Modelli di calcolo - Models of computation

MOD 2016/17 (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.

Preliminary test for the course on Models of Computation

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.

Main text:

• Roberto Bruni, Ugo Montanari, “Models of Computation”, Springer Texts in Computer Science, 2017.

Other readings:

• 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.

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: thursday 06/04/2017, 11:00-13:00, room A1
• Second (written) mid-term exam: thursday 01/06/2017, 11:00-13:00, room A1

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 MOD16-17 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. 2015/16
• A.A. 2014/15
• A.A. 2013/14