Finite State Automata Research Articles

Utilization of the Whale Optimization Algorithm in Finite State Automata Design for Advanced Pattern Recognition Systems

This research explores the application of the Whale Optimization Algorithm (WOA) in designing Finite State Automata (FSA) for advanced pattern recognition systems. Pattern recognition plays a crucial role in various fields, requiring high accuracy and efficiency. Traditional approaches to FSA design often face limitations in adaptability and optimization. By integrating WOA, a nature-inspired metaheuristic algorithm, this study aims to optimize FSA structures to improve recognition capabilities. The research process involves implementing WOA within the FSA design framework, testing it on multiple artificial pattern recognition tasks to assess effectiveness, and comparing results with other optimization methods. The findings reveal that after 10 iterations, the WOA achieved a best score of 14.01% error, indicating initial progress but room for further improvement. At 50 iterations, the performance plateaued, maintaining a score of 9.43% error, suggesting a need for additional exploration of the parameter space. However, by 100 iterations, the WOA produced a significantly improved score of 0.0022% error, demonstrating a highly optimized solution as the parameters converged closely to their target values. After 100 iterations, the error value did not decrease any further, indicating that the effective iteration count for optimization is 100 iterations. These results highlight the effectiveness of WOA in enhancing FSA performance, showcasing its potential as a robust solution for complex pattern recognition needs. This study contributes to the development of intelligent recognition systems, advancing the state of the art in pattern recognition technology.

Symbolic Automata: Omega-Regularity Modulo Theories

Symbolic automata are finite state automata that support potentially infinite alphabets, such as the set of rational numbers, generally applied to regular expressions and languages over finite words. In symbolic automata (or automata modulo A ), an alphabet is represented by an effective Boolean algebra A , supported by a decision procedure for satisfiability. Regular languages over infinite words (so called ω-regular languages) have a rich history paralleling that of regular languages over finite words, with well-known applications to model checking via Büchi automata and temporal logics. We generalize symbolic automata to support ω-regular languages via transition terms and symbolic derivatives , bringing together a variety of classic automata and logics in a unified framework that provides all the necessary ingredients to support symbolic model checking modulo A . In particular, we define: (1) alternating Büchi automata modulo A ( ABW A ) as well (non-alternating) nondeterministic Büchi automata modulo A ( NBW A ); (2) an alternation elimination algorithm Æ that incrementally constructs an NBW A from an ABW A , and can also be used for constructing the product of two NBW A ; (3) a definition of linear temporal logic modulo A , LTL ( A ), that generalizes Vardi’s construction of alternating Büchi automata from LTL, using (2) to go from LTL modulo A to NBW A via ABW A . Finally, we present RLTL ( A ), a combination of LTL ( A ) with extended regular expressions modulo A that generalizes the Property Specification Language (PSL). Our combination allows regex complement , that is not supported in PSL but can be supported naturally by using transition terms. We formalize the semantics of RLTL ( A ) using the Lean proof assistant and formally establish correctness of the main derivation theorem.

Implementation of Finite State Automata (FSA) Chart in the Process of Calculation of the Remainder of Two Numbers with an Infinite Many Digits

Electronic devices similar to calculator, both physical and application, are equipped with a feature to calculate the remainder (read: modulo) of two independent numbers. The problem is that there is a limited size of the display screen and memory to accommodate data on the device so that the number of digits to be processed is very limited. This research offers a solution in the form of using a Finite State Automata (FSA) chart to carry out the process ofcalculating the remainder of two independent numbers A and B with an unlimited number of digits, where A is the numerator and B is the denominator, written in the format A mod B. Second A and B values must be integers. The value of numerator must be greater than the denominator so that the process of calculating the remainder can be carried out, because if the value of the numerator is the same as the denominator then the remainder is 0 (zero), whereas if the value of the numerator is less than the denominator then the remainder is the same as the numerator itself. The remainder of the quotient is a number between 0..(B-1). The use of FSA chart in this research will ensure that the calculation process will take place in stages for each digit of the numerator being processed. This method also allows the process to be stopped at any time to see the remainder of the results from the starting digit to the digit at the stopping point. From the experiments that have been carried out, we obtained perfect accuracy results from the FSA chart when used to calculate the remainder for any value A and B even though the number of A digits is very large. Thus, this research can be an alternative method for calculating the remainder of two independent numbers.

Rational gluing in edge replacement systems

In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite state automaton that recognizes pairs of equivalent sequences that are glued in the fractal. This fits in recent interest toward the rationality of gluing relations on totally disconnected compact metrizable spaces.

