State Automata Research Articles

Overlay Automata and Algorithms for Fast and Scalable Regular Expression Matching

Regular expression (RegEx) matching, the core operation of intrusion detection and prevention systems, remains a fundamentally challenging problem. A desired RegEx matching scheme should satisfy four requirements: deterministic finite state automata (DFA) speed, nondeterministic finite state automata (NFA) size, automated construction, and scalable construction. Despite lots of work on RegEx matching, no prior scheme satisfies all four of these requirements. In this paper, we approach this holy grail by proposing OverlayCAM, a RegEx matching scheme that satisfies all four requirements. The theoretical underpinning of our scheme is overlay delayed input DFA, a new automata model proposed in this paper that captures both state replication and transition replication, which are inherent in DFAs. Our RegEx matching solution processes one input character per lookup like a DFA, requires only the space of an NFA, is grounded in sound automata models, is easy to deploy in existing network devices, and comes with scalable and automated construction algorithms.

Finite State Automata as Analyzers of certain Grammar Class Rules in the Khasi Language

In this paper the concept of Finite states is applied to design Recognizers for certain morphemes in Khasi language. Individual Grammar Class is implemented using Finite State Automata. Then Finite state automata are implemented to design a Morphological Analyzer for Nouns and Verbs. These Finite state automata can be concatenated one after the other to recognize Sentence Rules. Hence these can be used to design a Morphological Analyzer for legitimate sentences in the Khasi language.

Quantum Actin Automata and Three-Valued Logics

Actin is a filament-forming protein responsible for communication, information processing and decision making in eukariotic cells. To show how computation can be implemented on actin filaments we model actin as a helix of two 1-D quantum automata arrays. The model advances our previous work by exploiting the quantum aspects of the automaton (superposition). We use selected functions of automaton state transitions to compute examples of actin automata evolution and to realize three-valued logical gates in the actin automata. Implementation of operators of several three-valued logical systems is demonstrated on examples. Our results lay a ground for theoretical studies, and possible future experimental laboratory implementations of multiple-valued logical circuits.

An Affordance-Based Model of Human Action Selection in a Human–Machine Interaction System with Cognitive Interpretations

Current technology is not sufficient to automate all desired tasks. Human–machine interaction (HMI) has thus become a key control and design factor for tasks requiring human-level decision-making or information synthesis. Such processes require a formal representation of human actions (including decision-making) when modeling HMI systems; however, successful prescriptive approaches to this end have still been elusive. This article extends the affordance-based finite state automata model, conditioning human prior experience and natural memory decay of task knowledge (or skill decay). The new model draws upon both reinforcement learning and natural memory decay for decision-making on action choice. An empirical study is carried out to specify how action choice is affected or updated by reinforcement learning based on past experience, and Wickelgren’s decay function is jointly employed to predict human decision-making behavior.

Coding tree languages based on lattice-valued logic

We consider tree automata based on complete residuated lattice-valued (for simplicity we write L-valued) logic. First, we define the concepts of response function and accessible states (with threshold c) of an L-valued tree automaton. Thereafter, we consider coding of trees and investigate the relation between response function on trees and their coding. Using the provided theorems, we give a pumping lemma for recognizable coding tree languages with threshold c. Moreover, we consider closure properties of recognizable coding tree languages. In this regard, we show that the class of recognizable coding tree languages with threshold c is closed under projection, intersection and union.

Two population three-player prisoner’s dilemma game

Due to the computational advantage in symmetric games, most researches have focused on the symmetric games instead of the asymmetric ones which need more computations. In this paper, we present prisoner’s dilemma game involving three players, and suppose that two players among them agree against the third player by choosing either to cooperate together or to defect together at each round. According to that assumption, the game is transformed from the symmetric three- player model to asymmetric two-player model such that, the identities of the players cannot be interchanged without interchanging the payoff of the strategies. Each strategy in the resulting model is expressed with two state automata. We determine the payoff matrix corresponding to the all possible strategies. We noticed that, for some strategies, it is better to be a player of the first type (independent player) than being of the second type (allies).

