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--- lfa:2025:lab01 [2025/10/05 23:39]
tpruteanu
+++ lfa:2025:lab01 [2025/10/07 12:02] (current)
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@@ Line 37: / Line 37: @@
 **2.1.3.** The language of binary words which contain **exactly** two ones.
 /*<hidden>
@@ Line 50: / Line 49: @@
 **2.1.4.** (*) The language of words which encode binary numbers divisible by 3.
-**2.1.5.** (* *) The language of words which encode binary numbers divisible by 3, represent in reverse order (the least significant digit is first).
+**2.1.5.** (* *) The language of words which encode binary numbers divisible by 3, represented in reverse order (the least significant digit is first).
 **2.1.6.** (*) The language of quaternary words (base 4), that follow the rule that every zero is immediately followed by a sequence of at least 2 consecutive threes and every one is immediately followed by a sequence of at most 2 consecutive twos.
-**2.1.7.** The set of all binary strings having the substring 00101.
+**2.1.7.** The language of all binary words having the substring 00101.
 /*<hidden>
@@ Line 61: / Line 60: @@
   * Analyze how each incoming character changes the current available sequence. For example, if we are in state **E** and we read character **1** we reach a final state, but if we read **0** we go back to state **C** since the available seq will be **00**
 </hidden>*/
+**2.1.8.** The language of binary words that start and end with different digits.
 /*<hidden>
@@ Line 78: / Line 79: @@
 **2.2.1**
+{{:lfa:2024:lab1-2_2_2.png?300|}}
+/* Cel puțin un grup de: 0 urmat de un număr impar de 1-uri urmat de un număr par de 0-uri */
+**2.2.2**
 {{:lfa:2024:lab1-2_2_1.png?500|}}
 /* Cuvinte nevide în care după un grup de 0-uri consecutive urmează fie nimic, fie un număr impar de 1-uri consecutive,
    și după un grup consecutiv de 1-uri urmează fie nimic, fie un număr par de 0-uri consecutive */
-**2.2.2**
-{{:lfa:2024:lab1-2_2_2.png?300|}}
-/* Cel puțin un grup de: 0 urmat de un număr impar de 1-uri urmat de un număr par de 0-uri */
 **2.2.3**
@@ Line 110: / Line 111: @@
    iar dacă începe cu b. prima secvență este de al doilea tip */
 ----
+**2.3.1** What happens if we switch all final states to non-final states and vice-versa in a DFA?
+**2.3.2** Prove that if L(M) is infinite, there has to be some cycle in the states graph, such that there is a path from the initial state to the cycle, and from the cycle to a final state.
+**2.3.3** If no such cycle described above exist, L(M) is finite.
+**2.3.4** Show that if you can construct a DFA to accept L, than you can also construct a DFA to accept $ L \cup \{a\}, \forall a \in \Sigma $.