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应用泛代数理论,建立模式匹配问题的泛代数学描述框架,研究模式匹配问题的数学基础,基于泛代数学理论的观点,模式是一类有限的结构(代数),模式匹配能够被形式化为寻找两个结构之间保持的映射关系,即为两个结构之间的同态,证明模式同态问题与模式匹配问题的等价关系,亦即模式匹配问题可以归约为模式同态问题,基于模式同态的框架,提出求解模式匹配问题的算法模型。
The generalized algebra theory is applied to establish a generic algebraic description framework for pattern matching problem and to study the mathematical basis of pattern matching. Based on the theory of universal algebraic theory, the model is a finite structure (algebra), and the pattern matching can be formalized as Find the mapping relationship between the two structures, that is, the homomorphism between the two structures to prove the equivalent relationship between the pattern homomorphism and the pattern matching, that is, the pattern matching can be reduced to the pattern homomorphism, Based on the framework of pattern homomorphism, an algorithm model for solving pattern matching problem is proposed.