speed up regular expression matching for signature-based intrusion detection. The proposed method supports dynamic updates and offers constant throughput so that it can be used to supplement the existing DFA-based methods in handling large pattern sets.     

Deciding unique decodability of bigram counts via finite automata

We revisit the problem of deciding by means of a finite automaton whether a string is uniquely decodable from its bigram counts. An efficient algorithm for constructing a polynomial-size Nondeterministic Finite Automaton (NFA) that decides unique decodability is given. This NFA may be simulated efficiently in time and space. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has exponentially many states in alphabet size, and compute the correct order of magnitude of the exponent.     

入侵检测系统中模式匹配自动机的构造研究

本文提出了一种新的用于构造入侵检测模式匹配自动机的方法。该方法从构造判定单个模式的NFA自动机入手,通过集成单个的NFA而得到全集的NFA,并将全集NFA转换为与之等价的DFA并化简,从而可得到全集的确定型模式匹配有限自动机。由于该方法可以完全自动完成,从而可以方便地为入侵检测系统构造模式匹配自动机。     

Bounded determinization of timed automata with silent transitions

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. We show how to apply the approach in a fault-based test-case generation method, called model-based mutation testing, that was previously restricted to deterministic timed automata. The approach is implemented in a prototype tool and evaluated on several scientific examples and one industrial case study. To our best knowledge, this is the first implementation of this type of procedure for timed automata.     

分组密码算法SMS4的暴力破解及模拟实现

加密算法的安全性在很大程度上取决于暴力破解的不可行性。暴力破解加密算法是密码学研究的一个重要方向。该文采用分布式计算方法,设计了暴力破解SMS4加密算法的软件。在局域网内对SMS4算法的暴力破解做了模拟实现,并对软件的性能进行了测试。最后对软件及SMS4算法的暴力破解结果进行了分析,并指明了下一步的工作方向。     

一种基于深度报文检测的FSM状态表压缩技术

针对深度报文检测中正则表达式模式匹配的状态表爆炸问题,提出并实现了一种集合交割的预编码方法(SI-precode),在正则表达式转换成DFA前对所有输入符号进行预编码,通过压缩输入,减少FSM中输入符号的种类,从而压缩状态转移表的空间.证明了预编码生成的状态机的正确性及其与原状态机的同态性.采用L7-filter模式进行实验表明SI-precode不仅提高了正则表达式的编译速度,针对单模式状态机,其状态转移表空间比不进行预编码压缩了87%～97%,50个模式的多模式状态机可压缩59%.预编码在软硬件结合体系结构下进行协议识别时不会对性能造成影响;对纯软件结构性能降低2%～4%.     

Minimized Thompson NFA

The problem of converting a regular expression to nondeterministic finite automaton (NFA) is a fundamental problem that has been well studied. However, the two basic construction algorithms: (1) Thompson, (2) McNaughton–Yamada and Glushkov, both have disadvantages. In this article: first, a ‘smart’ parsing algorithm is developed which constructs a parse tree with at most (3l???1) nodes form a regular expression with l literals; second, we propose an algorithm that works on the resulting NFA from Thompson's construction, eliminating as many auxiliary states as possible while maintaining Thompson's properties. It is shown that the resulting NFA is minimized. This means that no auxiliary states can be eliminated without violating the defining properties of Thompson NFA. The time and space requirements for the above algorithms are linear with respect to the length of the regular expression.     

基于层次自动机模型的复杂事件层次实现研究

复杂事件处理技术从数据流中提取满足特定模式的事件序列,具有实时、海量、智能的特点,近年来引起了学术界和商业界的广泛关注。但是,之前的工作侧重于对单层复杂事件检测的研究。事实上,由于业务系统对信息有不同层次的需求,需要对事件进行分层处理,单层复杂事件检测并不能充分支持事件分层的需求。针对这种情况,在事件层次概念以及传统NFA模型的基础上,定义了分层复杂事件检测模型层次自动机NHA,基于NHA模型设计了更为直观高效的EH-Tree结构,并给出了分层复杂事件检测HCED算法和代价模型。最后以吞吐量和内存占用为指标,进行了大量的实验,对比并分析了HCED算法与传统基于NFA模型的SASE算法的时间性能和空间性能。实验结果表明,HCED算法能有效且高效地实现分层复杂事件检测,填补了CEP不支持分层复杂事件检测的空白,为下一步研究提供了基础。     

A specialized on-the-fly algorithm for lexicon and language model composition

This paper presents an algorithm for the composition of weighted finite-state transducers which is specially tailored to speech recognition applications: it composes the lexicon with the language model while simultaneously optimizing the resulting transducer. Furthermore, it performs these computations "on-the-fly" to allow easier management of the tradeoff between offline and online computation and memory. The algorithm is exact for local knowledge integration and optimization operations such as composition and determinization. Minimization and pushing operations are approximated. Our results have confirmed the efficiency of these approximations.     

