Reduction of the Nondeterministic Finite Automata

Nedeterministický konečný automat je důležitým nástrojem, který se používá pro zpracování řetězců v mnoha různých oblastech programování. V rámci zvýšení efektivity programů je důležité snažit se o zmenšování jeho velikosti. Tento problém je však velmi výpočetně náročný, proto je potřeba hledat nové postupy. V této práci jsou uvedeny základy konečných automatů a poté jsou představeny různé metody zabývající se jejich redukcí. Použitelné redukční algoritmy jsou v práci podrobněji popsány, dále implementovány a otestovány. Nakonec jsou výsledky zhodnoceny.Nondeterministic finite automaton is an important tool, which is used to process strings in many different areas of programming. It is important to try to reduce its size for increasing programs' effectiveness. However, this problem is computationally hard, so we need to search for new techniques. Basics of finite automata are described in this work. Some methods for their reduction are then introduced. Usable reduction algorithms are described in greater detail. Then they are implemented and tested. The test results are finally evaluated.

Advantages and challenges of programming the Micron Automata Processor

Non-Von Neumann computer architectures are being explored for acceleration of difficult problems. The Automata Processor is a unique non Von Neumann architecture capable of efficient modeling and execution of non-deterministic finite automata. The Automata Processor is shown to be excellent in string comparison operations, specifically with regard to bioinformatics problems. A greatly accelerated solution for Prosite pattern matching using the Automata Processor called PROTOMOTA is presented. Furthermore, a developers\u27 guide detailing the lessons learnt while designing and implementing PROTOMOTA is provided. It is hoped that the developers\u27 guide would aid future developers to avoid critical pitfalls, while exploiting the capabilities of the Automata Processor to the fullest

Non-Deterministic Finite Cover Automata

The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA ’98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language using a Non-deterministic Finite Automata (NFA) may significantly reduce the number of required states. The combined power of the succinctness of the representation of finite languages using both cover languages and non-determinism has been suggested, but never systematically studied. In the present paper, for non-deterministic finite cover automata (NFCA) and l-non-deterministic finite cover automaton (l-NFCA), we show that minimization can be as hard as minimizing NFAs for regular languages, even in the case of NFCAs using unary alphabets. Moreover, we show how we can adapt the methods used to reduce, or minimize the size of NFAs/DFCAs/l-DFCAs, for simplifying NFCAs/l-NFCAs

Decomposition and Descriptional Complexity of Shuffle on Words and Finite Languages

We investigate various questions related to the shuffle operation on words and finite languages. First we investigate a special variant of the shuffle decomposition problem for regular languages, namely, when the given regular language is the shuffle of finite languages. The shuffle decomposition into finite languages is, in general not unique. Thatis,therearelanguagesL^,L2,L3,L4withLiluL2= £3luT4but{L\,L2}^ {I/3, L4}. However, if all four languages are singletons (with at least two combined letters), it follows by a result of Berstel and Boasson [6], that the solution is unique; that is {L\,L2} = {L3,L4}. We extend this result to show that if L\ and L2 are arbitrary finite sets and Lz and Z-4 are singletons (with at least two letters in each), the solution is unique. This is as strong as it can be, since we provide examples showing that the solution can be non-unique already when (1) both L\ and L2 are singleton sets over different unary alphabets; or (2) L\ contains two words and L2 is singleton. We furthermore investigate the size of shuffle automata for words. It was shown by Campeanu, K. Salomaa and Yu in [11] that the minimal shuffle automaton of two regular languages requires 2mn states in the worst case (where the minimal automata of the two component languages had m and n states, respectively). It was also recently shown that there exist words u and v such that the minimal shuffle iii DFA for u and v requires an exponential number of states. We study the size of shuffle DFAs for restricted cases of words, namely when the words u and v are both periods of a common underlying word. We show that, when the underlying word obeys certain conditions, then the size of the minimal shuffle DFA for u and v is at most quadratic. Moreover we provide an efficient algorithm, which decides for a given DFA A and two words u and v, whether u lu u C L(A)

Logic and Automata

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field