Nondeterministic Finite Automata Research Articles

Fixing Nondeterminism in Large Discrete-Event Knowledge

Discrete-event knowledge (DEK) consists in a variety of automaton-based data structures which are generated by knowledge-based and engineering systems, including intelligent diagnosis systems. Model-based diagnosis methods for discrete-event systems (DESs) are typically supported by large automata that allow for the efficient generation of the candidate diagnoses when the DES is being operated. However, the generation of the DEK may involve a determinization step, where a nondeterministic finite automaton (NFA) is transformed into an equivalent deterministic finite automaton (DFA) by means of the classical Subset Construction algorithm. When this determinization is performed online and the NFA is large, the diagnosis engine may slow down to such an extent that the entire diagnosis task is jeopardized. This is why a novel determinization algorithm is proposed, called Quick Subset Construction, which, instead of generating from scratch the equivalent DFA, removes the nondeterminism by operating directly on the NFA. This way, the larger the NFA and the smaller the portion of nondeterminism involved, the faster Quick Subset Construction will be over Subset Construction. Massive experimentation on large automata has confirmed this result empirically.

Text Backdoor Detection Using an Interpretable RNN Abstract Model

Deep neural networks (DNNs) are known to be inherently vulnerable to malicious attacks such as the adversarial attack and the backdoor attack. The former is crafted by adding small perturbations to benign inputs so as to fool a DNN. The latter generally embeds a hidden pattern in a DNN by poisoning the dataset during the training process, which causes the infected model to misbehave on predefined inputs with a specific trigger and normally perform for others. Much work has been conducted on defending against the adversarial samples, while the backdoor attack received much less attention, especially in recurrent neural networks (RNNs), which play an important role in the text processing field. Two main limitations make it hard to directly apply existing image backdoor detection approaches to RNN-based text classification systems. First, a layer in an RNN does not preserve the same feature latent space function for different inputs, making it impossible to map the inserted specific pattern with the neural activations. Second, the text data is inherently discrete, making it hard to optimize the text like image pixels. In this work, we propose a novel backdoor detection approach named InterRNN for RNN-based text classification systems from the interpretation perspective. Specifically, we first propose a novel RNN interpretation technique by constructing a nondeterministic finite automaton (NFA) based abstract model, which can effectively reduce the analysis complexity of an RNN while preserving its original logic rules. Then, based on the abstract model, we can obtain interpretation results that explain the fundamental reason behind the decision for each input. We then detect trigger words by leveraging the differences between the behaviors in the backdoor sentences and those in the normal sentences. The extensive experiment results on four benchmark datasets demonstrate that our approach can generate better interpretation results compared to state-of-the-art approaches and effectively detect backdoors in RNNs.

О вычислении веса подзадач при вершинной минимизации недетерминированных конечных автоматов методом ветвей и границ

О вычислении веса подзадач при вершинной минимизации недетерминированных конечных автоматов методом ветвей и границ

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The article considers the method for describing program modeling where predicates are used to create a model in the form of a nondeterministic finite automaton. A format of the description of predicates with the division of their semantic and conditional parts is offered in the paper. Arithmetic operators, parentheses, standard functions, as well as temporal logic operators U and N should be used to describe the content of the predicate. For the logical part of predicates, in addition to their logical functions, it is proposed to use relation operations, arithmetic operators, parentheses and standard functions. The formation of the description of each state of the pro-gram automaton model should be completed by dividing into different branches of the model. To describe the models of parallel programs, the following special states have been introduced: a state-monitor for the access of various processes to shared resources and a state-protocol for the description of independent parallel branches. The model is created in the process of its de-scription, so it does not require further verification. If the description of the model is performed correctly and the optimal algorithm of the future program is selected, such model will fully cor-respond to its description. Unlike MODEL CHECKING technology, which requires verification, it eliminates the need for model verification. The graph of the obtained model is processed by its sequential traversal on all branches with returns to the previous states and subsequent soft-ware implementation. Consecutive traversing should be performed for each branch of the model either to its final state or to the state that has already been processed during the traversal. Model processing includes transmission of the model description into an internal representation for subsequent conversion into a program in the target procedural programming language. In this case all actions in the substantive parts of the predicates, as well as the conditions of the branches in the process of transmission are converted into an internal representation of the pro-gram. This technology provides a direct conversion of the description of the program model in-to the program itself.

