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 partial derivative automaton (Apd) is usually smaller than other non-deterministic finite automata constructed from a regular expression, and it can be seen as a quotient of the Glushkov automaton (Apos). By estimating the number of regular expressions that have ε as a partial derivative, we compute a lower bound of the average number of mergings of states in Apos and describe its asymptoti...

We propose a new algorithm for checking language equivalence of non-deterministic Büchi automata. start from construction proposed by Calbrix, Nivat and Podelski, which makes it possible to reduce the problem that automata on finite words. Although this generates large highly automata, we show how exploit their specific structure apply state-of-the art techniques based coinduction state-space h...

We compare parametrized automata, a class of automata recently introduced by the authors, against finite memory automata with non-deterministic assignment, an existing class of automata used to model services. We prove that both classes have the same expressive power, while parametrized automata can be exponentially succinct in some cases. We then prove that deciding simulation preorder for par...

We improve on an existing [P.A. Abdulla, J. Högberg, L. Kaati. Bisimulation Minimization of Tree Automata. Int. J. Found. Comput. Sci. 18(4): 699–713, 2007] bisimulation minimization algorithm for finite-state tree automata by introducing backward and forward bisimulation and developing minimization algorithms for them. Minimization via forward bisimulation is also effective on deterministic tr...

We prove that no recursive function can upper bound the increase in the size of description when a two-way deterministic finite automaton with k + 1 heads is replaced by an equivalent two-way deterministic finite automaton with k heads. This is true for all k, and remains true if the automata are unary and/or nondeterministic.

In this paper, we introduce a new model of deterministic Watson-Crick automaton namely restricted deterministic WatsonCrick automaton which is a deterministic Watson-Crick automaton where the complementarity string in the lower strand is restricted to a language L. We examine the computational power of the restricted model with respect to L being in different language classes such as regular, u...

We initiate the theory and applications of biautomata. A biautomaton can read a word alternately from the left and from the right. We assign to each regular language L its canonical biautomaton. This structure plays, among all biautomata recognizing the language L, the same role as the minimal deterministic automaton has among all deterministic automata recognizing the language L. We expect tha...

We survey in this paper some variants of the notion of determinism, refining the spectrum betweennon-determinism and determinism. We present unambiguous automata, strongly unambiguousautomata, prophetic automata, guidable automata, and history-deterministic automata. Weinstantiate these various notions for finite words, infinite words, finite trees, infinite trees, datalanguages...