On the number of accepting states of finite automata

In this paper, we start a systematic study of the number of accepting states. For a regular language L, we define the complexity asc(L) as the minimal number of accepting states necessary to accept...

Computation of regular expression derivatives

The conversion of regular expressions into finite state automata and finite state automata into regular expression is an important area of research in automata theory. The notion of derivatives of regular expressions has been introduced to make the construction of finite state automata from regular expressions in a natural way. Recently, a general structure has been proposed to find the derivatives of regular expressions to reduce the difficulties arising out of the earlier methods. In this paper, some properties of the derivatives of regular expressions, the quotient language, and how the derivatives are found through a general structure, have been discussed in detail.

Investigations on Automata and Languages Over a Unary Alphabet

The investigation of automata and languages defined over a one letter alphabet shows interesting differences with respect to the case of alphabets with at least two letters. Probably, the oldest example emphasizing one of these differences is the collapse of the classes of regular and context-free languages in the unary case (Ginsburg and Rice, 1962). Many differences have been proved concerning the state costs of the simulations between different variants of unary finite state automata (Chrobak, 1986, Mereghetti and Pighizzini, 2001). We present an overview of these results. Because important connections with fundamental questions in space complexity, we give emphasis to unary two-way automata. Furthermore, we discuss unary versions of other computational models, as probabilistic automata, one-way and two-way pushdown automata, even extended with auxiliary workspace, and multi-head automata.

Symbolic Computation Using Cellular Automata-Based Hyperdimensional Computing.

This letter introduces a novel framework of reservoir computing that is capable of both connectionist machine intelligence and symbolic computation. A cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells, and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is shown to be capable of long-term memory, and it requires orders of magnitude less computation compared to echo state networks. As the focus of the letter, we suggest that binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing. To demonstrate the capability of the proposed system, we make analogies directly on image data by asking, What is the automobile of air?

Design knowledge representation to support personalised additive manufacturing

ABSTRACTThis research aims to develop a set of new formal design representations that captures design requirements to improve the level of personalisation while taking advantage of the additive manufacturing (AM)-enabled design freedom. We propose a formal design process structure called design for AM-facilitated personalisation that merges design for personalisation and design for additive manufacturing. Also, we propose formal representations for an artefact–user interaction using finite state automata and goal-oriented user behaviours in the artefact use as formal language sets based on discrete event systems. By adopting the relational properties of affordance, effectivity, and preference, the proposed formal representations systemically link user behaviour-related artefact properties and user preferences to the design requirements for additive manufactured artefacts. This paper presents a case study of personalised chair design and a simulation of user behaviours in the chair–user interaction.

Directable Fuzzy Automata

The aim of this paper is testing the directability of a given fuzzy automaton. A fuzzy automaton is directable if there exists a word, a directing word, which takes each state of a fuzzy automaton to a single state with some membership value. In this paper, we proposed a method for testing the directability of a fuzzy automaton using the mergeability relation.

The effect of noise and average relatedness between players in iterated games

In the real world, repetitive game theory has an influential and effective role, especially in political, economic, biological, social sciences and many other sciences. In this work we are exposed to study the effect of noise on the degree of relatedness between the players with respect to the behavior of strategies and its payoff. Our model in this work is the infinitely repeated prisoner’s dilemma (PD) game. Because our game is infinitely repeated, we consider any strategy of the game represented by a finite states of automaton (two states). By considering the possibility of a small error in implementation of an automaton, we obtained the payoff matrix for all strategies. Consequently we could identify the behavior of some of the strategies.

Profile trees for Büchi word automata, with application to determinization

The determinization of Büchi automata is a celebrated problem, with applications in synthesis, probabilistic verification, and multi-agent systems. Since the 1960s, there has been a steady progress of constructions: by McNaughton, Safra, Piterman, Schewe, and others. Despite the proliferation of solutions, they are all essentially ad-hoc constructions, with little theory behind them other than proofs of correctness. Since Safra, all optimal constructions employ trees as states of the deterministic automaton, and transitions between states are defined operationally over these trees. The operational nature of these constructions complicates understanding, implementing, and reasoning about them, and should be contrasted with complementation, where a solid theory in terms of automata run dags underlies modern constructions.In 2010, we described a profile-based approach to Büchi complementation, where a profile is simply the history of visits to accepting states. We developed a structural theory of profiles and used it to describe a complementation construction that is deterministic in the limit. Here we extend the theory of profiles to prove that every run dag contains a profile tree with at most a finite number of infinite branches. We then show that this property provides a theoretical grounding for a new determinization construction where macrostates are doubly preordered sets of states. In contrast to extant determinization constructions, transitions in the new construction are described declaratively rather than operationally.