Nondeterministic finite automata based on quantum logic: Language equivalence relation and robustness

Automata theory based on quantum logic has been established by Ying. Nondeterministic fuzzy finite automata theory has been proposed by Cao, and further generalized by Pan et al. In this paper, we propose the notion of nondeterministic finite automaton based on quantum logic whose underlying structure is a complete orthomodular lattice l, called nondeterministic l-valued finite automaton (Nl-FA, for short). We show that nondeterministic l-valued finite automata, deterministic l-valued finite automata, and nondeterministic l-valued finite automata with ε-moves are equivalent if and only if l satisfies the distributive law. Next, two l-valued relations in terms of language equivalence are given. Some properties of the two l-valued relations under various operations such as reversal, union, product, and concatenation, are investigated. Finally, we give the degree of the closeness between two Nl-FAs with the same set of states to reflect the robustness, and obtain some interesting results. The theory developed in this paper enriches the automata theory based on quantum logic.

Answer Set Programming for Regular Inference

We propose an approach to non-deterministic finite automaton (NFA) inductive synthesis that is based on answer set programming (ASP) solvers. To that end, we explain how an NFA and its response to input samples can be encoded as rules in a logic program. We then ask an ASP solver to find an answer set for the program, which we use to extract the automaton of the required size. We conduct a series of experiments on some benchmark sets, using the implementation of our approach. The results show that our method outperforms, in terms of CPU time, a SAT approach and other exact algorithms on all benchmarks.

Teaching concepts related to finite automata using ComVis

AbstractThis paper describes educational software for visualization and finite automata simulation. The system was developed in Java programming language, and its main purpose is learning process improvement. Using this software, finite automata can be defined in a graphical editor in the form of a state diagram, or by defining the transition function using the transition table. Upon defining an automaton, it is possible to run a visual simulation of the automaton operation for an arbitrary input string, whereby a textual description of the automaton simulation is also obtained. Furthermore, the system allows for conversion of regular expressions to deterministic finite automata and nondeterministic finite automata. The simulation of Thompson's construction algorithm is implemented, so that transformation of a regular expression to the corresponding NFA can be monitored in a step‐by‐step process. The quantitative analysis and evaluation of the effectiveness of the simulator are based on a survey of undergraduate students at two universities. The majority of students found the tool a useful means for better understanding and mastering of finite automata concepts.

Efficient POSIX submatch extraction on nondeterministic finite automata

SummaryIn this paper we study the performance of POSIX submatch extraction algorithms based on nondeterministic finite automata (NFA). We propose an algorithm that combines Laurikari tagged NFA and extended Okui‐Suzuki disambiguation. The algorithm works in worst‐case O(n m2 t) time and O(m2) space (including preprocessing), where n is the length of input, m is the size of the regular expression with bounded repetition expanded and t is the number of capturing groups and subexpressions that contain them. On real‐world benchmarks our algorithm performs close to the O(n m t) complexity of leftmost‐greedy matching, although on artificial benchmarks it can be significantly slower. We propose a lazy version of the algorithm that runs much faster, but requires O(n m2) space. We show that the Kuklewicz algorithm is slower in practice, and the backward matching algorithm proposed by Cox is incorrect.

Closest substring problems for regular languages

The Closest Substring problem asks whether there exists a consensus string w of given length ℓ such that each string in a set of strings L has a substring whose edit distance is at most r (called the radius) from w. The Closest Substring problem has been studied for finite sets of strings and is known to be NP-hard. We show that the Closest Substring problem for regular languages represented by nondeterministic finite automata (NFA) is PSPACE-complete. The problem remains PSPACE-hard even when the input is a deterministic finite automaton and the length ℓ and radius r are given in unary. Also we show that the Closest Substring problem for acyclic NFAs lies in the second level of the polynomial-time hierarchy and is both NP-hard and coNP-hard.

