https://ocw.cs.pub.ro/ppcarte/ 2026-05-21T14:46:45+03:00 https://ocw.cs.pub.ro/ppcarte/ https://ocw.cs.pub.ro/ppcarte/lib/tpl/bootstrap3/images/favicon.ico text/html 2023-01-25T08:31:21+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:ei1&rev=1674628281&do=diff https://forms.gle/Vdty9FM2hgHD1UHZ7 text/html 2023-01-25T10:57:29+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:ei2&rev=1674637049&do=diff https://forms.gle/Cicx9m2a7snd5Bmu8 text/html 2022-10-14T13:13:06+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab01-programming-intro&rev=1665742386&do=diff Programming introduction 1. Scala introduction Exercise 1.1. Write a function startStop which retrieves the elements of a list from within bounds. Use patterns in your implementation. Define an object Main as shown below. Any code within the object can be directly executed. (Hint: use a simply-recursive function)/ text/html 2023-10-17T00:01:43+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab02-dfa&rev=1697490103&do=diff 2. Deterministic Finite Automata 2.1. DFA practice * Blue = final state * Orange = non-final state * Sink state = a state that is not final; once reached, there is no transition that leaves it, thus the DFA will reject; there is a transition that loops in this state for each possible character$ L=\{w \in \{0,1\}^* \text{ | w contains an odd number of ones} \} $$ L=\{w \in \{0,1,2,3\}^* \text{ | w follows the rule that every zero is immediately followed by a sequence of at least 2 consecu… text/html 2022-10-28T22:42:20+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab03-dfa-regexp&rev=1666986140&do=diff 3. Regular expressions 3.1. Formation rules (concatenation, reunion, Kleene star) 3.1.1. $ A=\{ 0^{2k} \mid k \geq 1 \}$ $ B = \{0, \epsilon \}$ $ AB = ? $ ... 00...<- * where the words in the language that have an even length are obtained by combining a word from A with the word ε from B * and those with an odd length are obtained by combining a word from A with the word 0 from B$ A = \{ 0^n 1^n \mid n \geq 1 \}$$ B = \{ 1^n \mid n \geq 1 \} $$ AB = ? $$ BA = ? $$ A = \emptyset $… text/html 2022-11-04T13:30:46+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab04-regexp-nfa&rev=1667561446&do=diff 4. Regex to DFA conversion 4.1. Nondeterministic Finite Automata 4.1.1. Consider the following NFA: What are all reachable configurations from (0,abba) ? ->->->->$\varepsilon$ ->->->->$\varepsilon$ ->->-> 4.1.2. What is the accepted language of the previous NFA? $\cup$$\cup$$\cup$$\cup$$\varepsilon$ 4.1.3. Write an NFA $ \varepsilon$$ L = \{abc,abd,aacd\}$$ \Sigma = \{a,b,c,d\}$$ (0,abbabbb)$$ (1 \cup \varepsilon)(00^*1)^*0^*$$ (1 \cup \varepsilon)(00^*1)^*0^*$$\in$$ \varepsilon$$ E(q)$ text/html 2022-11-12T20:49:08+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab05-mindfa&rev=1668278948&do=diff 5. Minimal DFAs Consider the following DFAs: DFA 1 DFA 2 5.1. Equivalence between states 5.1.1. Identify a pair of states which are indistinguishable. (Solve the exercise for the 2 given DFAs.) DFA 1 “”“” DFA 2 “”“” 5.1.2. Identify a pair of final or non-final states which are $ \delta$$ \delta(q,c)=q'$$ q$$ c$$ \delta(q,c)$$ c$$ \delta$$ (1\cup\epsilon)(00^*1)^*0^*$$ (10\cup 0)^*(01 \cup 1)^*(0 \cup \epsilon)$$ E1 = ((ab^*a)^+b)^* $$ E2 = (a(b\mid aa)^*ab)^* $$\varepsilon$… text/html 