# Some terminologies in Wirth's book and the satisfying of deterministic algorithm

I am going through Wirth's Textbook on Compiler design . After proceeding though some pages , I realized I have taken for granted my understanding of some of the terminologies that have been used . For example ,the following terms :

the examples mentioned in the lines in the screenshot refer to the following set of equations :

Later on while describing the possibility of the conditions of deterministic algorithms being satisfied it says for an expresion of the following form :

"term_0 | term_1"

the terms must not feature any common starting symbols .And then it says this results in the exclusion of left recusrsion . If we consider the left recursive production :

A = A "a" | "b"

then the requirement is violated "b" is also a start symbol of "A" .

How is "b" a start symbol of "A" ? Basically from the definitions given I understood start symbol means the symbol for which an equation is deifined first ?

Why does common start symbol disturb the conditions of deterministic algorithm ?

• Please replace the image with text, to make the text searchable. – Yuval Filmus Sep 22 '17 at 21:16
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The definition of start symbol that you quote has nothing to do with the definition of start symbol in the context of deterministic grammars. Here is a correct definition:

A terminal $a$ is a start symbol of a sequential form $\alpha$ if $\alpha \Rightarrow^* aw$ for some $w \in \Sigma^*$.

In words, $a$ is a start symbol of $\alpha$ if $\alpha$ generates some word starting in $a$.

In your example, $Aa$ generates the word $ba$, and so it shares a start symbol with $b$.

Why is sharing a start symbol bad? Suppose you are trying to parse $A$, and are encountering $b$. Which production do you choose? $Aa$ or $b$? It is impossible to tell without looking ahead. The deterministic algorithm considered by Wirth has no lookahead, and so this situation is problematic for it.

• Thanks a lot for your reply . Any material that you can suggest for learning about this topic ? – Eddie Dorphy Sep 23 '17 at 6:42
• Wirth's book is really old fashioned. Pick up a more recent one. – Yuval Filmus Sep 23 '17 at 6:43
• Would I be right if i say that the pre-requisites haven't been arranged in a proper sequence , like , it comes up with few things which requires prior explanation which are missing ? Any suggestions for other books ? A one that is legally available for free in pdf format will be nice . – Eddie Dorphy Sep 23 '17 at 6:50
• Where can I find the definition of start symbok that you have quoted in your anser ? – Eddie Dorphy Sep 23 '17 at 6:52
• The definition is pretty standard. I bet you can find it in the "dragon" book. Unfortunately textbooks tend not to be freely available, but you can find them on libraries. – Yuval Filmus Sep 23 '17 at 6:54