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FORMAL LANGUAGES AND COMPILERS prof.s Luca Breveglieri and Angelo Morzenti Exam of Tue 21 February 2017 - Part Theory WITH SOLUTIONS - FOR TEACHING PURPOSES HERE THE SOLUTIONS ARE WIDEL Y COMMENTED LAST + FIRST NAME: (capital letters please) MATRICOLA: SIGNATURE: (or PERSON CODE) INSTRUCTIONS - READ CAREFULLY: • The exam is in written form and consists of two parts: 1. Theory (80%): Syntax and Semantics of Languages – regular expressions and finite automata – free grammars and pushdown automata – syntax analysis and parsing methodologies – language translation and semantic analysis 2. Lab (20%): Compiler Design by Flex and Bison • To pass the exam, the candidate must succeed in both parts (th eory and lab), in one call or more calls separately, but within one year (12 months ) between the two parts. • To pass part theory, the candidate must answer the mandatory (not optional) ques- tions; notice that the full grade is achieved by answering th e optional questions. • The exam is open book: textbooks and personal notes are permi tted. • Please write in the free space left and if necessary continue on the back side of the sheet; do not attach new sheets and do not replace the existin g ones. • Time: part lab 60m - part theory 2h.15m 1 Regular Expressions and Finite Automata 20% 1. Consider the following regular expression e, over the two-letter alphabet Σ = { a, b }: e = ( a b | a )+ ( b a )∗ Consider also the finite-state automaton A below, over the same alphabet Σ, with initial state 1 and final states 1, 2: 1 2A → −→ → a b Answer the following questions: (a) Find the shortest ambiguous string of the regular langua ge L (e) and suitably justify your answer. Provide evidence that the string is amb iguous and that it is the shortest ambiguous one. (b) By using the…