Fuzzy L Algebraic Power Series

Formal power series plays an important role in many diverse areas of theoretical computer science and mathematics. In1968, in order to use formal language to describe the occurrence and growth process of plant morphological, biologist Aristid Lindenmayer put forward a mathematical model, called Lindenmayer system (L system, in short). Based on that, J.Honkala and Kuich defined the power series generated by L system. Furthermore, in order to study this kind of power series deeply, a new mathematical model (called L algebraic system) was introduced, and the L algebraic power series was defined. The power series generated by the L system can be considered as a special case of L algebraic power series. So we can define this kind of power series under the framework of L algebraic system. and study it using the notion of the L algebraic system.The theory of L algebraic system studies the iteration of semi-algebra S<Σ*). On different semirings S, the iteration of semi-algebra S(Σ*) is distinct, and the properties of L algebraic power series are also different. This paper extends L alge-braic system to fuzzy semiring F, and studies the properties of the fuzzy L algebraic power series.The work of this paper is summed as follows:1. The relevant theory of fuzzy L algebraic system is introduced. First, this paper gives the concept of fuzzy formal power series, and defines the fuzzy algebraic system and different types of fuzzy L algebraic power series. Second, this paper studies the fixed point properties of fuzzy L algebraic power series. Finally, the closure properties of fuzzy L algebraic power series are studied.2. The relevant theory of fuzzy DOL power series is introduced. First, this paper gives two different definitions of fuzzy DOL power from the two viewpoints of the framework L system and fuzzy L algebraic system, respectively then verifies the equivalence of two definitions. Second, this paper proposes the notion of fuzzy DOL multiplicity sequence, and studies the properties of the multiplicity sequence and some decidability problems. Finally, this paper proves that it is decidable whether two given fuzzy DOL power series are equal or not and it is also decidable whether a given fuzzy DOL power series is F-rational, F-algebraic or F-context-free or not.