Fuzzy alternating Büchi automata over distributive lattices

Alternation was first proposed by Chandra et al. for obtaining a theoretical model of parallel computations. Compared with nondeterminism, alternation gives computing devices the power of universal choice in addition to existential choice. In this paper, we put forward a notion of fuzzy alternating Büchi automata over a distributive lattice L (L-ABAs, for short). In our setting, a weight is the label of a leaf node of the run tree when executing a transition, which is helpful in complementing L-ABAs. Taking the dual operation on the transition function and negating final costs on states, we can get the complement of a given L-ABA. We point out that L-ABAs have the same expressive power as L-valued fuzzy nondeterministic Büchi automata (L-NBAs). A construction presented here shows that languages accepted by L-valued fuzzy alternating co-Büchi automata (L-ACAs) are also ω-regular languages. Moreover, closure properties of L-ABAs and decision problems for L-ABAs are also discussed.