Topic
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.
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TL;DR: The oblivious multi-head one-way finite automata (OMFA) model presented in this paper is characterized by having its heads moving only forward, on a trajectory that only depends on the length of the input.
Abstract: In this paper, we present the simulation of a simple, yet significantly powerful, sequential model by cellular automata. The simulated model is called oblivious multi-head one-way finite automata and is characterized by having its heads moving only forward, on a trajectory that only depends on the length of the input. While the original finite automaton works in linear time, its corresponding cellular automaton performs the same task in real time, that is, exactly the length of the input. Although not truly a speed-up, the simulation may be interesting and reminds us of the open question about the equivalence of linear and real times on cellular automata.
01 Jan 2009
TL;DR: It is shown that the super-exponential lower bound on the witness applies already for universal co-Buchi word and tree automata.
Abstract: The nonemptiness problem for nondeterministic automata on infinite words can be reduced to a sequence of reachability queries. The length of a shortest witness to the nonemptiness is then polynomial in the automaton. Nonemptiness algorithms for alternating automata translate them to nondeterministic automata. The exponential blow-up that the translation involves is justified by lower bounds for the nonemptiness problem, which is exponentially harder for alternating au- tomata. The translation to nondeterministic automata also entails a blow-up in the length of the shortest witness. A matching lower bound here is known for cases where the translation involves a 2 O(n) blow up, as is the case for finite words or Buchi automata. Alternating co-Buchi automata and witnesses to their nonemptiness have appli- cations in model checking (complementing a nondeterministic Buchi word automa- ton results in a universal co-Buchi automaton) and synthesis (an LTL specification can be translated to a universal co-Buchi tree automaton accepting exactly all the transducers that realize it). Emptiness algorithms for alternating co-Buchi automata proceed by a translation to nondeterministic Buchi automata. The blow up here is 2 O(n log n) , and it follows from the fact that, on top of the subset construction, the nondeterministic automaton maintains ranks to the states of the alternating automa- ton. It has been conjectured that this super-exponential blow-up need not apply to the length of the shortest witness. Intuitively, since co-Buchi automata are memo- ryless, it looks like a shortest witness need not visit a state associated with the same set of states more than once. A similar conjecture has been made for the width of a transducer generating a tree accepted by an alternating co-Buchi tree automaton. We show that, unfortunately, this is not the case, and that the super-exponential lower bound on the witness applies already for universal co-Buchi word and tree automata.
Posted Content•
TL;DR: Another type of automata model is introduced and it is studied how these automata are related to cascade connections of Automata of the first type.
Abstract: The paper is devoted to two types of algebraic models of automata. The usual (first type) model leads to the developed decomposition theory (Krohn-Rhodes theory). We introduce another type of automata model and study how these automata are related to cascade connections of automata of the first type. The introduced automata play a significant role in group theory and, hopefully, in the theory of formal languages.
30 Aug 1993
TL;DR: Strong monoid recognizability of infinite tree languages is introduced and it is shown that there exists an infinite tree language L which is not Rabin recognizable, but its associated language L is monoid recognizable (in the standard sense).
Abstract: We incorporate finite monoids into the theory of Rabin recognizability of infinite tree languages. We define a free monoid of infinite trees and associate with each infinite tree language L a language L of infinite words over this monoid. Using this correspondence we introduce strong monoid recognizability of infinite tree languages (strengthening the standard notion for infinite words) and show that it is equivalent to Rabin recognizability. We also show that there exists an infinite tree language L which is not Rabin recognizable, but its associated language L is monoid recognizable (in the standard sense). Our positive result opens the theory of varieties of infinite tree languages, extending those for finite and infinite words and finite trees.
21 Aug 2006
TL;DR: New bounds on the number of new transitions for several e-transitions-removal problems for weighted finite automata are presented, including the case of acyclic WFA.
Abstract: Weighted finite automata (WFA) are used with accelerating hardware to scan large genomic banks. Hardwiring such automata raise surface area and clock frequency constraints, requiring efficient e-transitions-removal techniques. In this paper, we present new bounds on the number of new transitions for several e-transitions-removal problems. We study the case of acyclic WFA. We introduce a new problem, the partial removal of e-transitions while accepting short chains of e-transitions.