https://file.aiquickdraw.com/mathbot/file/1726074051727bv8juqnb.jpg

Let's break down the mathematical and algorithmic questions from the image you provided:

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### **Θέμα 2 (Topic 2):**

1. The first statement discusses DFA and NFA:
   - DFA (Deterministic Finite Automaton) is **not more powerful** than NFA (Non-deterministic Finite Automaton). Both can recognize the same set of regular languages, even though DFA might be more efficient.
   
2. The second statement discusses languages:
   - Not every context-free language is a regular language. This implies that **not every infinite language** is regular.

Thus, the answer would be **b.** (Both statements are incorrect).

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### **Θέμα 3 (Topic 3):**

- The statement compares logical equivalence:
  1. "When it rains, there is no sun" is equivalent to "When there is sun, it doesn't rain."
  2. The second proposition involves logical contradiction, depending on the interpretation.

Answer: **a.** (Both statements are correct).

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### **Θέμα 4 (Topic 4):**

- This deals with algorithm runtimes:
  1. Bellman-Ford has a longer execution time compared to Dijkstra in general, as Bellman-Ford solves more general cases (handles negative weights).
  2. Prim’s algorithm generally has a different execution time but is often faster in connected graphs.

Answer: **b.** (Both statements are incorrect).

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### **Θέμα 5 (Topic 5):**

- The algorithm behavior is described for iterative deepening and depth-first search. This problem relates to how many steps each algorithm takes before looping.

Answer: **a.** (The iterative deepening converges to depth-first search behavior).

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### **Θέμα 6 (Topic 6):**

- Best-first search and hill-climbing algorithms differ in how they explore the search space:
  - Hill-climbing can get stuck in local maxima, while best-first search uses a broader view.

Answer: **b.** (Best-first typically explores a wider frontier).

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Feel free to ask if you'd like more detailed explanations!

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**5 Related Questions:**
1. What are the differences in the time complexity between DFA and NFA?
2. How does logical equivalence work in formal logic?
3. Why is Dijkstra faster than Bellman-Ford for specific types of graphs?
4. Can depth-first search always guarantee the shortest path in a search space?
5. What are the practical advantages of using best-first search over hill-climbing?

**Tip:** Understanding algorithm efficiency (time and space complexity) is crucial when analyzing different approaches for graph-based problems.

Solve the algorithmic and logical problems from the image (Θέμα 2 - Θέμα 6).

Solve algorithm and logic problems involving DFA vs NFA, logical equivalence, and the complexity of search algorithms like Bellman-Ford and Dijkstra. Includes topics on best-first search, hill-climbing, and iterative deepening.

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