Nondeterministic Finite Automata Research Articles

Robust models to infer flexible nondeterministic finite automata

Grammatical inference involves learning a formal grammar as a finite state machine or a set of rewrite rules. This paper focuses on inferring nondeterministic finite automata (NFA) from a given sample of words: the NFA must accept some words, and reject the others. To address this task we construct several over-constrained inference models capable of finding NFA of size k+1, which are directly convertible to NFA of size k. Additionally, we propose an NFA evaluation method based on random walks along with two methods used to enhance the acceptance rates of the inferred NFA. The effectiveness of our approach is demonstrated through the results of comprehensive experiments conducted on several benchmark sets. This paper is an extended version of the ICCS 2023 paper entitled “Inference of over-constrained NFA of size k+1 to efficiently and systematically derive NFA of size k for grammar learning” (Jastrzab et al., 2023 [1]).

Converting finite width AFAs to nondeterministic and universal finite automata

The maximal existential (respectively, universal) width of an alternating finite automaton (AFA) on a string w is the maximal number of existential choices encountered in one branch (respectively, the maximal number of universal parallel branches) of a computation of A on w. We give upper bounds for the size of a nondeterministic finite automaton simulating an AFA of finite maximal universal width and for the size of a universal finite automaton simulating an AFA of finite maximal existential width. We give lower bounds for the transformations that are tight within a multiplicative factor that depends only on the universal (respectively, existential) width of the AFA.

Jump complexity of finite automata with translucent letters

We define the jump complexity of a finite automaton with translucent letters as a function that computes the smallest upper bound on the number of jumps needed by the automaton in order to accept each word of length n, for any positive integer n. We prove that a sufficient condition for a finite automaton with translucent letters to accept a regular language is to have a jump complexity bounded by a constant. Along the same lines, we show that there are languages which require a jump complexity in Ω(n) of any finite automaton with translucent letters accepting one of these languages. We also show that there exist nondeterministic finite automata with translucent letters of jump complexity in O(log⁡n) and O(n) that accept non-regular languages. Several open problems and directions for further developments are finally discussed.

Efficient Matching of Regular Expressions with Lookaround Assertions

Regular expressions have been extended with lookaround assertions, which are subdivided into lookahead and lookbehind assertions. These constructs are used to refine when a match for a pattern occurs in the input text based on the surrounding context. Current implementation techniques for lookaround involve backtracking search, which can give rise to running time that is super-linear in the length of input text. In this paper, we first consider a formal mathematical semantics for lookaround, which complements the commonly used operational understanding of lookaround in terms of a backtracking implementation. Our formal semantics allows us to establish several equational properties for simplifying lookaround assertions. Additionally, we propose a new algorithm for matching regular expressions with lookaround that has time complexity O ( m · n ), where m is the size of the regular expression and n is the length of the input text. The algorithm works by evaluating lookaround assertions in a bottom-up manner. Our algorithm makes use of a new notion of nondeterministic finite automata (NFAs), which we call oracle-NFAs. These automata are augmented with epsilon-transitions that are guarded by oracle queries that provide the truth values of lookaround assertions at every position in the text. We provide an implementation of our algorithm that incorporates three performance optimizations for reducing the work performed and memory used. We present an experimental comparison against PCRE and Java’s regex library, which are state-of-the-art regex engines that support lookaround assertions. Our experimental results show that, in contrast to PCRE and Java, our implementation does not suffer from super-linear running time and is several times faster.

Error- and Tamper-Tolerant State Estimation for Discrete Event Systems Under Cost Constraints

This paper deals with the state estimation problem in discrete-event systems modeled with nondeterministic finite automata, partially observed via a sensor measuring unit whose measurements (reported observed symbols) may be vitiated by a malicious attacker. The attacks considered in this paper include arbitrary deletions, insertions, or substitutions of observed symbols by taking into account a bounded number of attacks or, more generally, a total cost constraint (assuming that each deletion, insertion, or substitution bears a positive cost to the attacker). We provide a characterization of the sequences of symbols that match the received sequence of possibly corrupted symbols, and subsequently use them to recursively perform tamper-tolerant state estimation subject to cost constraints. Each step of the recursive state estimation procedure has complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(|X||\Sigma |C)$</tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$|X|$</tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$|\Sigma |$</tex-math></inline-formula> ) is the number of states (events) of the given finite automaton and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C$</tex-math></inline-formula> is the maximum total cost that is allowed for all deletions, insertions, and substitutions.

