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a+b+c+d algorithm alternative ambiguous analysis arithmetic expressions b x c id begin symb belong bottom-to-top methods bottom-to-top parsing called cells Chapter compilation computer languages concatenate Consider the grammar context-free grammar correct parse current word cxd+e derivation Lt described duction equivalent grammar example given go to z3 gram grammar with actions id id axb id id id id(symb id\id indicates kind of grammar left-recursive classes left-to-right list processing mars matrix methods of parsing natural languages NIL,T operator grammar operator precedence grammar parse fails parse the sentence parse tree parser parsing methods partial parses phrases derived possible prime phrase priori rules problem of parsing procedure push-down list push(concatenate(pull recursive remainder second grammar SENTENCE GOAL PRODUCTION sentence symbol sequence of items sequence of words set of sentences sets of words step T-+id tence tion top-to-bottom method Top-to-bottom Parsing transformed grammar typical parsing words and classes