State Automata Research Articles

Inferring regular languages and ω-languages

In 1987 Angluin proposed an algorithm, termed L⁎ for inferring an unknown regular language using membership and equivalence queries. This algorithm has found many applications, amongst which in the area of system design and verification. These applications challenge the state-of-the art solutions in various directions, in particular, scaling or working with more succinct representations, and dealing with ω-languages, the main model for reasoning about reactive systems.Both extensions confront a similar difficulty. Inference algorithms typically rely on the correspondence between the automata states and the right congruence, henceforth, the residuality property. DFAs enjoy the residuality property (as stated by the Myhill–Nerode Theorem) but more succinct representations such as non-deterministic and alternating finite automata (NFAs and AFAs) in general do not. The situation in the ω-languages realm is even worse, since none of the traditional automata that can express all regular ω-languages enjoys the residuality property.This paper surveys residual models for regular languages and ω-languages and the learning algorithms that can infer these models.

Functional Diagnosis of Digital State Automation Networks

The problem of functional diagnosis of digital devices forming a network of state automata is considered. This task for the network components is supposed to be solved, and the corresponding diagnostic devices for them are provided. The possibility of their population transformation into the tools for the entire network diagnostics is shown. The result of the transformation with the restrictions on the number of components with errors is simplified in compare with the original population. A procedure is proposed allowing to find analytical expressions defining an auxiliary control and an error discriminator for the most probable case of error localization (all errors are concentrated in a certain component of the network). The first part of the article provides a solution of the functional diagnosis problem for the case when the parity functions of all components are scalar, and the class of detectable errors is given by unit multiplicity. Next, the result generalizes for the case of vector functions, where multiple errors can occur. The procedure minimizes the sought for functional diagnosis devices with respect to the order when preserving the initial detecting ability within any network component. The obtained results are illustrated by an example of construction of functional diagnosis equipment for ranging signal processing device in broadband short-range radio engineering navigation system.

Lumping-based equivalences in Markovian automata: Algorithms and applications to product-form analyses

In this paper we consider two relations over stochastic automata, named lumpable bisimulation and exact equivalence, that induce a strong and an exact lumping, respectively, on the underlying Markov chains. We show that an exact equivalence over the states of a non-synchronising automaton is indeed a lumpable bisimulation for the corresponding reversed automaton and then it induces a strong lumping on the time-reversed Markov chain underlying the model. This property allows us to prove that the class of quasi-reversible models is closed under exact equivalence. Quasi-reversibility is a pivotal property to study product-form models. Hence, exact equivalence turns out to be a theoretical tool to prove the product-form of models by showing that they are exactly equivalent to models which are known to be quasi-reversible. Algorithms for computing both lumpable bisimulation and exact equivalence are introduced. Case studies as well as performance tests are also presented.

Strongly connected synchronizing automata and the language of minimal reset words

We approach the problem of finding strongly connected synchronizing automata with a given ideal I that serves as the set of reset words, by studying the set of minimal words M of the ideal I (no proper factor is a reset word). We first show the existence of an infinite strongly connected synchronizing automaton A having I as the set of reset words and such that every other strongly connected synchronizing automaton having I as the set of reset words is an homomorphic image of A. Finally, we show that for any non-unary regular ideal I there is a strongly connected synchronizing automaton having I as the set of reset words with at most (kmk)2kmkn states, where k is the dimension of the alphabet, m is twice the length of a shortest word in I, and n is the number of states of the smallest automaton recognizing M. This synchronizing automaton is computable and we exhibit an algorithm to compute it in time O((k2mk)2kmkn).

Police‐less multi‐party traffic violation detection and reporting system with privacy preservation

This study presents a traffic violation detection and reporting system, that does not rely on costly infrastructure or the presence of law enforcement. It relies solely on broadcast messages among vehicles and reports delivery to the transportation authority. A vehicle is modelled as an automaton (in the computational sense) that has its own state and has a read access to the state of other automata of other vehicles in a constant size neighbourhood. The common traffic rules and communication rules make the program of these automata that guide the transitions of the vehicles in space and time. By observing the transitions of the vehicles in their neighbourhood, a vehicle can decide if these comply with the traffic rules encoded in the system. Whenever a transition is not performed according to the program, a violation occurs. These violations are reported and witnessed to the transportation authority by the vehicles in the neighbourhood, which act as witnesses and reporters. The system preserves privacy and allows no false positives.

