In this note, we define bisimulation for BL-general fuzzy automata and show that if there is a bisimulation between two BL-general fuzzy automata, then they have the same behavior.For a given BL-general fuzzy automata, we obtain the greatest bisimulation for the BL-general fuzzy automata. Thereafter, if we use the greatest bisimulation, then we obtain a quotient BL-general fuzzy automata and th...

Taking into account the notion of BL-general fuzzy automaton, in the present study we define the notation of BL-intuitionistic general L-fuzzy automaton and I-bisimulation for BL-intuitionistic general L-fuzzy automaton.Then for a given BL-intuitionistic general L-fuzzy automaton, we obtain the greatest I-bisimulation. According to this notion, we give the structure of quotient BL-intuiti...

Quotient is a basic operation of formal languages, which plays key role in the construction minimal deterministic finite automata (DFA) and universal automata. In this paper, we extend to power series systemically investigate its implications study weighted particular, define two quotient operations for are called (left or right) quotients residuals respectively. Algebraic properties closure (w...

We consider the state complexity of extensions of the Kleene star and quotient operations to unranked tree languages. Due to the nature of the tree structure, there are two distinct ways to define the star operation for trees, we call these operations, respectively, bottom-up and top-down star. We show that (n+ 3 2 )2 states are sufficient and necessary in the worst case to recognize the bottom...

We show how to use duality theory to construct minimized versions of a wide class of automata. We work out three cases in detail: (a variant of) ordinary automata, weighted automata and probabilistic automata. The basic idea is that instead of constructing a maximal quotient we go to the dual and look for a minimal subalgebra and then return to the original category. Duality ensures that the mi...

Three natural equivalence relations on the in nite state space of a hybrid automaton are language equivalence, simulation equivalence, and bisimulation equivalence. When one of these equivalence relations has a nite quotient, certain model checking and controller synthesis problems are decidable. When bounds on the number of equivalence classes are obtained, bounds on the running times of model...