Fault diagnosis of dynamical systems using recurrent fuzzy systems with application to an electrohydraulic servo axis

This paper presents a novel approach for fault isolation based on discrete-time recurrent fuzzy systems (DTRFS) extending the well-known static fuzzy systems for fault isolation. The DTRFS additionally allows for the isolation of faults causing dynamic residuals and the isolation of multiple subsequently occurring faults. Due to the flexibility of the DTRFS, multiplicative as well as additive faults can be handled. The approach is applied to an electrohydraulic servo axis with a duplex valve system. Experimental results at the testbed underline the effectiveness and applicability of the approach and show the enhanced performance compared to static fuzzy systems and state automata.

Comparison of modeling formalisms for Safety Analyses: SAML and AltaRica

Many states/transitions formalisms have been proposed in the literature to perform Safety Analyses. In this paper we compare two of them: SAML and AltaRica. These formalisms have been developed by different communities. Their “look-and-feel” are thus quite different. Yet, their underlying mathematical foundations are very similar: both of them rely on state automata. It is therefore of interest to study their ability to assess the reliability of systems, their respective advantages and drawbacks and to seek for opportunities of a cross fertilization.

LR Rotation Rule for Creating Minimal NFA

The problem of creating a minimal NFA is a primal (fundamental) problem. Reducing the size of NFA by using LR rotation rule has been shown to reduce importantly the search time. In [1] Ilie and Yu describe a construction of a right invariant equivalence relation on the states of a nondeterministic finite state automaton. We give a more efficient LR Rotation rule for constructing the minimal NFA. In this paper we represent new LR Rotation rule for the state minimization of NFA. The description of the proposed methods is given and we also shown the results of the numerical experiments. We conceive the problem of reducing the number of state and transition of Non Deterministic Finite Automata. Numerical experiments show that NFA reduction algorithm produces a minimal automation in all most cases. NFA reduction algorithm also reduces the complexity of Kameda-Weiner algorithm. We have shown empirically that these algorithms are effective in largely reducing the memory requirement of NFA minimization algorithm and algorithm minimization of the number of rules for NFA grows each year.

Actin quantum automata: Communication and computation in molecular networks

Actin is filament-forming protein forming a communication and information processing cytoskeletal network of eukaryotic cells. Actin filaments play a key role in developing synaptic structure, memory and leaning of animals and humans; many psychiatric and neurological disorders are due to disfunction in the assembly of actin fibres. This is why it is important to develop abstractions of the information processing on the actin filaments. We model actin filaments as two chains of one-dimensional quantum automata arrays to describe hypothetical signalling events propagating along the chains. We study in detail several functions of automaton state transitions and compute examples of evolution to illustrate behaviour of the functions and a role of the superposition of the initial states. We uncover and analyse localisations, or particles, propagating along the actin chains. We demonstrate that logical gates can be realised in the result of the collisions. Using collisions between the travelling particles we implement binary adder.

Cardinality estimates for some classes of regular languages

AbstractWe consider a method that modifies regular expressions in order to solve the “exponential explosion” problem on the number of states of the finite automaton that recognizes a set of regular languages defined by the union of regular expressions of the form .∗ R

Конечные автоматы в теории алгебраических схем программ

Algebraic models of programs considered in this paper generalize two models of programs introduced by A.A. Lyapunov and A.A. Letichevsky. The theory of these models focuses on the equivalence checking problem for program schemata which are formalization of imperative programs. We prove that this problem is decidable for a wide class of algebraic models of programs. Our decision techniques are based on the approach to the equivalence checking problem for finite state automata. The aim of this paper is to reveal this relationship.