2022-11-19T10:34:30+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab06-dfa-to-regex&rev=1668846870&do=diff 6. Dfa to Regex conversions 6.1. State elimination Consider the following DFAs: DFA1 DFA2 Convert the given DFAs to a Regex (using the state-elimination strategy). Hint: is it easier to apply conversion on another DFA? Step 1: Step 2:$ X, A$$ B$$ X = A\cdot X \cup B$$ X = A^*B$$ e_A, e_B$$ X = L(e_A)\cdot X \cup L(e_B)$$ X = L(e_A^*e_B)$$ q$$ q = c_1 q_1 \cup c_2 q_2 \ldots c_n q_n$$ \delta(q,c_i) = q_i$$ c_i\in\Sigma$$ q_i$$ c_i$$ q$$ q$$ \epsilon$$ q = c_1 q_1 \cup c_2 q… text/html 2022-11-27T00:39:18+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab07-closure-properties&rev=1669502358&do=diff 7. Closure properties 7.1.1. Identify different strategies to verify that two regular expressions generate the same language. State them as algorithmic procedures. * You can use an existing minimisation algorithm to find the minimal DFAs. Then, label each state from each DFA from 0 to |K|. Fix an ordering of the symbols of the alphabet. Sort the transitions by symbol. Make a textual representation of each DFA which includes the number of states and the sorted transition function. If the t… text/html 2022-12-09T08:55:54+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab08-the-pumping-lemma&rev=1670568954&do=diff 8. Proving languages are not regular Pumping Lemma $\forall w \in L$$\exists n \in \mathbf{N}$$ |w| \ge n $$ w = xyz $$ |xy| \le n $$ y \neq \varepsilon $$ \forall k \ge 0, w_{k} = xy^{k}z \in L$ Complement of Pumping Lemma $\forall n \in \mathbf{N}$$\exists w_{n} \in L $$ |w| \ge n $$ w_{n} $$ w_{n} = xyz $$ |xy| \le n $$ y \neq \varepsilon $$\exists k \ge 0 $$ w_{n} = xy^{k}z \notin L $not 8.1. The pumping lemma 8.1.1. Show that the pumping lemma holds for finite languages. $ n \gt max_… text/html 2022-12-17T11:05:32+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab09-cfl&rev=1671267932&do=diff 9. Context-Free Languages 9.1. Accepting and generating a CF language Write a PDA as well as a CF grammar for the following languages. Specify - for each PDA, the way it accepts (by empty-stack or by final state). For each grammar, make sure it is not ambiguous. (Start with any CF grammar that accepts L. Then write another non-ambiguous grammar for the same language).$ L = \{\: w \in \{A,B\}^* \ | \:w \text{ is a palindrome}\} $$ S \leftarrow ASA | BSB | A | B | \epsilon $$ L = \{ A^{m} B^{m+n… text/html 2022-12-29T00:59:12+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab10-cfl_2&rev=1672268352&do=diff 10. Context-Free Languages & Lexers 10.1. Context-Free Grammar to PDA conversion For each context-free grammar G: * describe L(G) * algoritmically construct a PDA that accepts the same language * run the PDA on the given inputs * is the grammar ambiguous? If yes, write a non ambiguous grammar that generates the same language $ S \leftarrow aS | aSb | \epsilon $$ A \leftarrow \gamma $$ \epsilon, S/aS $$ \epsilon, S/aSb $$ \epsilon, S/\epsilon $$ a, a/\epsilon $$ b, b/\epsilon $… text/html 2022-12-18T23:26:32+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:lab11-cfl_3&rev=1671398792&do=diff 11. Context-Free Grammars AGAIN 11.1. Chomsky Normal Form Write the following grammars in CNF: 11.1.1 $ S \leftarrow ABC \\ A \leftarrow aAb \mid \epsilon \\ B \leftarrow bBc \mid bc \\ C \leftarrow cC \mid c $ Step 1: $ X \leftarrow \alpha y \beta $$ X \leftarrow \alpha Y \beta, Y \leftarrow y $ $ S \leftarrow ABC \\ A \leftarrow L_aAL_b | \epsilon \\ B \leftarrow L_bBL_c | L_bL_c \\ C \leftarrow L_cC | L_c \\ L_a \leftarrow a \\ L_b \leftarrow b \\ L_c \leftarrow c $ Step 2: $ S \lef… text/html 2022-10-31T14:10:41+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:proiect-wip&rev=1667218241&do=diff Schelet si checker pentru fiecare limbaj: * [python] * [scala] Proiect Proiectul consta in implementarea unui lexer in python sau scala. Ce este un lexer? Un lexer este un program care imparte un sir de caractere in subsiruri numite lexeme, fiecare dintre acestea fiind clasificat ca un $ e^+$$ ee^*$$ e?$$ e \cup \epsilon$$ a \cup b$$ (ab)\cup(c^*)$$ (a\cup b)(c\cup d)$$ (a\cup b)^*(b\cup c)$$ ( (ab) \cup ( b(d^*) ) )^*$$ c^+( a \cup (b^+) )$ text/html 2022-11-16T12:33:46+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:proiect&rev=1668594826&do=diff Schelet si checker pentru fiecare limbaj: * [python] * [scala] Deadline etapa 1: 21.11.2022 23.11.2022 ora 23:00 Proiect Proiectul consta in implementarea unui lexer in python sau scala. Ce este un lexer? Un lexer este un program care imparte un sir de caractere in subsiruri numite $ e^+$$ ee^*$$ e?$$ e \cup \epsilon$$ a \cup b$$ (ab)\cup(c^*)$$ (a\cup b)(c\cup d)$$ (a\cup b)^*(b\cup c)$$ ( (ab) \cup ( b(d^*) ) )^*$$ c^+( a \cup (b^+) )$$ a\cup \epsilon$ text/html 2022-11-27T13:43:19+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:proiect_etapa2&rev=1669549399&do=diff Forma prenex, intermediara in proiectul nostru intre cea conventionala si arborele de parsare (AST) construit de programul vostru, nu este standard pentru o astfel de implementare. De altfel, ea nici nu este folosita in mod curent. Insa cum limbajul expresiilor regulate valide este independent de context (din cauza parantezelor), este dificil de implementat parsarea regexurilor fara cunostinte despre gramatici si in special APD-uri. Tocmai de aceea aceasta etapa de parsare, care in mod natural a… text/html 2022-12-12T12:48:57+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:proiect_etapa3&rev=1670842137&do=diff Schelet si checker pentru fiecare limbaj: * * Deadline etapa 3: 8 ianuarie 2023 ora 23:00 (deadline hard) Proiect Etapa 3 a proiectul consta in implementarea unui lexer in python sau scala. Ce este un lexer? Un lexer este un program care imparte un sir de caractere in subsiruri numite text/html 2023-09-25T17:08:24+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:sidebar&rev=1695650904&do=diff * Echipa * Regulament 2022-2023 * Examen 2022-2023 * Proiect Etapa 1 * Proiect Etapa 2 * Proiect Etapa 3 * Labs * 1. Introduction to Scala/Python * 2. Deterministic finite automaton * 3. Regular Expressions * 4. Regex to NFA * 5. Minimal DFA * 6. DFA to Regex * 7. Closure properties * 8. The pumping lemma * 9. Context-free languages * 10. Context-Free Languages & Lexers * 11. Context-Free Languages, Regular grammars and CNF * … text/html 2022-10-06T22:53:35+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=lfa:2022:team&rev=1665086015&do=diff Limbaje Formale și Automate 2021-2022 Echipa Curs * Matei POPOVICI Seminarii * 331CB Alexandra UDRESCU * 332CB Bogdan DEAC * 333CB Matei POPOVICI * 334CB Mihai CALITESCU * 335CB Alexandru ILIE * 336CB Mihai UDUBASA Orar Curs Frecevență Zi Interval orar Profesor săptămânal Miercuri 10:00-12:00 Matei POPOVICI săptămâni pare