[FOM] Formal grammar question

[A.P. Hazen]

Ignorance speaking, here!
It seems to me that most of us HUMANS find it easier to read 
conventional (lots of parentheses, infixed operators) logical 
notation than we do parenthesis-free ("Polish") notation.  Are there 
results about computational difficulty that this might be a symptom 
of?
For instance: the usual, go left to right counting the parentheses 
(adding 1 for left parens, subtracting for right), way of checking a 
formula for well-formedness in conventional notation amounts to 
having the human checker simulate the operation of a push-down 
automaton making a single pass through the string.  At least the 
obvious intuitive way of checking Polish formulas involvesd more 
back-and-forthing.  Is this essential?
Again, the definition of well-formed formula given by Goodman and 
Quine in "Steps Toward a Constructive Nominalism" (JSL v. 12 (1947), 
pp. 105-122) makes essential reference to numbers of parentheses in 
strings, and it isn't IMMEDIATELY obvious how to define 
well-formedness for polish notation on their basis.
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Allen Hazen
Philosophy Department
University of Melbourne