Efficient Logspace Classes for Enumeration, Counting, and Uniform Generation

We study two simple yet general complexity classes, which provide a unifying framework for efficient query evaluation in areas like graph databases and information extraction, among others. We investigate the complexity of three fundamental algorithmic problems for these classes: enumeration, counting and uniform generation of solutions, and show that they have several desirable properties in this respect. Both complexity classes are defined in terms of non deterministic logarithmic-space transducers (NL transducers). For the first class, we consider the case of unambiguous NL transducers, and we prove constant delay enumeration, and both counting and uniform generation of solutions in polynomial time. For the second class, we consider unrestricted NL transducers, and we obtain polynomial delay enumeration, approximate counting in polynomial time, and polynomialtime randomized algorithms for uniform generation. More specifically, we show that each problem in this second class admits a fully polynomial-time randomized approximation scheme (FPRAS) and a polynomial-time Las Vegas algorithm (with preprocessing) for uniform generation. Remarkably, the key idea to prove these results is to show that the fundamental problem #NFA admits an FPRAS, where #NFA is the problem of counting the number of strings of length n (given in unary) accepted by a non-deterministic finite automaton (NFA). While this problem is known to be #P-complete and, more precisely, SpanL-complete, it was open whether this problem admits an FPRAS. In this work, we solve this open problem, and obtain as a welcome corollary that every function in SpanL admits an FPRAS.

Lengths of words accepted by nondeterministic finite automata

We consider two natural problems about nondeterministic finite automata (NFA). First, given an NFA M of n states, and a length ℓ, does M accept a word of length ℓ? We show that the classic problem of triangle-free graph recognition reduces to this problem, and give an O(nω(log⁡n)1+ϵlog⁡ℓ)-time algorithm to solve it, where ω is the optimal exponent for matrix multiplication. Second, provided L(M) is finite, we consider the problem of listing the lengths of all words accepted by M. Although this problem seems like it might be significantly harder, we show that in the unary case this problem can be solved in O(nω(log⁡n)2+ϵ) time. Finally, we give a connection between NFA acceptance and the strong exponential-time hypothesis.

Privacy-Preserving Medical Treatment System Through Nondeterministic Finite Automata

In this article, we propose a privacy-preserving medical treatment system using nondeterministic finite automata (NFA), hereafter referred to as P-Med, designed for remote medical environment. P-Med makes use of the nondeterministic transition characteristic of NFA to flexibly represent medical model, which includes illness states, treatment methods and state transitions caused by exerting different treatment methods. A medical model is encrypted and outsourced to cloud to deliver telemedicine service. Using P-Med, patient-centric diagnosis and treatment can be made on-the-fly while protecting the confidentiality of patient’s illness states and treatment recommendation results. Moreover, a new privacy-preserving NFA evaluation method is given in P-Med to get a confidential match result for the evaluation of an encrypted NFA and an encrypted data set, which avoids the cumbersome inner state transition determination. We demonstrate that P-Med realizes treatment procedure recommendation without privacy leakage to unauthorized parties. We conduct extensive experiments and analysis to evaluate the efficiency.

Robust biomolecular finite automata

We present a uniform method for translating an arbitrary nondeterministic finite automaton (NFA) into a deterministic mass action input/output chemical reaction network (I/O CRN) that simulates it. The I/O CRN receives its input as a continuous time signal consisting of concentrations of chemical species that vary to represent the NFA's input string in a natural way. The I/O CRN exploits the inherent parallelism of chemical kinetics to simulate the NFA in real time with a number of chemical species that is linear in the size of the NFA. We prove that the simulation is correct and that it is robust with respect to perturbations of the input signal, the initial concentrations of species, the output (decision), and the rate constants of the reactions of the I/O CRN.

A Method to Convert Regular Expression into Non-Deterministic Finite Automata

A Method to Convert Regular Expression into Non-Deterministic Finite Automata

Temporal determinization of mutating finite automata: Reconstructing or restructuring

SummaryA 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.

Multi-period data driven control strategy for real-time management of energy storages in virtual power plants integrated with power grid

This paper investigates a novel real-time stochastic multi-period management strategy of a virtual power plant (VPP) using a three-layer language protocol based on computer program compiler principle, which takes advantage of the availability of the battery storage in a VPP to maximize the revenue of the VPP over the entire trading horizon considering the predicted prices in each slice of that horizon. When the conventional scenario tree method is used to solve the computational complexity of the multi-period stochastic optimization problem, it may cause the problem to become intractable when the problem-scale increases. This paper proposes a deterministic lookahead approach that makes use of a novel formal language that implements a special formal grammar to manage the real-time control on the battery storages of the VPP. The control of charging/discharging of the battery storages, which is driven by the real-time spot price and the rolling price prediction, is formalized by using the proposed recursive grammar and the corresponding non-deterministic finite automaton (NFA). For validation, the proposed approach is applied to a simple three-bus and an adapted IEEE 14-bus test system. The simulation results show that the proposed method can obtain optimal revenue by managing each battery in the VPP to operate as a local generator, a local load, an energy buyer, an energy seller, or by being in an idle state when the battery is full or empty.