Critical Observability Enforcement in Discrete Event Systems Using Differential Privacy

In the context of discrete event systems (DESs), critical states usually refer to a system configuration of interest, describing certain important system properties, e.g., fault diagnosability, state/language opacity, and state/event concealment. Technically, a DES is critically observable if an intruder can always unambiguously infer, by observing the system output, whether the plant is currently in a predefined set of critical states or the current state set is disjointed with the critical states. In this paper, given a partially observable DES modeled with a finite-state automaton that is not critically observable, we focus on how to make it critically observable, which is achieved by proposing a novel enforcement mechanism based on differential privacy (DP). Specifically, we consider two observations where one observation cannot determine whether a system is currently in the predefined critical states (i.e., the observation violating the critical observability) while the other is randomly generated by the system. When these two observations are processed separately by the differential privacy mechanism (DPM), the system generates an output, exposed to the intruder, that is randomly modified such that its probability approximates the two observations. In other words, the intruder cannot determine the original input of a system by observing its output. In this way, even if the utilized DPM is published to the intruder, they are unable to identify whether critical observability is violated.

Construction of a probabilistic finite state automaton by entropy reduction over context trees

Construction of a probabilistic finite state automaton by entropy reduction over context trees

Variable-State-Trigger: A Formal Model of Smart Contracts Based on Conditional Response and Finite State Automata and Its Application

As one of the technical elements supporting the blockchain to realize decentralized autonomous organizations, smart contracts are crucial for understanding the inherent properties of blockchain systems through formal research. Most existing formal models of smart contracts focus primarily on static properties, lacking the depiction of dynamic processes such as conditional responses and internal state migration during contract execution, which complicates effective supervision. In this paper, a novel formal model of smart contracts, based on finite state automata, named Variable-State-Trigger (VST), is proposed, which presents state migration and conditional response mechanisms during smart contract execution. The VST model is verified to portray both the static and dynamic properties of smart contracts, providing new avenues for effective supervision during contract execution. Moreover, the VST model is used to illustrate the life cycle of a UAV mission smart contract, demonstrating its feasibility. With the growing integration of blockchain and emerging technologies, smart contracts have found applications in various fields, including drone swarm coordination. In this context, smart contracts enable secure, decentralized management and automation of interactions between autonomous drones, ensuring compliance with predefined conditions and enhancing the reliability of complex drone operations. The VST model can be extended to such applications, offering dynamic supervision and enhancing the coordination efficiency in decentralized autonomous drone systems.

Latvian Quantum Finite State Automata for Unary Languages

We design Latvian quantum finite state automata (LQFAs) recognizing unary regular languages with isolated cut point [Formula: see text]. From an architectural viewpoint, we suitably combine two LQFAs recognizing with isolated cut point, respectively, the finite part and the ultimately periodic part any given unary regular language [Formula: see text] consists of. In particular, both these LQFAs incorporate a sub-module discriminating strings on the basis of their length. Both the number of basis states and the isolation around the cut point of the resulting LQFAs for [Formula: see text] exponentially depend on the size of the minimal deterministic finite state automaton for [Formula: see text]. Moreover, the recognition of [Formula: see text] tends to becoming deterministic as the number of the basis states employed in the length-discriminating sub-module grows.

Sentiment Mining in E-Commerce

Sentiment analysis is crucial for comprehending customer feedback and enhancing workplace culture, as well as improving products and services. By employing natural language processing (NLP) techniques to meticulously analyze this feedback, organizations can identify specific areas that require improvement, address employee issues, and cultivate a positive work environment. These deep learning models powered by NLP offer invaluable tools for HR and sales departments in the e-commerce sector, enabling them to track sentiment trends among employees and users over time and implement targeted interventions. Focusing on the e-commerce industry, this study employs NLP-driven deep learning methodologies to analyze both employee and user feedback, with the objective of identifying underlying sentiments. The proposed framework leverages these advanced techniques to categorize user feedback into positive, negative, or neutral sentiments. This approach aims to develop a robust and effective system for sentiment analysis, providing significant insights that can help drive organizational improvements and enhance customer satisfaction. The key steps of this framework include data collection, NLP-enhanced feature extraction, sentiment detection, and final classification using finite-state automata. The effectiveness of this NLP-centric approach was tested on diverse datasets of customer feedback collected from an e-commerce industry. Evaluation metrics such as accuracy, precision, and recall were utilized to assess the performance of the system. The results demonstrate the effectiveness of the proposed framework, achieving a 93.75% accuracy rate and surpassing existing benchmark methods. The outcomes of this study are particularly consequential for the e-commerce sector, offering them a strategic advantage in refining their product portfolios and cultivating a more dynamic workplace culture

Representation of Vending Device using Finite State Automata

Automata theory predominates in a number of applications derived using the technique of a finite state machine . In the paper, we study the representation of a vending machine (VM) that enhances the academic institution’s book delivery service using the concepts of the computation theories. The effectiveness regarding the virtual machine(VM) is viewed as a problem. Automata theory relies on the finite state machine (FSM) design to increase efficiency. The different components of a vending machine are examined at, and it is determined how they can be modelled as finite state machines. We go over the architectural considerations for vending machines, such as the selection of components, the layout of the machine, and the selection of input and output approaches. We use the theory of computation to examine the constraints and difficulties in vending machine design. The paper will design an FSM with fewer states in the end. As a result, we will learn how to increase the VM’s design effectiveness and cost.