Compositional Approach to Distributed System Behavior Modeling and Formal Validation of Infrastructure Operations with Finite State Automata: Application to Viewpoint-Driven Verification of Functionality in Waterways

Now that modern infrastructure systems are moving toward an increased use of automation in their day-to-day operations, there is an emerging need for new approaches to the formal analysis and validation of system functionality with respect to correctness of operations. This paper describes a compositional approach to the multi-level behavior modeling and formal validation of large-scale distributed system operations with hierarchies and networks of finite state automata. To avoid the well-known state explosion problem, we develop a new procedure for viewpoint-action-process traceability, thereby allowing parts of a behavior model not relevant to a specific decision to be removed from consideration. Key features of the methodology are illustrated through the development of behavior models and validation procedures for polite conversation between two individuals, and lockset- and system-level concerns for ships traversing a large-scale waterway system.

Trajectory Planning under Current-State Opacity Constraints

Privacy and security guarantee against curious observers or malicious actors has recently emerged as a critical aspect for maintaining, protecting, and securing complex automated systems that are implemented over shared (thus, non-secure) cyber-infrastructures, such as the Internet. In this paper, we discuss how current-state opacity formulations can be used to capture privacy properties of interest in automated systems that are modeled as controlled finite automata that need to be steered from one state (initial location) to another state (target location), while maintaining certain privacy guarantees. More specifically, given a deterministic finite automaton that is externally observed via some output mapping, along with a subset of states S that are considered critical/secret, we aim to drive it from a given initial state (starting location) to a given target state (final location) while ensuring that, in the process, the state (location) of the finite automaton at any given time is not exposed (i.e., the external observer cannot be certain that the state of the system belongs to the set of critical/secret states S). We develop two algorithms that can be used to solve this constrained trajectory planning problem and obtain an appropriate sequence of inputs (if one exists) or conclude that no such sequence exists (otherwise). The first algorithm has complexity O(N2N) and the second algorithm has complexity O(NK+2), where N (K) is the number of states (secret states).

State hyperstructures of tree automata based on lattice-valued logic

In this paper, an association is organized between the theory of tree automata on one hand and the hyperstructures on the other hand, over complete residuated lattices. To this end, the concept of order of the states of a complete residuated lattice-valued tree automaton (simply L-valued tree automaton) is introduced along with several equivalence relations in the set of the states of an L-valued tree automaton. We obtain two main results from this study: one of the relations can lead to the creation of Kleene’s theorem for L-valued tree automata, and the other one leads to the creation of a minimal v-valued tree automaton that accepts the same language as the given one.

To improve the Recovery of an Arab Stemmer for Information Retrieval

The automatic processing of the Arabic language is a growing discipline, in which one sees more and more research and technologies to examine the specificities of this language and to propose tools necessary to the development of its automatic processing. The old techniques of rooting have limits that weaken the process of root extraction. In this article, the author proposes a new approach to rooting based on two finite state automata. The technique proposed is based on finite state automata in the root extraction process, with the aim of minimizing the error rate and ambiguity, usually due to the removal of the affixes. The author is currently focusing on the development and improvement of the rooting technique while trying to overcome the various problems encountered. The author is working on the compilation of a corpus of evaluation which will allow him to evaluate and compare their approach to others

Spelling Correction for Text Documents in Bahasa Indonesia Using Finite State Automata and Levinshtein Distance Method

Any mistake in writing of a document will cause the information to be told falsely. These days, most of the document is written with a computer. For that reason, spelling correction is needed to solve any writing mistakes. This design process discuss about the making of spelling correction for document text in Indonesian language with document's text as its input and a .txt file as its output. For the realization, 5 000 news articles have been used as training data. Methods used includes Finite State Automata (FSA), Levenshtein distance, and N-gram. The results of this designing process are shown by perplexity evaluation, correction hit rate and false positive rate. Perplexity with the smallest value is a unigram with value 1.14. On the other hand, the highest percentage of correction hit rate is bigram and trigram with value 71.20 %, but bigram is superior in processing time average which is 01:21.23 min. The false positive rate of unigram, bigram, and trigram has the same percentage which is 4.15 %. Due to the disadvantages at using FSA method, modification is done and produce bigram's correction hit rate as high as 85.44 %.

