除了括号不匹配之外，还可以使用正则表达式来验证有效表达式。 （如维基百科页面所示，分流场算法将捕获不匹配的括号，因此我忽略它们。）
正则表达式如下：
PRE* OP POST* (INF PRE* OP POST*)*
where:
PRE is a prefix operator or (
POST is a postfix operator or )
INF is an infix operator
OP is an operand (a literal or a variable name)
您链接的维基百科页面包含函数调用，但不包含数组下标；如果你想处理这些情况，那么：
PRE is a prefix operator or (
POST is a postfix operator or ) or ]
INF is an infix operator or ( or ,
OP is an operand, including function names
上面需要注意的一点是PRE and INF处于不相交的环境中；也就是说，如果PRE是有效的，那么INF不是，反之亦然。这意味着对前缀运算符和中缀运算符使用相同的符号是明确的。还，PRE and POST处于不相交的上下文中，因此您可以对前缀和后缀运算符使用相同的符号。但是，后缀和中缀运算符不能使用相同的符号。作为示例，请考虑 C/C++ 运算符：
- prefix or infix
+ prefix or infix
-- prefix or postfix
++ prefix or postfix
我隐式地使用了上面的这个功能来允许(既可以用作表达式分组（实际上是前缀），也可以用作函数调用（中缀，因为它位于函数名称和参数列表之间；运算符是“call”。）
最常见的是将该正则表达式实现为状态机，因为只有两种状态：
+-----+ +-----+
|State|-----OP---->|State|
| 1 |<----INF----| 2 |
| |---+ | |---+
+-----+ | +-----+ |
^ PRE ^ POST
| | | |
+------+ +------+
我们可以将状态 1 称为“想要操作数”，将状态 2 称为“有操作数”。一个简单的实现只需将维基百科中介绍的调车场算法分成两个循环，就像这样（如果您不喜欢goto，它可以被消除，但它确实是呈现状态机的最清晰的方式）。
want_operand:
read a token. If there are no more tokens, announce an error.
if the token is an prefix operator or an '(':
mark it as prefix and push it onto the operator stack
goto want_operand
if the token is an operand (identifier or variable):
add it to the output queue
goto have_operand
if the token is anything else, announce an error and stop. (**)
have_operand:
read a token
if there are no more tokens:
pop all operators off the stack, adding each one to the output queue.
if a `(` is found on the stack, announce an error and stop.
if the token is a postfix operator:
mark it as postfix and add it to the output queue
goto have_operand.
if the token is a ')':
while the top of the stack is not '(':
pop an operator off the stack and add it to the output queue
if the stack becomes empty, announce an error and stop.
if the '(' is marked infix, add a "call" operator to the output queue (*)
pop the '(' off the top of the stack
goto have_operand
if the token is a ',':
while the top of the stack is not '(':
pop an operator off the stack and add it to the output queue
if the stack becomes empty, announce an error
goto want_operand
if the token is an infix operator:
(see the wikipeda entry for precedence handling)
(normally, all prefix operators are considered to have higher precedence
than infix operators.)
got to want_operand
otherwise, token is an operand. Announce an error
(*) The procedure as described above does not deal gracefully with parameter lists;
when the postfix expression is being evaluated and a "call" operator is found, it's
not clear how many arguments need to be evaluated. It might be that function names
are clearly identifiable, so that the evaluator can just attach arguments to the
"call" until a function name is found. But a cleaner solution is for the "," handler
to increment the argument count of the "call" operator (that is, the open
parenthesis marked as "infix"). The ")" handler also needs to increment the
argument count.
(**) The state machine as presented does not correctly handle function calls with 0
arguments. This call will show up as a ")" read in the want_operand state and with
a "call" operator on top of the stack. If the "call" operator is marked with an
argument count, as above, then the argument count must be 0 when the ")" is read,
and in this case, unlike the have_operand case, the argument count must not be
incremented.