支持得分矩阵的音乐检索技术

作为音乐检索的重要方式,哼唱检索由于其有效性和方便性,引起了广泛的关注。对此提出了一种新的基于得分矩阵的音乐哼唱快速检索技术,可以实现哼唱音乐的快速检索。首先根据哼唱音乐特征,将音乐数据库和用户提供的哼唱片段,按自然停顿方式划分音乐的语句,同时使用K-means聚类算法对音乐的语句片段进行音高相似性计算,并根据聚类情况提取出位置特异性得分矩阵。此外,基于得分矩阵提出NA匹配算法和两种加速分段计分方法,分别是顺序前瞻计分SLS算法和置换矩阵前瞻计分PLA算法。实验结果表明所提出的基于得分矩阵的音乐检索技术能够快速有效地返回查询结果,同时PLA算法具有更有效的哼唱音乐检索结果。     

Determinization of fuzzy automata with membership values in complete residuated lattices

In this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices. In comparison with the previous methods, developed by Bělohlávek [R. Bělohlávek, Determinism and fuzzy automata, Information Sciences 143 (2002), 205-209] and Li and Pedrycz [Y.M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005), 68-92], our method always gives a smaller automaton, and in some cases, when the previous methods result in infinite automata, our method can result in a finite one. We also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them, and in particular, to the concept of the Nerode’s fuzzy right congruence of a fuzzy automaton, which we introduce and study here.     

Efficient and Robust Music Identification With Weighted Finite-State Transducers

We present an approach to music identification based on weighted finite-state transducers and Gaussian mixture models, inspired by techniques used in large-vocabulary speech recognition. Our modeling approach is based on learning a set of elementary music sounds in a fully unsupervised manner. While the space of possible music sound sequences is very large, our method enables the construction of a compact and efficient representation for the song collection using finite-state transducers. This paper gives a novel and substantially faster algorithm for the construction of factor transducers, the key representation of song snippets supporting our music identification technique. The complexity of our algorithm is linear with respect to the size of the suffix automaton constructed. Our experiments further show that it helps speed up the construction of the weighted suffix automaton in our task by a factor of 17 with respect to our previous method using the intermediate steps of determinization and minimization. We show that, using these techniques, a large-scale music identification system can be constructed for a database of over 15 000 songs while achieving an identification accuracy of 99.4% on undistorted test data, and performing robustly in the presence of noise and distortions.      

基于实时自动机的连续时段演算的验证

时段演算是描述和推导嵌入式实时系统和混成系统性质的一种区间时态逻辑.扩展线性时段不变式是时段演算的重要子集.针对实时自动机,提出一种连续时间语义下扩展线性时段不变式的有界模型检验方法.该方法将扩展线性时段不变式的有界模型检验问题转化为量词线性算术公式的正确性问题,从而可以采用量词消去技术进行求解.首先,运用符号化的思想,在实时自动机上利用深度优先搜索找到所有满足观测时长约束的符号化路径片段;然后,将每条符号化路径片段转化为一个量词线性算术公式;最后,利用量词消去工具求解.与已有工作相比,基于实时自动机设计了验证算法.另外,降低了验证复杂度,并且加速了验证过程的实际速度.     

From LTL to deterministic automata

We present a new algorithm to construct a (generalized) deterministic Rabin automaton for an LTL formula \(\varphi \). The automaton is the product of a co-Büchi automaton for \(\varphi \) and an array of Rabin automata, one for each \({\mathbf {G}}\)-subformula of \(\varphi \). The Rabin automaton for \({\mathbf {G}}\psi \) is in charge of recognizing whether \({\mathbf {F}}{\mathbf {G}}\psi \) holds. This information is passed to the co-Büchi automaton that decides on acceptance. As opposed to standard procedures based on Safra’s determinization, the states of all our automata have a clear logical structure, which allows for various optimizations. Experimental results show improvement in the sizes of the resulting automata compared to existing methods.