A Novel Approach to Data Extraction on Hyperlinked Webpages

The World Wide Web has an enormous amount of useful data presented as HTML tables. These tables are often linked to other web pages, providing further detailed information to certain attribute values. Extracting schema of such relational tables is a challenge due to the non-existence of a standard format and a lack of published algorithms. We downloaded 15,000 web pages using our in-house developed web-crawler, from various web sites. Tables from the HTML code were extracted and table rows were labeled with appropriate class labels. Conditional random fields (CRF) were used for the classification of table rows, and a nondeterministic finite automaton (NFA) algorithm was designed to identify simple, complex, hyperlinked, or non-linked tables. A simple schema for non-linked tables was extracted and for the linked-tables, relational schema in the form of primary and foreign-keys (PK and FK) were developed. Child tables were concatenated with the parent table’s attribute value (PK), serving as foreign keys (FKs). Resultantly, these tables could assist with performing better and stronger queries using the join operation. A manual checking of the linked web table results revealed a 99% precision and 68% recall values. Our 15,000-strong downloadable corpus and a novel algorithm will provide the basis for further research in this field.

On the stabilization of nondeterministic finite automata via static output feedback

A nondeterministic finite automaton (NDFA) can exhibit an uncertain behavior in modeling and analysis, and its stabilization is viewed as an essential component of theoretical research. In this paper, we focused on the problem of static output feedback stabilization of NDFA under the framework of matrix semi-tensor product (matrix STP). First, the dynamics of Moore-type NDFA can be described as a discrete-time bilinear expression by a matrix-based modeling approach. Subsequently, equilibrium point and closed transition matrix of NDFA are introduced, and the corresponding computational formulas are given based on the new matrix expression. By utilizing the matrix STP approach, we can obtain the necessary and sufficient conditions to implement the static state output feedback stabilization for NDFA. Meanwhile, starting from the matrix STP, we designed a systematic procedure to seek the controller through an extended output feedback feasible event set. Finally, an illustrative example is provided to prove the efficacy of newly proposed method. Current results are conducive to better understand and devise the effective finite automata for discrete event systems.

Branching Measures and Nearly Acyclic NFAs

To get a more comprehensive understanding of the amount of branching in computations of a nondeterministic finite automaton (NFA), we introduce and study the string path width and depth path width measures. For a given NFA, the string path width on a string [Formula: see text] counts the number of all complete computations on [Formula: see text], and the depth path width on an integer [Formula: see text] counts the number of complete computations on all strings of length [Formula: see text]. We give an algorithm to decide the finiteness of the depth path width of an NFA. Deciding finiteness of string path width can be reduced to the corresponding question on ambiguity. An NFA is nearly acyclic if any computation can pass through at most one cycle. The class of nearly acyclic NFAs consists of exactly all NFAs with finite depth path width. Using this characterization we show that the finite depth path width of an [Formula: see text]-state NFA over a [Formula: see text]-letter alphabet is at most [Formula: see text] and that this bound is tight. The nearly acyclic NFAs recognize exactly the class of constant density regular languages.

One-Time Nondeterministic Computations

We introduce the concept of one-time nondeterminism as a new kind of limited nondeterminism for finite state machines and pushdown automata. Roughly speaking, one-time nondeterminism means that at the outset the computation is nondeterministic, but whenever it performs a guess, this guess is fixed for the rest of the computation. We characterize the computational power of one-time nondeterministic finite automata (OTNFAs) and one-time nondeterministic pushdown devices. Moreover, we study the descriptional complexity of these machines. For instance, we show that for an [Formula: see text]-state OTNFA with a sole nondeterministic state, that is nondeterministic for only one input symbol, [Formula: see text] states are sufficient and necessary in the worst case for an equivalent deterministic finite automaton. In case of pushdown automata, the conversion of a nondeterministic to a one-time nondeterministic as well as the conversion of a one-time nondeterministic to a deterministic one turn out to be non-recursive, that is, the trade-offs in size cannot be bounded by any recursive function.