Automated anomalous child repetitive head movement identification through transformer networks.

The increasing prevalence of behavioral disorders in children is of growing concern within the medical community. Recognising the significance of early identification and intervention for atypical behaviors, there is a consensus on their pivotal role in improving outcomes. Due to inadequate facilities and a shortage of medical professionals with specialized expertise, traditional diagnostic methods have been unable to effectively address the rising incidence of behavioral disorders. Hence, there is a need to develop automated approaches for the diagnosis of behavioral disorders in children, to overcome the challenges with traditional methods. The purpose of this study is to develop an automated model capable of analyzing videos to differentiate between typical and atypical repetitive head movements in. To address problems resulting from the limited availability of child datasets, various learning methods are employed to mitigate these issues. In this work, we present a fusion of transformer networks, and Non-deterministic Finite Automata (NFA) techniques, which classify repetitive head movements of a child as typical or atypical based on an analysis of gender, age, and type of repetitive head movement, along with count, duration, and frequency of each repetitive head movement. Experimentation was carried out with different transfer learning methods to enhance the performance of the model. The experimental results on five datasets: NIR face dataset, Bosphorus 3D face dataset, ASD dataset, SSBD dataset, and the Head Movements in the Wild dataset, indicate that our proposed model has outperformed many state-of-the-art frameworks when distinguishing typical and atypical repetitive head movements in children.

Real-time, constant-space, constant-randomness verifiers

We study the class of languages that have membership proofs which can be verified by real-time finite-state machines using only a constant number of random bits, regardless of the size of their inputs. Since any further restriction on the verifiers would preclude the verification of nonregular languages, this is the tightest computational budget which allows the checking of externally provided proofs to have meaningful use. We provide a full characterization of this class of languages in terms of a restricted version of the one-way nondeterministic multihead finite automaton model. For any k>0, there exist languages that cannot be recognized by any k-head one-way nondeterministic finite automaton, but that are nonetheless real-time verifiable in this sense. The set of nonpalindromes, which cannot be recognized by any one-way multihead deterministic finite automaton, is also demonstrated to be verifiable within these restrictions.

On the complexity of decision problems for some classes of machines and applications

We study the computational complexity of important decision problems — including general membership, fixed-machine membership, emptiness, disjointness, equivalence, containment, universe, and finiteness problems — for various restrictions and combinations of two-way nondeterministic reversal-bounded multicounter machines (2NCM) and two-way pushdown automata. We show that the general membership problem (respectively fixed membership problem) for 2NCM is NP-complete (respectively in P).We then give applications to some problems in coding theory. We examine generalizations of various types of codes with marginal errors. For example, a language L is k-infix-free if there is no non-empty string y in L that is an infix of more than k strings in L−{y}. Our general results imply the complexity of determining whether a given machine accepts a k-infix-free language, for one- and two-way deterministic and nondeterministic finite automata (answering an open question from the literature).

NAPOLY: A Non-deterministic Automata Processor OverLaY

Deterministic and Non-deterministic Finite Automata (DFA and NFA) comprise the core of many big data applications. Recent efforts to develop Domain-Specific Architectures (DSAs) for DFA/NFA have taken divergent approaches, but achieving consistent throughput for arbitrarily-large pattern sets, state activation rates, and pattern match rates remains a challenge. In this article, we present NAPOLY (Non-Deterministic Automata Processor OverLaY), an FPGA overlay and associated compiler. A common limitation of prior efforts is a limit on NFA size for achieving the advertised throughput. NAPOLY is optimized for fast re-programming to permit practical time-division multiplexing of the hardware and permit high asymptotic throughput for NFAs of unlimited size, unlimited state activation rate, and high pattern reporting rate. NAPOLY also allows for offline generation of configurations having tradeoffs between state capacity and transition capacity. In this article, we (1) evaluate NAPOLY using benchmarks packaged in the ANMLZoo benchmark suite, (2) evaluate the use of an SAT solver for allocating physical resources, and (3) compare NAPOLY’s performance against existing solutions. NAPOLY performs most favorably on larger benchmarks, benchmarks with higher state activation frequency, and benchmarks with higher reporting frequency. NAPOLY outperforms the fastest of the CPU and GPU implementations in 10 out of 12 benchmarks.

