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.

Some formal properties of asynchronous callular automata

Abstract: We study the dynamical behaviour of asynchronous cellular automata by considering some formal properties of classical cellular automata and adapting them to the asynchronous case.

The automata theory of semigroup embeddings

Abstract: An automaton M (without output) is a triple (Q, X, d) where Q is the set of states, X is the input set, and 6 : QxX ->• Q. The semigroup S(M) is the subsemigroup of Q generated by the maps d(-, x) : Q -»• Q. M is called countable [finite] if Q is countable [finite]. Given a countable semigroup S with generators G(S), we may represent it as the semigroup of the machine Ms = (S , G(S), ds) where ds is multiplication in the semigroup S, and S is 5 with a unit adjoined only if 5 is not a monoid. We then replace Ms by a machine which has input set {0, 1} and which reads in strings until a code (i.e., a monomorphism of ^GCS)' the free semigroup generated by G(S), into ^iOti\) for an element of G(S) has been read, and then acts accordingly. We now give two examples of codes and the corresponding constructions. One which works whether or not G(S) = {s1( s2, • • •} is finite is to code Sj as F'O, i.e. a string of / ones followed by a zero. Then M1 = (NxS , {0, 1}, d2) (taking N = {1, 2, 3, • • •}) with d1((n,s),0) = ( O . s s J d^in, s), 1) = (n+l,s) and the map s3->l 0 yields an embedding of 5 in the twc-generator 568

Transition function complexity of finite automata

Abstract: State complexity of finite automata in some cases gives the same complexity value for automata which intuitively seem to have completely different complexities. In this paper we consider a new measure of descriptional complexity of finite automata -- BC-complexity. Comparison of it with the state complexity is carried out here as well as some interesting minimization properties are discussed. It is shown that minimization of the number of states can lead to a superpolynomial increase of BC-complexity.

Closure properties of hyper-minimized automata

Abstract: Two deterministic finite automata are almost equivalent if they disagree in acceptance only for finitely many inputs. An automaton A is hyper-minimized if no automaton with fewer states is almost equivalent to A . A regular language L is canonical if the minimal automaton accepting L is hyper-minimized. The asymptotic state complexity s ∗ (L ) of a regular language L is the number of states of a hyper-minimized automaton for a language finitely different from L . In this paper we show that: (1) the class of canonical regular languages is not closed under: intersection, union, concatenation, Kleene closure, difference, symmetric difference, reversal, homomorphism, and inverse homomorphism; (2) for any regular languages L 1 and L 2 the asymptotic state complexity of their sum L 1 ∪ L 2 , intersection L 1 ∩ L 2 , difference L 1 − L 2 , and symmetric difference L 1 ⊕ L 2 can be bounded by s ∗ (L 1 )·s ∗ (L 2 ). This bound is tight in binary case and in unary case can be met in infinitely many cases. (3) For any regular language L the asymptotic state complexity of its reversal L R can be bounded by 2s ∗ (L ) . This bound is tight in binary case. (4) The asymptotic state complexity of Kleene closure and concatenation cannot be bounded. Namely, for every k ≥ 3, there exist languages K , L , and M such that s ∗ (K ) = s ∗ (L ) = s ∗ (M ) = 1 and s ∗ (K ∗ ) = s ∗ (L ·M ) = k . These are answers to open problems formulated by Badr et al. [RAIRO-Theor. Inf. Appl. 43 (2009) 69–94].

The Equivalence and Learning of Probabilistic Automata (Extended Abstract)

Abstract: We prove that the equivalence problem for probabilistic automata is solvable in time O((n1 + n2)4) , where RI and n2 are numbers of states of two given probabilistic automata. This result improves over the best previous upper-bound of coNP. This algorithm has some interesting applications to, for example, the covering and equivalence problems for uninitiated probabilistic automata, the equivalence and containment problems for unambiguous nondeterministic finite automata and the path equivalence problem for nondeterministic finite automata. Using the same technique, we present a polynomial-time algorithm for learning probabilistic automata. Our learning protocol is learning via queries.