Advancements in Cooperative Mobile Robots Control Strategies for Large-Scale Material Transport

This paper explores groundbreaking advancements in control strategies for cooperative mobile robots used in large-scale material transport, a critical aspect of modern industrial, manufacturing, logistics, and construction sectors. It delves into the development of sophisticated systems that enable seamless coordination among multiple mobile robot systems. The research presents a novel hierarchical finite state automaton for dynamic mission adaptation and a null space-based control scheme for precise task execution and enhanced system resilience. The introduction of Mecanum wheels facilitates flexible movement and manipulation of materials, thereby increasing operational efficiency and safety. Cutting-edge sensory technology, including LiDAR, and the implementation of the Robot Operating System are highlighted for their roles in enhancing autonomous navigation and intelligent operation. Additionally, the paper discusses the impact of centralized and decentralized control methods in ensuring safe, cooperative object transport. The findings contribute to the vision of Industry 4.0 by promoting the integration of automation and robotic cooperation in complex environments and present a foundational blueprint for further research. Challenges for future work such as scalability, communication efficiency, collision avoidance, and energy efficiency are also considered, underscoring the need for ongoing development of robust and scalable robotic systems to address modern transport challenges.

Transliteration of Latin Letters to Bali Characters Based on Unicode for Mobile Devices using Finite State Automata and Levenshtein Distance

The preservation of Balinese script writing has been pursued by the local government with the issuance of the Bali Province Regional Regulation Number 1 of 2018 concerning Balinese Language, Script, and Literature. However, the use of Balinese script in daily life is declining, especially among generation Z, most of whom find Balinese language difficult to use and have never been taught it. Technological advances, particularly smartphone technology, can play an important role in shaping generation Z's habits, values, and social interaction patterns. This research uses the Finite State Automata (FSA) method to convert Latin letters to the Balinese script Unicode standard, following the Balinese script writing rules. FSA governs transliteration behavior by using the working principles of State, Event, and Action. Besides transliterating sentences typed by users, the application produced by this research also displays Balinese script words related to the words typed by users using the Levenshtein Distance method. The ‘related words’ feature allows users to know more about Balinese script than just the typed word. From the test results conducted through two different test cases, the first test case tested the application's ability to transliterate words/sentences typed by users without selecting words from the application's suggestions. The results showed that of the 50 words tested, 39 were correctly transliterated. The second test case tested the app's ability when the user selects a word from the suggestions given by the app. The result shows that out of 50 words tested, 43 transliteration data are correct, with the total accuracy of both test cases being 82%.

Cascade products and Wheeler automata

The Krohn-Rhodes Decomposition Theorem (KRDT) holds a central position in automata and semigroup theories. It asserts that any finite-state automaton can be broken down into a collection, a cascade, of automata of two simple types (reset and permutation) that, combined, simulate the original automaton.In this paper we show how the cascade product operation and the related decomposition are particularly well-suited for the class of Wheeler automata. In these automata, recently introduced in the context of data compression, states are ordered and transitions map state-intervals to state-intervals. First, we prove that Wheeler DFAs are closed under cascade products in an efficient way: the cascade product of two Wheeler automata is still a Wheeler automaton and has always a number of states which is at most the sum (after removing unreachable states) of the number of states of the two input automata, a result that cannot be achieved for general (even counter-free) automata. Second, we prove that each Wheeler automaton can be decomposed into a cascade of a linear number of reset blocks. Crucially, our line of reasoning avoids the necessity of using full KRDT and proves our results directly by an inductive argument.

Design and Implementation of English to Yorùbá Verb Phrase Machine Translation System

The Yorùbá ethnic group has diverse language speakers across the world, and translating the language to other widely spoken languages must be emphasized. This study aims to develop an English to Yorùbá machine translation system which can translate the English verb phrase text to its Yorùbá equivalent. Words from both languages (Source Language and Target Language) were collected for the verb phrase group in the home domain. Lexical translation was done by assigning values of the matching word in the dictionary. The syntax of the two languages was realized using Context Free Grammar, the rewrite rules were validated with finite state automata. Human evaluation method was used and expert opinion scored. The evaluation shows the system performed better than that of sampled Google translation with over 70% of the responses matching that of the system’s output.

