Modelli di calcolo - Models of computation

MOD 2015/16 (375AA, 9 CFU)

Lecturer: Roberto Bruni
web - email - phone 050 2212785 - fax 050 2212726

Office hours: Wednesday 15:00-17:00 or by appointment

The objective of the course is to present:

• different models of computation,
• their programming paradigms,
• their mathematical descriptions, both concrete and abstract,

and also to present some intellectual tools/techniques:

• for reasoning on models, and
• for proving (some of) their properties.

To this aim, a rigorous approach will be followed for both the syntax and the semantics of the paradigms we work on:

• IMP: imperative models
• HOFL: functional models
• CCS, pi-calculus: concurrent, non-deterministic and interactive models
• PEPA: probabilistic/stochastic models

The focus will be on basic proof techniques (there will be not time to introduce more advanced topics in detail).

In doing so, several important notions will be presented (not necessarily in this order): context-free grammars, proof systems (axioms and inference rules), goal-driven derivations, various incarnations of well-founded induction, structural recursion, lambda-calculus, program equivalence, compositionality, completeness and correctness, type systems, domain theory (complete partial orders, continuous functions, fixpoint), labelled transition systems, bisimulation equivalences, temporal and modal logics, Markov chains, probabilistic reactive and generative systems.

We introduce the principles of operational semantics, the principles of denotational semantics, and the techniques to relate one to the other for an imperative language and for a higher order functional language. Operational and observational semantics of two process description languages (CCS and pi-calculus) are presented. Several examples of temporal and modal logics are also discussed (HM, LTL, CTL*, mu-calculus). Finally, we consider operational nondeterministic models with discrete probabilities, and we present them from the perspective of probabilistic and stochastic automata, and of the PEPA calculus.

• Glynn Winskel, “The formal Semantics of Programming Languages”, MIT Press, 1993. Chapters: 1.3, 2, 3, 4, 5, 8, 11.
  “La Semantica Formale dei Linguaggi di Programmazione”, traduzione italiana a cura di Franco Turini, UTET 1999.
• Robin Milner, “Communication and Concurrency, Prentice Hall, 1989. Chapters: 1-7, 10.
• Lecture notes: a monograph is under preparation, drafts of the chapters are made available (with errata), comments are welcome
  • Chapters 01-10: Introduction, IMP, HOFL, revised version, with solutions to selected exercises
    • P23, factorial example: the inclusion symbol is missing between {(1,1)} and {(1,1),(2,2)}
    • P86, text of the proof of Th.4.5: implication is written several times (three occurrences) as a single arrow; a double arrow should be used instead
    • P95, line -5: x₁,…,x_k should be n₁,…,n_k
    • P96, statement of Th.4.2: < should be \prec
    • P97, end of first part of the proof: f(a)=F(y,f… )=F(y,g…)=g(a) should be f(a)=F(a,f…)=F(a,g…)=g(a)
    • P182, line 8: “the element” should be deleted
    • P200, last line: the bottom element returned as a result is in (V_tau)_bottom not in Z_bottom
    • P351, Problem 3.4, lines -10 and -8: the subscript \sigma'=\sigma must be deleted
    • P354, line 4: false should be true
    • P358, Solution to Problem 6.4: B[skip] should be C[skip]
    • P364, Solution to Problem 8.5, last line: apply(f₁,d₁) should be apply(f₂,d₂)
  • Chapters 11-16: Concurrent systems, probabilistic systems, revised version, with solutions to selected exercises
    • P234, line -3: delete the sentence: “all process names in X and all recursively defined names in p occur guarded in p.”
    • P25, line 11: r should be q (twice)
    • P277, line 6: X p should be O p
    • P294, Fig. 13.1, line 5: [x=y].p should be [x=y]p (twice)
    • P294, Fig. 13.1, line 8: (y).p should be (y)p (twice)
    • P304, Ex. 13.5, line 7: tau.nil should be nil
    • P322, Def. 14.14: X_n+1= shoudl be X_n+1=x
    • P328, P329, P330, P337: the domain and codomain of all transformations \Phi is the powerset of S x S, not the powerset of S
    • P363, Problem 3.4, lines -10 and -8: the subscript \sigma'=\sigma must be deleted
    • P366, line 4: false should be true
  • link to previous versions of all chapters, with errata

The evaluation will be based on written and oral exams.

The written exam is not necessary if the two (written) mid-terms exams are evaluated positively.

• First (written) mid-term exam: 30-03-2016, 14:00-16:00, room B
• Second (written) mid-term exam: 25-05-2016, 9:00-11:00, room C1

Registration to written exams (mandatory): Exams registration system

In the written exam the student must demonstrate

• knowledge: his/her knowledge of the course material
• problem solving: the ability to solve some exercises, and
• organisation: the ability to organise an effective and correctly written reply.

During the oral exam the student must demonstrate

• knowledge: his/her knowledge of the course material, and
• understanding: the ability to discuss the reading matter thoughtfully and with propriety of expression.

• as the course starts:
  Each student should send an email to the professor from his/her favourite email account with subject MOD15 and the following data
  (by doing so, the account will be included in the class mailing-list, where important announcements can be sent):
  1. first name and last name (please clarify which is which, to avoid ambiguities)
  2. enrolment number (numero di matricola)
  3. bachelor degree (course of study and university)
  4. your favourite topics in computer science (optional)

• A.A. 2014/15
• A.A. 2013/14