G. Fici proved that a finite word has a minimal suffix automaton if and only if all its left special factors occur as prefixes. He called LSP all finite and infinite words having this latter property. We characterize here infinite LSP words in terms of S-adicity. More precisely we provide a finite set of morphisms S and an automaton A such that an infinite word is LSP if and only if it is S-adi...

The minimal deterministic finite automaton is generally used to determine regular languages equality. Antimirov and Mosses proposed a rewrite system for deciding regular expressions equivalence of which Almeida et al. presented an improved variant. Hopcroft and Karp proposed an almost linear algorithm for testing the equivalence of two deterministic finite automata that avoids minimisation. In ...

The Moore-Myhill Garden of Eden theorem asserts that a cellular automaton with finite alphabet over a free abelian group of rank 2 is surjective if and only if it is pre-injective. Here, pre-injectivity means that two configurations which coincide outside of a finite subset of the group must coincide everywhere if they have the same image under the cellular automaton. The Garden of Eden theorem...

We exhibit a family {Ln} of finite regular languages such that any 1-way quantum finite automaton (QFA) accepting Ln with probability 1 2 + ǫ (for any constant ǫ > 0) must have 2 Ω(n/ logn) states. On the other hand, each language Ln can be recognized by a deterministic finite automaton (DFA) of size O(n). This is in immediate contrast to the result of [1] which shows that for some regular lang...

Bisemigroups are algebras equipped with two independent associative operations. Labeled finite sp-biposets may serve as a possible representation of the elements of the free bisemigroups. For finite sp-biposets, an accepting device, called parenthesizing automaton, was introduced in [6], and it was proved that its expressive power is equivalent to both algebraic recognizability and monadic seco...

Weighted nite automata (WFA) were introduced as a device for generating and transforming pixel images. The inference problem is the determination of a WFA that generates a given image. There are two basic results in this paper. First, a general solution to the inference problem is given which always yields a minimum state WFA for any image. This algorithm uses only addition and inner products o...

Merging states in finite automata is a main method of reducing the size of the representation of regular languages. The process has been extensively studied for deterministic finite automata (DFA), where the conditions for merging states can be efficiently computed. The matter is more complex in the case of nondeterministic finite automata (NFA), where merging states can be done in different wa...

We investigate the shuffle operation on regular languages represented by complete deterministic finite automata. We prove that f(m,n) = 2+2(2−1)(2−1) is an upper bound on the state complexity of the shuffle of two regular languages having state complexities m and n, respectively. We also state partial results about the tightness of this bound. We show that there exist witness languages meeting ...

The problem of finding the most probable string for a distribution generated by a weighted finite automaton or a probabilistic grammar is related to a number of important questions: computing the distance between two distributions or finding the best translation (the most probable one) given a probabilistic finite state transducer. The problem is undecidable with general weights and is NP-hard ...

Given a timed automaton G accepting the timed language L a finite state machine G 0 can be constructed, known as the region automaton, which accepts the untimed language Untime (L). In this paper we construct an alternative finite state machine which also accepts the language Untime (L), but has fewer states than G 0. This is shown for languages of both finite and infinite traces given that the...