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--- lfa:2023:lab02 [2023/10/16 22:14]
mihai.udubasa
+++ lfa:2023:lab02 [2024/10/06 21:30] (current)
stefan.sterea old revision restored (2023/10/31 11:44)
@@ Line 1: / Line 1: @@
-====== 2. Deterministic Finite Automata ======
+====== 2. Deterministic Finite Automata and Regular Expressions ======
 ===== 2.1. DFA practice =====
@@ Line 83: / Line 83: @@
 {{:lfa:2022:lfa2022_lab2_ex6_v2.png?400|}}
-/*{{:lfa:2022:lfa2022_lab2_ex6.png?400|}} - this is wrong, some transitions are missing*/
   * injuraturile redirectati-le catre AU :)) (si MP)
   * All missing transitions lead to a sink state (where there is a transition that loops in that state for any character)
+</hidden>
+**2.1.7.** The set of all binary strings having the substring 00101
+<hidden>
+{{:lfa:2022:ex_8_dfa.png?400|}}
+  * Every state corresponds to a certain current configuration (eg. state **B** translates to a sequence of **0**; **C** to a seq of **00**; **D** -> **001** and so on)
+  * 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>
@@ Line 91: / Line 100: @@
 === Describe the language of the following DFAs and simulate them on the given inputs: ===
-**2.1.7.** w<sub>1</sub> = 10011110, w<sub>2</sub> = 00110010
+**2.1.8.** w<sub>1</sub> = 10011110, w<sub>2</sub> = 00110010
 {{:lfa:2022:lfa2022_lab2_ex8.png?400|}}
@@ Line 101: / Line 110: @@
   * (0, **00110010**) |--<sub>A</sub> (01, 0110010) |--<sub>A</sub> (02, 110010) |--<sub>A</sub> (11, 10010) |--<sub>A</sub> (12, 0010) |--<sub>A</sub> (01, 010) |--<sub>A</sub> (02, 10) |--<sub>A</sub> (11, 0) |--<sub>A</sub> (01, $math[\epsilon]) The word is **accepted** by the DFA because we reached a final state (blue).
 </hidden>
 ===== 2.2. Regex practice =====
 For each of the exercises from DFA practice write a regex describing the same language.
 <hidden 2.2.1.>
@@ Line 138: / Line 147: @@
 This language is a good example of a language which is significantly easier to describe using a dfa rather than a regex. The regex is very hard to build intuitively and is very long. For a way to algorithmically build this regex from the dfa built during the first part, wait until the lab/lecture about the dfa->regex transformation.
 </hidden>
+<hidden 2.2.7>
+$math[(0 \cup 1)^*00101(0 \cup 1)^*]
+</hidden>