We solve the following problem proposed by H. Straubing. Given a two letter alphabet A, what is the maximal number of states f(n) of the minimal automaton of a subset of An, the set of all words of length n. We give an explicit formula to compute f(n) and we show that 1 = lim n→∞ nf(n)/2n ≤ limn→∞ nf(n)/2 n = 2. The purpose of this note is to solve the following question, raised by H. Straubing...

A word w is called a reset word for a deterministic finite automaton A if it maps all states of A to one state. A word w is called a compressing to M states for a deterministic finite automaton A if it maps all states of A to at most M states. We consider several subclasses of automata: aperiodic, Dtrivial, monotonic, partially monotonic automata and automata with a zero state. For these subcla...

In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...

On equivalence and emptiness problems of multi-letter (measure many) quantum finite automata Abstract In this paper, we study some decision problems both for multi-letter quantum finite au-tomata and measure many multi-letter quantum finite automata. We first show that given a k1-letter quantum finite automaton A1 and a k2-letter quantum finite automaton A2 over the same input alphabet Σ, they ...

Okhotin [9] showed an exponential trade-off in the conversion from nondeterministic unary finite automata to unambiguous nondeterministic unary finite automata. In this paper, we consider the trade-off in the case of unary symmetric difference finite automata to finitely ambiguous unary symmetric difference finite automata. Surprisingly, the trade-off is linear in the number of states of the fi...

A deterministic finite automaton A is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton A to a particular one. We prove that it is a PSPACEcomplete problem to check whether the language of reset words for a given automaton coincides with the language of reset words for some particular automaton.

Finite tree automata consist of a set of states and a set of transitions. Input trees are accepted if it is possible to label the tree with states such that the relationship between the state at every node and the state at its child nodes conforms to a transition. Thus, the transitions only define how a state must be labeled with respect to its children or vice versa. This work investigates how...

In this paper, we outline the design of a nondeterministic finite state automaton (NFSA) for natural language morphology, and compare it to previous work in unsupervised learning of morphology. In Section 2, we describe the nature of an MDL-based system for unsupervised learning of morphology, using the signature-based model of Goldsmith 2001 as an example, and we describe some drawbacks of the...

We resolve an open problem raised by Ravikumar and Ibarra [SIAM J. Comput., 18 (1989), pp. 1263–1282] on the succinctness of representations relating to the types of ambiguity of finite automata. We show that there exists a family of nondeterministic finite automata {An} over a two-letter alphabet such that, for any positive integer n, An is exponentially ambiguous and has n states, whereas the...

Consider an extension of the classical model of finite automata operating on finite strings in which the machine simultaneously reads a fixed advice tape — an infinite string A. A deterministic finite-string automaton with advice A is like a deterministic finite-string automaton, except that at step n the next state depends on the current state, the nth symbol of the input w ∈ Σ∗, and the nth s...