The nondeterministic state complexity of the site-directed deletion language operation

Site-directed deletion is a language operation inspired by the laboratory procedures entailed by polymerase chain reaction. Site-directed deletion contextually removes a contiguous substring provided it matches a guiding template string. The matching template must match the non-empty prefix and suffix of the substring, where upon the middle section not contained in the outfix is deleted. We consider the nondeterministic state complexity of site-directed deletion over the general alphabet as well as several special restricted forms.For regular languages recognized by nondeterministic finite automata with N and M states, respectively, we establish a new upper bound of 2NM+N and a new worst case lower bound of 2NM. The upper bound improves a previously established upper bound, and no non-trivial lower bound was previously known for the nondeterministic state complexity of site-directed deletion.

PSEUDO RANDOM KEY GENERATOR USING FRACTAL BASED TRELLIS CODED GENETIC ALGORITHM FOR IMAGE ENCRYPTION

Cryptographic applications such as online banking, and securing medical and military data require the usage of random keys, which should remain unpredictable by adversaries. This paper focuses on the strengths and limitations of the techniques and algorithms that are used in the generation of random keys and a new method to generate random keys is proposed using fractals. Fractals are generated using the Sierpinski triangle and fed as input for Non-Deterministic Finite Automata (NDFA) to generate an Initial Vector (IV). Trellis Coded Genetic Algorithm (TCGA) code generator generates seed value using IV as input. Pseudo-Random Key Generator (PRKG) generates a Session Key matrix (SKM) using a seed value. Images are encrypted using SKM to generate cipher images. The randomness of the TCGA code is tested using entropy measure and efficiency based on NIST Tests. SKM with high entropy value is used for image encryption. The Number of Pixel Change Rate (NPCR) and Unified Average Changing Intensity (UACI) values are used for calculating the randomness of cipher images.

Parsing as a lifting problem and the Chomsky-Sch\"utzenberger representation theorem

We begin by explaining how any context-free grammar encodes a functor of operads from a freely generated operad into a certain "operad of spliced words". This motivates a more general notion of CFG over any category $C$, defined as a finite species $S$ equipped with a color denoting the start symbol and a functor of operads $p : Free[S] \to W[C]$ into the operad of spliced arrows in $C$. We show that many standard properties of CFGs can be formulated within this framework, and that usual closure properties of CF languages generalize to CF languages of arrows. We also discuss a dual fibrational perspective on the functor $p$ via the notion of "displayed" operad, corresponding to a lax functor of operads $W[C] \to Span(Set)$. We then turn to the Chomsky-Sch\"utzenberger Representation Theorem. We describe how a non-deterministic finite state automaton can be seen as a category $Q$ equipped with a pair of objects denoting initial and accepting states and a functor of categories $Q \to C$ satisfying the unique lifting of factorizations property and the finite fiber property. Then, we explain how to extend this notion of automaton to functors of operads, which generalize tree automata, allowing us to lift an automaton over a category to an automaton over its operad of spliced arrows. We show that every CFG over a category can be pulled back along a ND finite state automaton over the same category, and hence that CF languages are closed under intersection with regular languages. The last important ingredient is the identification of a left adjoint $C[-] : Operad \to Cat$ to the operad of spliced arrows functor, building the "contour category" of an operad. Using this, we generalize the C-S representation theorem, proving that any context-free language of arrows over a category $C$ is the functorial image of the intersection of a $C$-chromatic tree contour language and a regular language.