Optimization of Time-Ordered Processes in the Finite and Asymptotic Regimes

Many problems in quantum information theory can be formulated as optimizations over the sequential outcomes of dynamical systems subject to unpredictable external influences. Such problems include many-body entanglement detection through adaptive measurements, computing the maximum average score of a preparation game over a continuous set of target states, and limiting the behavior of a (quantum) finite-state automaton. In this work, we introduce tractable relaxations of this class of optimization problems. To illustrate their performance, we use them to: (a) compute the probability that a finite-state automaton outputs a given sequence of bits; (b) develop a new many-body entanglement-detection protocol; and (c) let the computer an adaptive protocol for magic state detection. As we further show, the maximum score of a sequential problem in the limit of infinitely many time steps is in general incomputable. Nonetheless, we provide general heuristics to bound this quantity and show that they provide useful estimates in relevant scenarios. Published by the American Physical Society 2024

A technical research survey on bio-inspired intelligent optimization grouping algorithms for finite state automata in intrusion detection system

A technical research survey on bio-inspired intelligent optimization grouping algorithms for finite state automata in intrusion detection system

Yet another canonical nondeterministic automaton

Several canonical forms of finite automata have been introduced over the decades. In particular, if one considers the minimal deterministic finite automaton (DFA), the canonical residual finite state automaton (RFSA), and the átomaton of a language, then the átomaton can be seen as the dual automaton of the minimal DFA, but no such dual has been presented for the canonical RFSA so far. We fill this gap by introducing a new canonical automaton that we call the maximized prime átomaton, and study its properties. We also describe how these four automata can be extracted from suitable observation tables used in the automata learning context.

A Learning-Based Approach for Diagnosis and Diagnosability of Unknown Discrete Event Systems.

This article develops a novel active-learning technique for fault diagnosis of an initially unknown finite-state discrete event system (DES). The proposed method constructs a diagnosis tool (termed diagnoser), which is able to detect and identify occurred faults by tracking the observable behaviors of the system under diagnosis. The proposed algorithm utilizes an active-learning mechanism to incrementally collect the information about the system to construct the diagnoser. This is achieved by completing a series of observation tables in a systematic way, resulting in the construction of the diagnoser. It is proven that the proposed algorithm terminates after a finite number of iterations and returns a correctly conjectured diagnoser. The developed diagnoser is a deterministic finite-state automaton. Furthermore, we have proven that the developed diagnoser consists of a minimum number of states. A sufficient condition for diagnosability of the system under diagnosis is derived, which guarantees the diagnosis of faults within a bounded number of observations. The developed method is applied to two case-studies, illustrating the steps of the proposed algorithm and its capability of diagnosing multiple faults.

Iterative Reconstruction of Micro Computed Tomography Scans Using Multiple Heterogeneous GPUs.

Graphics processing units (GPUs) facilitate massive parallelism and high-capacity storage, and thus are suitable for the iterative reconstruction of ultrahigh-resolution micro computed tomography (CT) scans by on-the-fly system matrix (OTFSM) calculation using ordered subsets expectation maximization (OSEM). We propose a finite state automaton (FSA) method that facilitates iterative reconstruction using a heterogeneous multi-GPU platform through parallelizing the matrix calculations derived from a ray tracing system of ordered subsets. The FSAs perform flow control for parallel threading of the heterogeneous GPUs, which minimizes the latency of launching ordered-subsets tasks, reduces the data transfer between the main system memory and local GPU memory, and solves the memory-bound of a single GPU. In the experiments, we compared the operation efficiency of OS-MLTR for three reconstruction environments. The heterogeneous multiple GPUs with job queues for high throughput calculation speed is up to five times faster than the single GPU environment, and that speed up is nine times faster than the heterogeneous multiple GPUs with the FIFO queues of the device scheduling control. Eventually, we proposed an event-triggered FSA method for iterative reconstruction using multiple heterogeneous GPUs that solves the memory-bound issue of a single GPU at ultrahigh resolutions, and the routines of the proposed method were successfully executed on each GPU simultaneously.

Finite-state relative dimension, dimensions of A. P. subsequences and a finite-state van Lambalgen's theorem

Finite-state dimension, introduced by Dai, Lathrop, Lutz and Mayordomo quantifies the information rate in an infinite sequence as measured by finite-state automata. In this paper, we define a relative version of finite-state dimension. The finite-state relative dimension dimFSY(X) of a sequence X relative to Y is the finite-state dimension of X measured using the class of finite-state gamblers with oracle access to Y. We show its mathematical robustness by equivalently characterizing this notion using the relative block entropy rate of X conditioned on Y.We derive inequalities relating the dimension of a sequence to the relative dimension of its subsequences along any arithmetic progression (A. P.). These enable us to obtain a strengthening of Wall's Theorem on the normality of A. P. subsequences of a normal sequence, in terms of relative dimension. In contrast to the original theorem, this stronger version has an exact converse yielding a new characterization of normality.We also obtain finite-state analogues of van Lambalgen's theorem on the symmetry of relative normality.