Affiliation:
1. Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
2. Department of CSED, Thapar Institute of Engineering and Technology, Patiala, India
Abstract
In this paper, we study fuzzy top-down tree automata over lattices ( LTA s , for short). The purpose of this contribution is to investigate the minimization problem for LTA s . We first define the concept of statewise equivalence between two LTA s . Thereafter, we show the existence of the statewise minimal form for an LTA . To this end, we find a statewise irreducible LTA which is equivalent to a given LTA . Then, we provide an algorithm to find the statewise minimal LTA and by a theorem, we show that the output statewise minimal LTA is statewise equivalent to the given input. Moreover, we compute the time complexity of the given algorithm. The proposed algorithm can be applied to any given LTA and, unlike some minimization algorithms given in the literature, the input doesn’t need to be a complete, deterministic, or reduced lattice-valued tree automaton. Finally, we provide some examples to show the efficiency of the presented algorithm.
Subject
Artificial Intelligence,General Engineering,Statistics and Probability
Reference30 articles.
1. Bisimulation minimization of tree automata;Abdulla;International Journal of Foundations of Computer Science,2007
2. A taxonomy of minimisation algorithms for deterministic tree automata;Björklund;Journal of Universal Computer Science,2016
3. Fuzzy tree language recognizability;Bozapalidis;Fuzzy Sets and Systems,2010
4. Decidability of the weak second-order theory of two successors;Doner;Notices Amer Math Soc,1965
5. Tree acceptors and some of their applications;Doner;Journal of Comput and Syst Sci,1970