We generalise a search algorithm by Mohri and Riley from strings to trees. The original algorithm takes as input a weighted automaton A over the tropical semiring, together with an integer N , and outputs N strings of minimal weight with respect to A. In our setting, the input automaton defines a weighted tree language, again over the tropical semiring, and the output is a set of N trees with m...

There exists a linear time algorithm for the minimization of acyclic deterministic finite-state automata (ADFA) due to Dominique Revuz [17]. The algorithm has different phases involving the computation of a height for each state, sorting states of the same height and joining equivalent states. We present a new linear time algorithm for the task at hand. The algorithm is conceptionally simpler a...

We investigate the magic number problem, that is, the question whether there exists a minimal n-state nondeterministic finite automaton (NFA) whose equivalent minimal deterministic finite automaton (DFA) has α states, for all n and α satisfying n ≤ α ≤ 2n. A number α not satisfying this condition is called a magic number (for n). It was shown in [11] that no magic numbers exist for general regu...

We present a fast incremental algorithm for constructing minimal DFCA for a given language. Since it was shown that the minimal DFCA for a language L has less states than the minimal DFA for the same language L, this technique seems to be the best choice for incrementally building the automaton for a large language, especially when the number of states in the DFCA is significantly less than the...

We present two solutions to the firing synchronization problem on the ring, an 8-state minimal-time solution and a 6-state non-minimal-time solution. Both solutions use fewer states than the previous best-known minimal-time automaton, a 16-state solution due to Culik. We also give the first lower bounds on the number of states needed for solutions to the ring firing synchronization problem. We ...

In this paper, relations among the membership values of gener- alized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized nite automaton with vague ( final) states for any vague regular language recog...

We present an algorithm to generate positive braids of a given length as words in Artin generators with a uniform probability. The complexity of this algorithm is polynomial in the number of strands and in the length of the generated braids. As a byproduct, we describe a finite state automaton accepting the language of lexicographically minimal representatives of positive braids that has the mi...

We devise a learning algorithm for deterministically recognizable tree series where the weights are taken from a commutative group. For this, we use an adaptation of the minimal adequate teacher model that was originally introduced by Angluin. The algorithm runs in polynomial time and constructs the unique minimal deterministic bottom-up finite state weighted tree automaton that recognizes the ...

Quasi-reversible automata is a suitable representation for reversible languages. In this work a method is proposed to obtain such an automaton for any given reversible language represented by its minimal DFA. Our method runs in polynomial time respect to the size of the minimal DFA and improves a previous exponential method. Previous bound for the size of quasi-reversible automata is also reduc...

We consider way k tape alternating pushdown automata k apa and way k tape alternating nite automata k afa We say that an alternating automaton accepts a language L with f n bounded maximal respectively minimal leaf size if arbitrary re spectively at least one accepting tree for any w L has no more than f jwj leaves The main results of the article are the following For way k tape alternating cou...