This paper presents and analyzes an incremental algorithm for the construction of Acyclic Nondeterministic Finite-state Automata (NFA). Automata of this type are quite useful in computational linguistics, especially for storing lexicons. The proposed algorithm produces compact NFAs, i.e. NFAs that do not contain equivalent states. Unlike Deterministic Finite-state Automata (DFA), this property ...

We give a new presentation of Brzozowski’s algorithm to minimize finite automata, using elementary facts from universal algebra and coalgebra, and building on earlier work by Arbib and Manes on a categorical presentation of Kalman duality between reachability and observability. This leads to a simple proof of its correctness and opens the door to further generalizations. Notably, we derive algo...

We propose algorithms that use Markov chain techniques to generate acyclic automata uniformly at random. We first consider deterministic, accessible and acyclic automata, then focus on the class of minimal acyclic automata. In each case we explain how to define random local transformations that describe an ergodic and symmetric Markov chain: the distribution of the automaton obtained after T ra...

Introduction In formal language theory, several models characterize regular languages: finite au-tomata, congruences of finite index, monadic second-order logic (MSO), see e.g. [Büc60, Elg61, Tra61]. Further connections exist between monoid varieties and logical fragments of MSO, for instance aperiodic monoids have been shown to recognize exactly the word languages defined by first-order (FO) f...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

A réversible automaton is a finite automaton in which each letter induces a partial one-to-one map from the set of states into itself. We solve the following problem proposed by Pin. Given an alphabet A, does there exist a séquence of languages Kn on A which can be accepted by a réversible automaton, and such that the number of states of the minimal automaton of Kn is in O(n), while the minimal...

A word w is called synchronizing (recurrent, reset, directed) word of a deterministic finite automaton (DFA) if w sends all states of the automaton on a unique state. Jan Černy had found in 1964 a sequence of n-state complete DFA with shortest synchronizing word of length (n− 1). He had conjectured that it is an upper bound for the length of the shortest synchronizing word for any n-state compl...

Semi-input-memory finite automata are a generalization of input-memory finite automata by appending an autonomous finite automaton component. This paper gives a decision criterion of weakly invertible semi-input-memory finite automata with delay 2 of which the minimal output weight of length 2 and the sizes of input and output alphabets are identical. The results are used to generate a kind of ...

We present several new results on minimal space requirements to recognize a nonregular language: (i) realtime nondeterministic Turing machines can recognize a nonregular unary language within weak log logn space, (ii) log logn is a tight space lower bound for accepting general nonregular languages on weak realtime pushdown automata, (iii) there exist unary nonregular languages accepted by realt...

The context of this article is the program to develop monoidal bicategories with a feedback operation as an algebra of processes with applications to concurrency theory The objective here is to study reachability minimization and minimal realization in these bicategories In this set ting the automata are cells in contrast with previous studies where they appeared as objects As a consequence we ...