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.

One-Way Jumping Finite Automata

Abstract: We propose the one-way jumping finite automaton model, restricting the jumping relation of the recently introduced jumping finite automaton so that the machine can only jump over symbols it cannot process in its current state. The reading head of a one-way jumping finite automaton moves deterministically in one direction within the input word, whereas movement of the reading head of jumping finite automaton is non-deterministic. The class of languages accepted by one-way jumping finite automata is different from that of jumping finite automata, in particular, it includes all regular languages, as opposed to the latter. We study one-way jumping finite automata and obtain closure properties, a pumping lemma, and separation results with respect to the classical language classes of the Chomsky hierarchy.

On the Power of Las Vegas II: Two-Way Finite Automata

Abstract: The investigation of the computational power of randomized computations is one of the central tasks of complexity and algorithm theory. While for one-way finite automata the power of different computational modes was successfully determined, one does not have any nontrivial result relating the power of determinism, Las Vegas and nondeterminism for two-way finite automata. The main results of this paper are as follows. (i) If, for a regular language L , there exist small two-way nondeterministic finite automata for both L and L ʗ , then there exists a small two-way Las Vegas finite automaton for L . (ii) There is a quadratic gap between nondeterminism and Las Vegas for two-way finite automata. (iii) For every k ∈ N , there is a regular language S k such that S k can be accepted by a two-way Las Vegas finite automaton with O (k) states, but every two-way deterministic finite automaton recognizing S k has at least Ω (k 2 / log 2 k) states.

Deciding the weak definability of Büchi definable tree languages

Abstract: Weakly definable languages of infinite trees are an expressive subclass of regular tree languages definable in terms of weak monadic second-order logic, or equivalently weak alternating automata. Our main result is that given a Buchi automaton, it is decidable whether the language is weakly definable. We also show that given a parity automaton, it is decidable whether the language is recognizable by a nondeterministic co-Buchi automaton. The decidability proofs build on recent results about cost automata over infinite trees. These automata use counters to define functions from infinite trees to the natural numbers extended with infinity. We reduce to testing whether the functions defined by certain "quasi-weak" cost automata are bounded by a finite value.

The cartesian composition of automata

Abstract: There are several known ways to define a product automaton on the cartesian product of the state sets of two given automata. This paper introduces a new product called the cartesian composition and discusses how various properties of the product automaton depend on the corresponding properties of the factors. A main result is that any finite connected automaton has a unique representation as a cartesian composition of prime automata.

Note on Minimal Finite Automata

Abstract: We show that for all n and α such that 1 ≤ n ≤ α ≤ 2n there is a minimal n-state nondeterministic finite automaton whose equivalent minimal deterministic automaton has exactly α states.