High-Performance Row Pattern Recognition Using Joins

The SQL standard introduced MATCH_RECOGNIZE in 2016 for row pattern recognition. Since then, MATCH_RECOGNIZE has been supported by several leading relation systems, they implemented this function using Non-Deterministic Finite Automaton (NFA). While NFA is suitable for pattern recognition in streaming scenarios, the current uses of NFA by the relational systems for historical data analysis scenarios overlook important optimization opportunities. We propose a new approach to use Join to speed up row pattern recognition in historical analysis scenarios for relational systems. Implemented as a logical plan rewrite rule, the new approach first filters the input relation to MATCH_RECOGNIZE using Joins constructed based on a subset of symbols taken from the PATTERN expression, then run the NFA-based MATCH_RECOGNIZE on the filtered rows, reducing the net cost. The rule also includes a specialized cardinality model for the Joins and a cost model for the NFA-based MATCH_RECOGNIZE operator for choosing an appropriate symbol set. The rewrite rule is applicable when the query pattern's definition is self-contained and either the input table has no duplicates or there is a window condition. Applying the rewrite rule to a query benchmark with 1,800 queries spanning over 6 patterns and 3 pattern definitions, we observed median speedups of 5.4X on Trino (v373 with ORC files on Hive), 57.5X on SQL Server (2019) using column store and 41.6X on row store.

Non-returning deterministic and nondeterministic finite automata with translucent letters

Here, we propose a variant of the nondeterministic finite automaton with translucent letters (NFAwtl), which, after reading and deleting a letter, does not return to the left end of its tape, but instead continues from the position of the letter just deleted. When the end-of-tape marker is reached, our automaton can decide whether to accept, reject, or continue, which means that it reads the remaining tape contents again from the beginning. This type of automaton, called a non-returning finite automaton with translucent letters or an nrNFAwtl, is strictly more expressive than the NFAwtl. We study the expressive capacity of this type of automaton and that of its deterministic variant, comparing them to various other types of finite automata that do not simply read their input from left to right. Also, we are interested in the closure properties of the resulting classes of languages and in the complexity of the fixed membership problem.

Non-Returning Finite Automata With Translucent Letters

Here we propose a variant of the nondeterministic finite automaton with translucent letters (NFAwtl) which, after reading and deleting a letter, does not return to the left end of its tape, but rather continues from the position of the letter just deleted. When the end-of-tape marker is reached, our automaton can decide whether to accept, to reject, or to continue, which means that it again reads the remaining tape contents from the beginning. This type of automaton, called a non-returning finite automaton with translucent letters or an nrNFAwtl, is strictly more expressive than the NFAwtl. We study the expressive capacity of this type of automaton and that of its deterministic variant. Also we are interested in closure properties of the resulting classes of languages and in decision problems.

Implementation of Finite State Automata in Graphic Design Class Process Online

The development of technology is growing rapidly, the number of increasingly sophisticated inventions can also help humans in carrying out their activities, one of which is online classes, especially graphic design from various official organizers such as from coursera, udemy, and other organizers. Online graphic design classes are currently in great demand by the general public, especially at the school level, some have to pay a certain nominal, there are also free ones to access the class, besides that the classes offered are starting to vary, ranging from the beginner level to the advanced level also with certain software such as Adobe Photoshop, Figma, and other design applications and also with different systems, online or offline, graphic design is much needed, especially in the world of work such as printing, advertising and other fields. In this study, it was designed by using the FSA (Finite State Automata) method with the TYPE of NFA (Non-deterministic Finite Automata) to help students in the process of online graphic design classes starting from registration on the website to getting a class certificate so that students do not feel confused about what to do after registering, and is expected to make students understand in the process of online graphic design classes, The results of using FSA with nfa type can help students to better understand the flow of the registration process for online graphic design classes, with the creation of an FSA with this type of NFA is also expected to help students in registering online to get a certificate because they have attended an online graphic design class. Keywords : desain grafis, FSA, NFA, corel, adobe.

