TUM - Chair VII - Foundations of Software Reliability and Theoretical Computer Science


	Automata and Formal Languages 2017/18

Exercises are voluntary and do not account for the final grades. Submitted exercises will be corrected and handed back. It is highly recommended to work on the exercises, as this is the best preparation for the exam.

Week	Topic	Exercise sheet	Solutions	Additional files	Comments
1	DFAs, NFAs, regular expressions
2	Conversions			Python NFA-ε to NFA converter:
3	Minimization, residuals
4	DFA operations
5	NFA operations
6	Pattern matching (extra topics: residuals, synchronizing automata)			Python implementation of the algorithms computing synchronizing words:
7	Transducers
8	Fixed-length languages			Python implementation of the master automaton:	19.02.18: There was a typo in the tree of #8.1(b). The node below the root should be labeled make(add-lang({bb}), add-lang({ba, bb})) and not make(add-lang({bb}), add-lang({bb})). It is now fixed. The rest of the tree was correct, so the rest of the answer is correct.
9	Verification of safety properties			Promela files: #9.1(c) naive_mutex.pml: #9.1(h) mutex_chan.pml: #9.1(h) alternative_solution.pml: #9.2(c) mutex.pml: #9.3(c) hyman.pml: #9.4(c) mutex_three.pml:	This week, we will use Spin to simulate and verify some algorithms. I will walk you through Spin in class, assuming no prior knowledge. Since the exercises were uploaded a bit late, I will also assume you have not done the exercises at home. If you want to, you can already try Spin by following these instructions: . To understand the basics of Promela, you can also have a look at this Wikipedia page: . The papers of Hyman and Knuth discussed in class are available at and . Unfortunately they are not freely available, but you can obtain them online through the library: . 21.01.18: The solutions of #9.2(b) and (e) were incorrect. They have been updated.
10	Presburger arithmetic, first-order and second-order logic on words (FO/MSO)			Python implementation of the algorithms of #10.1: MONA files: #10.3(b) partial_solution.mona: #10.3(b) solution.mona:	We will use MONA in class for Ex. #10.3(b). MONA is available here: . You can either install it or use it online here: . In the online version, you may derive an automaton from a formula by selecting Output whole automaton in Graphviz format. MONA uses a slightly different bit-vector encoding than the one we have seen in class: the first position of bit-vectors is -1, which you can ignore for our purposes since first/second-order variables can never hold -1; first/second-order variables can hold 0; the value of a first-order variables is represented by the position of the first "1" in a bit-vector (it needs not to be unique); e.g. "y: X001010" is a valid encoding of y = 2. For more information on MONA, have a look at Sections 1 and 2 of its user manual: .
11	ω-automata (Büchi, Rabin, Muller and parity automata)
12	Büchi automata: conversions and operations
13	Emptiness check, linear temporal logic (LTL)
14	Linear temporal logic (LTL), verification of liveness properties				Spot's online translator can be found here: . Check "state-based degeneralized Büchi automaton" to obtain Büchi automata. The full version of Spot is available here .
15	Recap				We will go through last year's exam in class on Feb. 8.

Past exercise sheets

Exercice Sheets 2016/2017:

Exercise sheet 14 (with solutions).
Exercise sheet 13 (with solutions). Spot commands to manipulate LTL formulas can be found here.
Exercise sheet 12 (with solutions).
Exercise sheet 11 (with solutions). Solutions of #2 in the Hanoi Omega-Automata format: DBA #11.2a, NBA #11.2b. As seen in class, these automata can be minimized by Spot using these commands.
Exercise sheet 10 (with solutions).
Exercise sheet 9 (with solutions).
Exercise sheet 8 (with solutions).
Exercise sheet 7 (with solutions). Python implementation of the master automaton: fixedlength.py.
Exercise sheet 6 (with solutions).
Exercise sheet 5 (with solutions).
Exercise sheet 4 (with solutions). Python implementations of the algorithms computing synchronizing words: synchronizing.py.
Exercise sheet 3 (with solutions). NFA-ε to NFA converter: nfa-eps2nfa.py.
Exercise sheet 2 (with solutions). JFLAP examples: DFA #2.1c.
Exercise sheet 1 (with solutions). JFLAP examples: DFA #1.2, NFA #1.3a, NFA #1.3b.

Exercice Sheets 2015/2016:

Exercise Sheet 1 (Wed 21.10.15) [Sample Solution]
Exercise Sheet 2 (Fri 23.10.15) Now equipped with solutions. Don't hesitate to let me know if you have any questions arising therefrom.
Exercise Sheet 3. [Sample Solution] Also discussed in the class: Exercises 1.3, 1.4
Exercise Sheet 4 (Wed 04.10.15). With solutions
Exercise Sheet 5. [Sample Solution]
Exercise Sheet 6 With solutions
Exercise Sheet 7 [Sample Solution]
Exercise Sheet 8 With solutions
Exercise Sheet 9 [Sample Solution]
Exercise Sheet 10 . With solutions
Exercise Sheet 11 [Sample Solution]
Exercise Sheet 12 . With solutions.
Exercise Sheet 13 [Sample Solution]
Exercise Sheet 14 . With solutions.
Exercise Sheet 15 (Mon 01.02.16) [Sample Solution]
Exercise Sheet 16 (Wed 03.02.16) . With solutions.

Exercise Sheets 2012/2013:

Exercise 1, solution to Ex.1.3
Exercise 2, solution to Ex.2.6 and 7
Exercise 3 (updated on Nov 6, two of the exercises originally posted here will be dealt with later)
Exercise 4
Exercise 5, transducer for Ex.5.3
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13: Q&A session + some LTL

Exercise Sheets 2011/2012:

Exercise Sheets 2010/2011:

Exercises with two stars form a necessary part of your preparation for the exam. One starred ones are recommended. Exercises with no star are useful for deeper understanding.

Exercise 1 (**: 1,3)
Exercise 2 (**: 1,2,4)
Exercise 3 (**: 1,2,3,5)
Exercise 4 (**: 1,2,5)
Exercise 5 (**: 2)
Exercise 6 (**: 1,2)
Exercise 7 (**: 1)
Exercise 8 (stars indicated in the sheet)
Exercise 9 (stars indicated in the sheet)
Exercise 10 (**: 1,2)
Exercise 11 (**: 2)
Exercise 12 (stars indicated in the sheet)
Last year's exam and its solution