ω-automaton

About: ω-automaton is a research topic. Over the lifetime, 2299 publications have been published within this topic receiving 68468 citations. The topic is also known as: stream automaton & ω-automata.

Cover languages and implementations

Abstract: A cover language is a superset of a given language. Deterministic Finite Cover Automata (DFCA) are Deterministic Finite Automata (DFA) accepting finite languages and other words longer than any word in the given language. Some papers from the 60's were constructing DFCAs as a byproduct using ad-hoc procedures, but DFCAs have never been defined until 1998. The notion of Deterministic Finite Cover Automaton, which is based on the concept of similarity relations, was introduced for the very first time at WIA'98, where the authors give the first rigorous formal definition and a clear minimization algorithm. We will present a survey of the most important results related to cover automata, and will show the importance of the implementation in obtaining, verifying, and solving new results. A list of open problems related to cover automata, together with some possible approaches will be presented. Features of the software packages Grail, miniGrail, and Lisa will be exposed. A list of open problems related to challenges and limitations encountered when using software packages implementing automata, languages, and related objects will be shown.

Structural Modification of the Finite State Machine to Solve the Exponential Explosion Problem

Abstract: In many modern applications, such as intrusion detection and prevention systems, expert knowledge can be formalized in the form of regular expressions. After this formalization, a finite automaton checks whether a word belongs to a regular language. Deterministic finite automata have an optimal time complexity, but the number of automaton states (space com­plexity) can grow exponentially with the length of the regular expression. At the same time, the time complexity is the main disadvantage of non-deterministic finite automata. Therefore, reducing spatial complexity while maintaining low time complexity is highly relevant. In applied problems of regular language recognition, a significant problem is the problem of the exponentially growing number of states of the recognizing deterministic finite automaton depending on the length of regular expressions of the recognized language — the exponential explosion problem. There are the following three main approaches to solving this problem using finite automata: 1) restriction on signatures given by experts; 2) regular language modification — this approach assumes the appearance in the solution of a practical problem of recognizing errors of the first and second kind; 3) finite automata modification without recognizing regular language changing. The third approach can be implemented as a finite automata modification through compression algorithms and particular structural elements. The paper presents a review of modern solutions, the main idea of which is the transition from an abstract finite automaton, represented by a table-specified function, to a structural automaton that combines the abstract part stored in the memory and various structural elements such as bit arrays and counters. Some ideas and algorithms have become especially successful when solving the exponential explosion problem by adding special structural elements. First, such successful solutions include the use of counters. Second, the idea of storing additional information about the state machine. Third, the combination of non-deterministic and deterministic finite automata. Fourth, the economic attitude to the state machine regarding its location to fast and slow memory allows us to consider the em­pirical experience of accumulated malicious traffic in intrusion detection systems.

Metamorphosis of Fuzzy Regular Expressions to Fuzzy Automata using the Follow Automata

Abstract: To deal with system uncertainty, finite automata have been generalized into fuzzy automata. Stamenkovic and Ciric proposed an approach using the position automata for the construction of fuzzy automata from fuzzy regular expressions. There exist multifarious methodologies for the construction of finite automata from regular expressions known as Thompson construction, Antimirov partial derivatives, Glushkov automata and follow automata etc. In this paper, we propose an approach for the conversion of fuzzy regular expressions into fuzzy automata using the concept of follow automata. The number of states of the obtained Fuzzy automata using the proposed approach is lesser than the extant approaches in the literature.