【摘 要】
：
由Lindenmayer创立的L系统既是一个描述生物生长的数学模型,又是一种并发的形式语言.它的研究历来为人所重视.但是,L系统及其种种变形刻画的都是同步的并发系统.实际上,在自
【机 构】
：
中国科学院数学与系统科学研究院数学研究所智能信息处理重点实验室,中国科学院数学与系统科学研究院数学研究所智能信息处理重点实验室,复旦大学智能信息处理开放实验室 北京100080,北京100080,上海
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由Lindenmayer创立的L系统既是一个描述生物生长的数学模型,又是一种并发的形式语言.它的研究历来为人所重视.但是,L系统及其种种变形刻画的都是同步的并发系统.实际上,在自然界中存在着许多异步的并发现象.因此,对传统的L系统作了推广,提出了广义L系统的概念,证明了广义L系统不能被传统的L系统所覆盖.还划分了广义L系统的子类,证明了各子类等价的充分必要条件,并得到一个基本定理:两个GPDOL系统（一种确定型广义L系统）L[m1,m2,…,mj]和L[n1,n2,…,nk]等价,当且仅当k=j并且存在诸mi的公因子g和诸ni的公因子h,使得（?）i:mi/g=ni/h.
The L system, founded by Lindenmayer, is not only a mathematical model describing biological growth, but also a concurrent formal language, and its research has always been valued. However, the L system and its variants are all characterized by concurrent concurrent systems. , There are many asynchronous concurrences in nature.Therefore, the traditional L system is generalized and the concept of generalized L system is proposed, which proves that the generalized L system can not be covered by the traditional L system, and the generalized L L system, the necessary and sufficient conditions for the equivalence of each subclass are proved and a basic theorem is obtained: two GPDOL systems, a deterministic generalized L system, L [m1, m2, ..., mj] and L [ n1, n2, ..., nk] if and only if k = j and there is a common factor g of ni and a common factor h of ni such that (?) i: mi / g = ni / h.
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