"Foundations of Computer Science II"
(“Fondamenti dell’Informatica II”)
(homepage: http://www.di.univaq.it/orefice/fond.html)
Academic Year 2015-16
Second Level Degree in Computer Science (Laurea Magistrale)
Lecturer: Prof. Sergio Orefice
SYLLABUS
1. Formal language basic notions. Chomsky hierarchy
2. Finite automata. Nondeterministic finite automata. Finite automata with epsilon-transitions
3. Regular expressions. The Kleene theorem. Pumping Lemma for regular sets. Properties of
regular sets
4. Context-free grammars. Pushdown automata. Properties of context-free languages. Chomsky
Normal Form. Pumping Lemma for context-free languages. The CYK algorithm
5. Nonlinear and visual formal languages. Syntactical models
6. Context-free positional grammars
DETAILED PROGRAM
Points 1-4 of the syllabus:
Textbooks (available at the Library):
(English) -Hopcroft, Motwani, Ullman, “Introduction to Automata Theory, Languages, and
Computation”, Addison-Wesley
(Italian) -Hopcroft, Motwani, Ullman, “Automi, Linguaggi e calcolabilità”, Addison-Wesley
Chapter 1:
- Section 1.5 (the central concepts of automata theory)
Chapter 2:
- Section 2.2.1 (DFA)
- Section 2.2.3 (transition diagrams, transition tables)
- Section 2.2.4 (extended transition function)
- Section 2.2.5 (the language of a DFA)
- Section 2.3.2 (NFA)
- Section 2.3.3 (extended transition function)
- Section 2.3.4 (the language of an NFA)
- Section 2.3.5 (equivalence of DFA and NFA: subset construction, accessible states)
(note: TH 2.11 proof yes; TH 2.12: part “if” proof yes, part “only-if” only the construction of
the equivalent NFA)
- Section 2.5.2 (epsilon-NFA)
- Section 2.5.3 (epsilon-closure)
- Section 2.5.4 (extended transition function and language of an epsilon-NFA)
- Section 2.5.5 (eliminating epsilon-transitions)
(note: only the subset construction for epsilon-NFA, TH 2.22 proof no)
Chapter 3:
- Section 3.1 (operations on languages, regular expressions)
(note: case-studies: example 3.2 and exercises 3.1.1.a, 3.1.1.b, 3.1.2.b)
- Section 3.2.1 (Kleene’s theorem)
(note: TH 3.4 proof yes)
- Section 3.2.3 (Thompson’s algorithm)
(note: TH 3.7 proof yes)
- Section 3.4 (algebraic laws for regular expressions)
(note: only the list of the laws, no proofs)
Chapter 4:
- Section 4.1 (pumping lemma for regular languages)
(note: "pigeonhole principle" from Chapter 2; TH 4.1 proof yes,
case-studies: examples 4.2, 4.3 and exercises 4.1.1.c, 4.1.2.a )
- Section 4.2 (closure properties of regular languages)
(note: union, concatenation, star, intersection, difference: proof yes;
complement, reversal: only the construction process; homomorphisms: only definitions;
(TH 4.4, 4.10 proof yes; TH 4.5, 4.8, 4.11, 4.14, 4.16 proof no))
- Section 4.3.2 (testing emptiness of regular languages)
- Section 4.3.3 (testing membership in a regular language)
- Sections 4.4.1, 4.4.2 (testing equivalence of regular languages: equivalent/distinguishable states of
a DFA + “table-filling” algorithm)
(note: TH 4.20 proof no)
- Section 4.4.3 (minimization of DFA’s)
(note: only the algorithm for minimizing DFA’s, TH 4.23, 4.24 proof no)
Chapter 5:
- Sections 5.1, 5.2, 5.4 (context-free grammars and languages)
(note: only formal definition of the following notions: context-free grammar,
derivation, leftmost and rightmost derivation, language of a grammar,
sentential form, parse tree and yield, ambiguity and inherent ambiguity.
TH 5.14, 5.16 proof no)
MIDTERM EXAM
Chapter 6:
- Section 6.1 (PDA and instantaneous descriptions)
- Section 6.2 (the languages of a PDA: acceptance by final state and by empty stack)
(note: TH 6.9 proof no, only the construction of PF;
TH 6.11 proof no, only the construction of PN)
- Section 6.3.1 (equivalence of PDA’s and CFG’s)
(note: only the construction of a PDA from a grammar; TH 6.13 proof no)
- Section 6.4 (DPDA)
(note: only definition of DPDA and characterization of the languages accepted by DPDA,
without proofs)
Chapter 7:
- Section 7.1.1 (eliminating useless symbols)
(note: definitions of the following notions: useful symbols, useless symbols,
generating symbols, reachable symbols; construction of a grammar
without useless symbols, TH 7.2 proof no)
- Section 7.1.2 (computing the generating and reachable symbols)
(note: only the algorithms to compute generating and reachable symbols, TH 7.4 and 7.6
proof no)
- Section 7.1.3 (eliminating epsilon-productions)
(note: only the algorithms to compute the nullable symbols and to construct a grammar
without epsilon-productions, TH 7.7 and 7.9 proof no)
- Section 7.1.4 (eliminating unit productions)
(note: only the algorithms to compute the unit pairs and to construct a grammar
without unit productions, TH 7.11, 7.13 and 7.14 proof no)
- Section 7.1.5 (chomsky normal form)
(note: only definition and construction of the normal form; TH 7.16 proof no)
- Section 7.2 (pumping lemma for CFL’s)
(note: TH 7.17 proof no, TH 7.18 proof yes, case-study: example 7.19)
- Sections 7.3.3, 7.3.4 (closure properties of CFL’s)
(note: list of the properties; theorem and proof in “FileA” for ‘union’, ‘concatenation’
and ‘closure’; only grammar construction for ‘reversal’; example 7.26 for ‘intersection’;
TH 7.25 and 7.27 proof no, TH 7.29 proof yes)
- Section 7.4.4 (testing membership in a CFL: CYK algorihtm)
From the book (available at the Library) Hopcroft, Ullman, "Introduction to Automata Theory,
Languages, and Computation" Addison Wesley:
- Chapter 9 (Chomsky hierarchy)
(note: only definitions of type 0-1-2-3 grammar and characterization of the language hierarchy,
without proofs)
Points 5-6 of the syllabus:
From “FileB”:
- Introduction and Section 2 (syntax of visual/nonlinear languages)
(note: just a quick look)
- Section 3 (syntactical models)
(note: characterization of the syntactical models: string, symbolic/iconic, box, plex, graph)
From “FileC”:
- Section 3 (syntax of visual/nonlinear languages)
(note: just a quick look)
- Section 4 (positional grammars)
(note: only formal definition of context-free positional grammar, example 4.1 and 4.2 no)
- Section 5 (positional grammars for plex languages)
(note: case-study: example 5.2, example 5.1 no)