Madhavan Mukund



Quantitative Automata Theory,
Jan-Apr 2015

Quantitative Automata Theory

Jan-Apr, 2015


Course plan

  • Weighted automata, timed automata, hybrid automata, probabilistic automata (to be elaborated)

  • Instructors: Madhavan Mukund, B Srivathsan


Reading Material

Weighted automata

Timed automata

Hybrid Systems

Probablistic Systems



Lecture summary

  • Lecture 1, 5 Jan 2015 (Madhavan)

    Introduction to weighted automata: examples, basic definitions

  • Lecture 2, 7 Jan 2015 (Madhavan)

    Weighted systems: generalized Floyd-Warshall algorithm; Weighted automata: NFAs and probabilistic systems.

    • Bollig and Zeitoun: Chapter 1, Chapter 2.1
  • Lecture 3, 19 Jan 2015 (Madhavan)

    Examples of semi-rings; Weighted automata: examples, typical decision problems; Probabilisitc automata: basic definitions, stochastic languages.

    • Bollig and Zeitoun: Chapter 1.2 (part), Chapter 2, Chapter 3.1, 3.2 (part)
  • Lecture 4, 28 Jan 2015 (Madhavan)

    Probabilistic automata: Stochastic languages are not r.e, threshold language for isolated cutpoint is regular .

    • Bollig and Zeitoun: Chapter 3.1, 3.2
  • Lecture 5, 30 Jan 2015 (Madhavan)

    Probabilistic automata: Undecidability of threshold languages in general, undecidability of identifying cut points, value 1 problem (sketch), decidability of equality (sketch).

    • Bollig and Zeitoun: Chapter 3.3, 3.4
  • Lecture 6, 04 Feb 2015 (Madhavan)

    Rational and recognizable formal power series: statement of Kleene-Schutzenberger theorem; Series over the integer semiring: encoding polynomials with integer coefficents, overview of negative and positive results; Transducers: overview of negative and positive results.

    • Bollig and Zeitoun: Chapters 4,5,6
  • Lecture 7, 16 Feb 2015 (Srivathsan)

    Introduction to timed languages and timed automata, closure properties of timed automata, non-closure under complement, effect of epsilon-transitions.

  • Lecture 8, 18 Feb 2015 (Srivathsan)

    The region construction.

  • Lecture 9, 02 Mar 2015 (Srivathsan)

    Undecidabiliy of language inclusion, universality (Section 5.2, Alur and Dill, TCS 1994).

  • Lecture 10, 04 Mar 2015 (Srivathsan)

    Universality is decidable for one-clock timed automata (Ouaknine and Worrell, LICS 2004).

  • Lecture 11, 09 Mar 2015 (Srivathsan)

    Reachability for timed automata using zones, Backward analysis and forward analysis (Section 3.1–3.5 of Bouyer's Habilitation thesis).

  • Lecture 12, 11 Mar 2015 (Srivathsan)

    Graph representation for zones, algorithms for operations needed in forward analysis (Sections 4.1, 4.2 and the Appendix of Bengtsson and Yi, 2004).

  • Lecture 13, 16 Mar 2015 (Srivathsan)

    Deterministic Timed Automata, a generic framework for determinization, some determinizable subclasses.

  • Lecture 14, 18 Mar 2015 (Srivathsan)

    Alternating timed automata, closure properties, expressiveness of 1-clock ATA, decidability questions (Lasota and Walukiewicz, ACM TOCL 2008).

  • Lecture 15, 23 Mar 2015 (Srivathsan)

    Non-Zeno infinite runs; using regions to find non-Zeno infinite runs that visit an accepting state infinitely often (Definitions 4.10 and 4.11, Lemma 4.13 of Alur and Dill, TCS 1994).

  • Lecture 16, 25 Mar 2015 (Srivathsan)

    Extending timed automata with diagonal guards; expressiveness and succinctness.

  • Lecture 17, 30 Mar 2015 (Madhavan)

    Hybrid automata: basic definitions, examples.

  • Lecture 18, 01 Apr 2015 (Madhavan)

    Hybrid automata: rectangular initialized automata, decidability (Sections 2, 3.1, 3.2 of Henzinger et al, JCSS 1998).

  • Lecture 19, 06 Apr 2015 (Madhavan)

    Hybrid automata: beyond rectangular initialized automata, undecidability (Section 4 of Henzinger et al, JCSS 1998).

  • Lecture 20, 08 Apr 2015 (Madhavan)

    Hybrid automata: lazy rectangular hybrid automata (from Agrawal and Thiagarajan, HSCC 2004).

  • Lecture 21, 13 Apr 2015 (Madhavan)

    Probabilistic systems: Discrete-time Markov chains, probability measure on paths, reachability properties (Chapters 10.1, 10.1.1, Baier and Katoen).

  • Lecture 22, 15 Apr 2015 (Madhavan)

    Discrete-time Markov chains: transient probabilities, qualititative properties, repeated reachability (Chapter 10.2, Baier and Katoen).

  • Lecture 23, 20 Apr 2015 (Madhavan)

    Markov Decision Processes: paths, probabilities and adversaries, end-components and long-run behaviour (Chapters 10.6 (part), 10.6.3 (part) Baier and Katoen).

  • Lecture 24, 22 Apr 2015 (Madhavan)

    Markov Decision Processes: Qualitative reachability, Optimality equation (Bellman), Memoryless adversaries, Quantitative reachability—value iteration, linear programming, policy iteration (Chapter 10.1 (part), Baier and Katoen).