We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent oneway and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for each one-way nondeterministic automaton with n states there exist Parikh equivalent one-way and two-way deterministic automata with e √ n·lnn) and p(n) states,...

Watson-Crick automata are finite state automata working on double-stranded tapes, introduced to investigate the potential of DNA molecules for computing. In this paper, we continue the investigation of descriptional complexity of Watson-Crick automata initiated in [9]. In particular, we show that any finite language as well as any unary regular language can be recognized by a Watson-Crick autom...

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 ...

One of the main topics of descriptional complexity is the question of how the size of the description of a formal language varies when being described by different formalisms. A fundamental result is the exponential trade-off between the number of states of nondeterministic (NFA) and deterministic finite automata (DFA) (see, for example, [12]). Additional exponential and double-exponential trad...

The minimal deterministic finite automaton is generally used to determine regular languages equality. Using Brzozowski’s notion of derivative, 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 fini...

Tree automata based algorithms are essential in many fields in computer science such as verification, specification, program analysis. They become also essential for databases with the development of standards such as XML. In this paper, we define new classes of non deterministic tree automata, namely residual finite tree automata (RFTA). In the bottom-up case, we obtain a new characterization ...

We improve a recent result [A. Badr: Hyper-Minimization in O(n). In Proc. CIAA, LNCS 5148, 2008] for hyper-minimized finite automata. Namely, we present an O(n logn) algorithm that computes for a given finite deterministic automaton (dfa) an almost equivalent dfa that is as small as possible—such an automaton is called hyper-minimal. Here two finite automata are almost equivalent if and only if...

We improve a recent result [A. Badr: Hyper-Minimization in O(n). In Proc. CIAA, LNCS 5148, 2008] for hyper-minimized finite automata. Namely, we present an O(n log n) algorithm that computes for a given finite deterministic automaton (dfa) an almost equivalent dfa that is as small as possible—such an automaton is called hyper-minimal. Here two finite automata are almost equivalent if and only i...

Finite languages are an important sub-regular language family, which were intensively studied during the last two decades in particular from a descriptional complexity perspective. An important contribution to the theory of finite languages are the deterministic and the recently introduced nondeterministic finite cover automata (DFCAs and NFCAs, respectively) as an alternative representation of...

Abstract We show the decidability of finite sequentiality problem for unambiguous max-plus tree automata. A automaton is called if there at most one accepting run on every tree. The asks whether a given automaton, exist finitely many deterministic automata whose pointwise maximum equivalent to automaton.