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FORMAL LANGUAGES AND COMPILERS prof.s Luca Breveglieri and Angelo Morzenti Exam of Tue 4 SEPTEMBER 2018 - 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 nondeterministic automaton A over the two-letter alphabet Σ = { a, b }: 2 1 3 4 A ↓ ↓ → b a b a b Answer the following questions: (a) Find the shortest strings of language L (A) from length 0 (included) to length 2 (included) and write their computations. (b) Through the Berry-Sethi method ( BS ), find a deterministic automaton A′ equiv- alent to automaton A and minimize it if necessary. Verify the correctness of (the minimal version of) A′ by means of the strings found at point (a).…