正则语言上二元运算的无限制状态复杂度
Unrestricted State Complexity of Binary Operations on Regular Languages
摘要：
我研究了不同字母表上正则语言的二元运算的状态复杂度。众所周知，如果$L'_m$和$L_n$是限制在相同字母表上的语言，分别具有$m$和$n$前缀，则在$L'_m$和$L_n$上的任何二进制布尔运算的状态复杂度是$mn$，并且乘积（级联）的状态复杂度是$(m-1)2^n +2^{n-1}$。与此相反，如果$L'_m$和$L_n$是在他们自己的不同的字母表，并和对称差的状态复杂性是$mn+m+n+1$，交叉是$mn$，差是$mn+m$，和产品是$m2^n+2^{n-1}$。
英文摘要：
I study the state complexity of binary operations on regular languages over different alphabets. It is well known that if $L'_m$ and $L_n$ are languages restricted to be over the same alphabet, with $m$ and $n$ quotients, respectively, the state complexity of any binary boolean operation on $L'_m$ and $L_n$ is $mn$, and that of the product (concatenation) is $(m-1)2^n +2^{n-1}$. In contrast to this, I show that if $L'_m$ and $L_n$ are over their own different alphabets, the state complexity of union and symmetric difference is $mn+m+n+1$, that of intersection is $mn$, that of difference is $mn+m$, and that of the product is $m2^n+2^{n-1}$.
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