A Novel Approach in Adopting Finite State Automata for Image Processing Applications

This article describes how robust image processing application rely heavily on image descriptors extracted. Limited work is carried out in adopting probabilistic finite state automata (PFSA) models for image processing. A finite state automata for image processing (FSAFIP) method is presented here. Texture classification and content based image retrieval (CBIR) is considered. In FSAFIP, foreground and background regions of an image are identified and later split into patches. Using a tristate PFSA model, feature descriptors corresponding to background/foreground regions are constructed. A distance based large margin nearest neighbor (LMNN) classifier is considered in FSAFIP to impart intelligence. A performance and experimental study to evaluate performance of FSAFIP for CBIR and texture classification is presented. Comparison results in CBIR obtained prove superior performance of FSAFIP over existing methods on Corel-1K dataset. High texture classification accuracy of 99.2% is reported using FSAFIP on KHT-TIPS dataset. An improved texture classification accuracy is achieved using FSAFIP in comparison to former methods.

Between primitive and 2-transitive: Synchronization and its friends

An automaton (consisting of a finite set of states with given transitions) is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by the Černý conjecture , one of the oldest and most famous problems in automata theory, according to which a synchronizing n -state automaton has a reset word of length at most (n-1)^2 .The transitions of an automaton generate a transformation monoid on the set of states, and so an automaton can be regarded as a transformation monoid with a prescribed set of generators. In this setting, an automaton is synchronizing if the transitions generate a constant map. A permutation group G on a set \Omega is said to synchronize a map f if the monoid \langle G,f\rangle generated by G and f is synchronizing in the above sense; we say G is synchronizing if it synchronizes every non-permutation. The classes of synchronizing groups and friends form an hierarchy of natural and elegant classes of groups lying strictly between the classes of primitive and 2-homogeneous groups. These classes have been floating around for some years and it is now time to provide a unified reference on them. The study of all these classes has been prompted by the Černý conjecture, but it is of independent interest since it involves a rich mix of group theory, combinatorics, graph endomorphisms, semigroup theory, finite geometry, and representation theory, and has interesting computational aspects as well. So as to make the paper self-contained, we have provided background material on these topics. Our purpose here is to present recent work on synchronizing groups and related topics. In addition to the results that show the connections between the various areas of mathematics mentioned above, we include a new result on the Černý conjecture (a strengthening of a theorem of Rystsov), some challenges to finite geometers (which classical polar spaces can be partitioned into ovoids?), some thoughts about infinite analogues, and a long list of open problems to stimulate further work.

DISTINGUISHABILITY AND COMPLETENESS OF CRISP DETERMINISTIC FUZZY AUTOMATA

In this paper, we introduce and study notions like state-\linebreak distinguishability, input-distinguishability and output completeness of states of a crisp deterministic fuzzy automaton. We show that for each crisp deterministic fuzzy automaton there corresponds a unique (up to isomorphism), equivalent distinguished crisp deterministic fuzzy automaton. Finally, we introduce two axioms related to output completeness of states and discuss the interrelationship between them.

Automata for regular expressions with shuffle

We generalize the partial derivative automaton and the position automaton to regular expressions with shuffle, and study their state complexity in the worst, as well as in the average case. The number of states of the partial derivative automaton (Apd) is, in the worst case, at most 2m, where m is the number of letters in the expression. The asymptotic average is bounded by (43)m. We define a position automaton (Apos) that is homogeneous, but in which several states can correspond to a same position, and we show that Apd is a quotient of Apos. The number of states of the position automaton is at most 1+m(2m−1), while the asymptotic average is no more than m(43)m.

A design of generalized minimum-state-change FSSP algorithms and their implementations

The firing squad synchronization problem (FSSP) on cellular automata has been studied extensively for more than 50 years, and a rich variety of FSSP algorithms has been proposed. Here we consider the FSSP from a view point of state-change complexity that models the energy consumption of SRAM-type storage with which cellular automata might be built. In the present paper, we propose minimum-state-change generalized FSSP (GFSSP) algorithms for synchronizing any one-dimensional (1D) cellular automaton, where the initial synchronization operation is started by any cell in the array. First, we construct two minimum-time, minimum-state-change GFSSP implementations on finite state automata: one is based on Goto’s algorithm, known as the first minimum-time FSSP algorithm that was reconstructed again recently in Umeo et al. (A new reconstruction and the first implementation of Goto’s FSSP algorithm, 2017), and the other is based on Gerken’s (Diplomarbeit, Institut fur Theoretische Informatik, Technische Universitat Braunschweig, pp 1–50, 1987) one. These implementations are optimal not only in time but also in the state-change complexity. The implementations of the minimum-time GFSSP algorithms are the first ones having the minimum-state-change complexity. In addition, we also present a six-state 145-rule non-minimum-time, minimum-state-change GFSSP implementation. The implemented GFSSP algorithm is the smallest one, known at present, in number of states of the finite state automaton.

