1. Parsing and Parser Parsing methods: top-down & bottom-up

2. Parsing and Parser
Parsing -- the process of determining if a string of tokens can be generated by a grammar.
Parser -- a software module in a compiler input: tokens, output: parse tree.
Parsing methods:
top-down root ---> leaves
bottom-up leaves ---> root

3. Lexical and Syntax Analysis
Lexical analysis -- linear analysis or scanning in a compiler design.
Syntax analysis -- hierarchical analysis and it is represented by a parse tree.
Example: position := initial + rate*60
tokens: a meaningful unit -- position, :=, +, 60
parse tree:
root -- assignment statement, leaves -- all the tokens,
internal nodes -- nonterminals, such as expression, identifier, and number

4. Parsing Method I Deterministic top-down parser
using the information available to make a correct choice (exposed input string, production rules, frontier)
a finite practical table, T
row: a nonterminal node (i)
column: the left-most exposed token (j)
T[i, j]: a fixed choice for next production rule

5. Left / Right most Derivation
Left/right most derivation -- a derivation in which only the left /right most nonterminal in any sentential form is replaced at each step.
Ambiguous grammar: a grammar that produces more than one left most or right most derivation for the same string.

6. Parsing Method II Deterministic bottom-up parser
rootline -- the left-to-right sequence of roots for the subtrees (see Fig. 2.12)
LR(1) parser, a bottom-up parsing machine for G3 -- L to R, right most, observe 1 symbol in input each time.
Read, v, and look ahead transition, {v}
Apply state #i