Implement a recursive descent parser in Python that evaluates arithmetic expressions containing integers, variables, addition, subtraction, multiplication, division, and parenthesis. The parser should support operator precedence and associativity. Additionally, implement a symbol table to store and retrieve variable values. The solution must include a Tokenizer class, a Parser class with methods for each grammar rule, and an Interpreter class to execute the parsed AST. Provide error handling for syntax errors and undefined variables.