Ranks of fuzzy matrices. Applications in state reduction of fuzzy automata

In this paper we consider different types of ranks of fuzzy matrices over residuated lattices. We investigate relations between ranks and prove that row rank, column rank and Schein rank of idempotent fuzzy matrices are equal. In particular, ranks and corresponding decompositions of fuzzy matrices representing fuzzy quasi-orders are studied in detail. We show that fuzzy matrix decomposition by ranks can be used in the state reduction of fuzzy automata. Moreover, we prove that using rank decomposition of fuzzy matrices improves results of any state reduction method based on merging indistinguishable states of fuzzy automata.

Checking Properties along Multiple Reconfiguration Paths for Component-Based Systems

Reconfiguration paths express sequences of successive reconfiguration operations within a component-based approach allowing dynamic reconfigurations. We use constructs from regular expressions-pin particular, alternatives-to introduce multiple reconfiguration paths. We show how to put into action procedures allowing architectural, event, and temporal properties to be proved. Our method, related to finite state automata and using marking techniques, generalises what we did within previous work, where the regular expressions we processed were more restricted. But we can only deal with a subset of first-order logic formulas.

A framework to specify system requirements using natural interpretation of UML/MARTE diagrams

The ever-increasing design complexity of embedded systems is constantly pressing the demand for more abstract design levels and possible methods for automatic verification and synthesis. Transforming a text-based user requirements document into semantically sound models is always difficult and error-prone as mostly these requirements are vague and improperly documented. This paper presents a framework to specify textual requirements graphically in standard modeling formalisms like uml and marte in the form of temporal and logical patterns. The underlying formal semantics of these graphical models allow to eliminate ambiguity in specifications and automatic design verification at different abstraction levels using these patterns. The semantics of these operators/patterns are presented formally as state automatons and a comparison is made to the existing ccsl relational operators. To reap the benefits of mde, a software plugin TemLoPAC is presented as part of the framework to transform the graphical patterns into ccsl and Verilog-based observers.

On Algebraic Study of Type-2 Fuzzy Finite State Automata

Theories of fuzzy sets and type-2 fuzzy sets are powerful mathematical tools for modeling various types of uncertainty. In this paper we introduce the concept of type-2 fuzzy finite state automata and discuss the algebraic study of type-2 fuzzy finite state automata, i.e., to introduce the concept of homomorphisms between two type-2 fuzzy finite state automata, to associate a type-2 fuzzy transformation semigroup with a type-2 fuzzy finite state automata. Finally, we discuss several product of type-2 fuzzy finite state automata and shown that these product is a categorical product.

An innovative finite state automata based approach for fault direction estimation in transmission lines

Abstract In this work finite state automata or finite state machine based directional protection scheme is proposed for transmission lines. Phase angle of positive sequence current is used as input to finite state automata based fault direction estimation module. Finite state automata is used as fault pattern recognizer which estimates the direction of fault. The output of the proposed FSM based scheme will be ‘−1’ for reverse section faults and ‘1’ for fault in primary section faults. The performance of the proposed technique is evaluated using data simulated for variation of fault type, fault inception angle, fault location, power flow angle, reverse power flow and fault resistance. Accuracy of the method is found to be 100% from all 11,500 fault cases. Proposed technique does not use voltage unlike conventional directional relaying schemes due to which there is no issue regarding close-in fault detection. The reach setting of the proposed method is up to 99.9% of line length which has advantage over conventional relaying schemes which have reach up to 80–85% of line. Although proposed method is a pattern recognition based technique, it does require an extra training module unlike artificial neural network to estimate the direction correctly. The proposed technique is effective because it do not require any training and the computation complexity is very less as compared to training based algorithms. Proposed method is also tested in an existing power system network of India, which shows accurate result in estimating fault direction.