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.

Antichains: A new algorithm for checking universality of finite automata

Abstract: We propose and evaluate a new algorithm for checking the universality of nondeterministic finite automata. In contrast to the standard algorithm, which uses the subset construction to explicitly determinize the automaton, we keep the determinization step implicit. Our algorithm computes the least fixed point of a monotone function on the lattice of antichains of state sets. We evaluate the performance of our algorithm experimentally using the random automaton model recently proposed by Tabakov and Vardi. We show that on the difficult instances of this probabilistic model, the antichain algorithm outperforms the standard one by several orders of magnitude. We also show how variations of the antichain method can be used for solving the language-inclusion problem for nondeterministic finite automata, and the emptiness problem for alternating finite automata.

The Theory of Stabilisation Monoids and Regular Cost Functions

Abstract: We introduce the notion of regular cost functions: a quantitative extension to the standard theory of regular languages. We provide equivalent characterisations of this notion by means of automata (extending the nested distance desert automata of Kirsten), of history-deterministic automata (history-determinism is a weakening of the standard notion of determinism, that replaces it in this context), and a suitable notion of recognisability by stabilisation monoids. We also provide closure and decidability results.

Control of Infinite Behavior of Finite Automata

Abstract: A problem in the control of automata on infinite strings is defined and analyzed. The key to the investigation is the development of a fixpoint characterization of the "controllability subset" of a deterministic Rabin automaton, the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition. The fixpoint representation allows straightforward computation of the controllability subset and the construction of a suitable state-feedback control for the automaton. The results have applications to control synthesis, automaton synthesis, and decision procedures for logical satisfiability; in particular, they represent a direct, efficient and natural solution to Church's problem, the construction of winning strategies for two-player zero-sum $\omega$-regular games of perfect information, and the emptiness problem for automata on infinite trees.

Extending finite automata to efficiently match Perl-compatible regular expressions

Abstract: Regular expression matching is a crucial task in several networking applications. Current implementations are based on one of two types of finite state machines. Non-deterministic finite automata (NFAs) have minimal storage demand but have high memory bandwidth requirements. Deterministic finite automata (DFAs) exhibit low and deterministic memory bandwidth requirements at the cost of increased memory space. It has already been shown how the presence of wildcards and repetitions of large character classes can render DFAs and NFAs impractical. Additionally, recent security-oriented rule-sets include patterns with advanced features, namely back-references, which add to the expressive power of traditional regular expressions and cannot therefore be supported through classical finite automata.In this work, we propose and evaluate an extended finite automaton designed to address these shortcomings. First, the automaton provides an alternative approach to handle character repetitions that limits memory space and bandwidth requirements. Second, it supports back-references without the need for back-tracking in the input string. In our discussion of this proposal, we address practical implementation issues and evaluate the automaton on real-world rule-sets. To our knowledge, this is the first high-speed automaton that can accommodate all the Perl-compatible regular expressions present in the Snort network intrusion and detection system.