МЕТОД И АЛГОРИТМ ПЛАНИРОВАНИЯ ОПЕРАЦИЙ НА ОСНОВЕ МОДЕЛИ НЕЧЕТКОГО КОНЕЧНОГО АВТОМАТА

In this paper the planning and scheduling problem as an important optimization problem inmany transportation and robotic applications is discussed. To solve planning problems, the mainapproaches are based on optimization methods, sampling-based methods, and usually such kindsof problems are NP-hard and high dimensional. In this work, the method for planning and schedulingbased on the fuzzy finite state machine model is developed. Fuzzy graph presentation of thescheduling problem and operation planning is given. The paper presents two approaches to theformulation of the planning problem with limited resources and temporal variables: state-oriented(with transitions between states), temporal ordering-oriented (on a time scale). Temporal modelingfor planning problems implies a qualitative approach to managing the distribution of operationsor topological ordering, as well as a quantitative approach to handling imprecise durationsrelationships between operations in multiple parameters. The concepts of fuzzy intervals and fuzzyrelations are introduced for planning operations on a graph. A planning algorithm based on thetheory of automata and temporal modeling under uncertainty has been developed. Using this formalism,a path planning problem is solved by successively altering a state using various operationsuntil a solution is found. The idea of temporal-ordered partial schedule associated with theplanning state of the system is discussed. A model of a finite automaton for a planning system underconditions of uncertainty is proposed. A method and algorithm for scheduling operationsbased on a non-deterministic finite automaton and an enumeration scheme have been developed.The non-deterministic computation for a scheduling problem is a decision tree whose root correspondsto the beginning of the scheduling process, and each branch point in the tree correspondsto a computation point at which the machine has multiple choices. And the finite state machinemodel (automata) for the planning system under uncertainty is suggested.

Formal Modeling of IoT-Based Distribution Management System for Smart Grids

The smart grid is characterized as a power system that integrates real-time measurements, bi-directional communication, a two-way flow of electricity, and evolutionary computation. The power distribution system is a fundamental aspect of the electric power system in order to deliver safe, efficient, reliable, and resilient power to consumers. A distribution management system (DMS) begins with the extension of the Supervisory Control and Data Acquisition (SCADA) system through a transmission network beyond the distribution network. These transmission networks oversee the distribution of energy generated at power plants to consumers via a complex system of transformers, substations, transmission lines, and distribution lines. The major challenges that existing distribution management systems are facing, maintaining constant power loads, user profiles, centralized communication, and the malfunctioning of system equipment and monitoring huge amounts of data of millions of micro-transactions, need to be addressed. Substation feeder protection abruptly shuts down power on the whole feeder in the event of a distribution network malfunction, causing service disruption to numerous end-user clients, including industrial, hospital, commercial, and residential users. Although there are already many traditional systems with the integration of smart things at present, there are few studies of those systems reporting runtime errors during their implementation and real-time use. This paper presents the systematic model of a distribution management system comprised of substations, distribution lines, and smart meters with the integration of Internet-of-Things (IoT), Nondeterministic Finite Automata (NFA), Unified Modeling Language (UML), and formal modeling approaches. Non-deterministic finite automata are used for automating the system procedures. UML is used to represent the actors involved in the distribution management system. Formal methods from the perspective of the Vienna Development Method-Specification Language (VDM-SL) are used for modeling the system. The model will be analyzed using the facilities available in the VDM-SL toolbox.

RESERVE VENDING MACHINE FOOD WASTE SEBAGAI DEPOSITO MELALUI QRIS BANK SAMPAH RUMAH TANGGA

The problem of waste is one of the things that need to be considered by society, especially food waste. Household waste management has begun to be carried out using the Reduce, Reuse and Recycle (3R) method but has not yet used technology. By using Finite State Automata (FSA) which is the basic concept of the Vending Machine (VM), waste management can be more economically by converting waste into balances for Rubbish Bank customers which of course becomes income for the society. In the payment method, QRIS applies where the customer does not get cash but immediately gets the balance which will go into the customer's own account. This implementation certainly reduces the amount of waste because it applies paper less and cashless. In this Reserve Vending Machine Food Waste process using Non-Deterministic Finite Automata (NFA).

IMPLEMENTASI METODE FINITE STATE AUTOMATA PADA SCREENING AWAL PENERIMAAN PEGAWAI

Every company always has a recruitment selection process with the hope that the company can get competent employees. The selection process usually has several criteria that are usually predetermined by the company which are needed in the initial selection process for hiring employees. Thus it is necessary for an application system that can carry out the initial screening process for employee recruitment to assist the implementation of the selection process. The design of this application uses the FSA implementation with the NFA type as an abstract machine to determine the stages and transitions contained in these stages which are used to determine the results of the initial screening of employee recruitment. If they meet the specified criteria, they will pass at this stage. This is a role in making abstract machines for the initial screening process for employee recruitment using Nondeterministic Finite Automata (NFA) because each stage can lead to several stages at once.