The objective of this course is to introduce the theory of formal languages and to illustrate techniques for modeling the architecture of complex software systems and verifying their properties by means of formal methods based on automata, algebra, and logics. Moreover, another goal is the presentation of the functional programming paradigm through the study of the language Haskell.

01. Introduction to modeling and verification:
      01.01 The need for formal methods in software development.
      01.02 Formal languages and automata.
      01.03 Grammars and Chomsky classification.
      01.04 Formal approaches to language semantics.
      01.05 Concurrency theory, logics, and algebra.

02. Regular languages and finite-state automata:
      02.01 Deterministic finite-state automata.
      02.02 Nondeterministic finite-state automata.
      02.03 Nondeterministic finite-state automata with epsilon-transitions.
      02.04 Minimization and equivalence for finite-state automata.
      02.05 Finite-state automata and linear grammars.
      02.06 Closure properties of regular languages and pumping lemma.
      02.07 Regular expressions.
      02.08 Regular expressions and finite-state automata.

03. Context-free languages and pushdown automata:
      03.01 Free grammars and syntax trees.
      03.02 Chomsky normal form.
      03.03 Properties of context-free languages.
      03.04 Pushdown automata and relation with free grammars.
      03.05 Top-down parsing.
      03.06 Bottom-up parsing.

04. Denotational semantics:
      04.01 Denotational semantics for an imperative language.
      04.02 Denotational semantics for an imperative language with blocks and procedures.

05. Operational semantics:
      05.01 Natural semantics for an imperative language.
      05.02 Natural semantics for an imperative language with blocks and procedures.
      05.03 Structural operational semantics for an imperative language.

06. Temporal logics and model checking:
      06.01 Kripke models.
      06.02 Temporal logics.
      06.03 Linear-time logics vs. branching-time logics.
      06.04 Model checking algorithms.

07. Process algebra and behavioral equivalences:
      07.01 Concurrency and nondeterminism.
      07.02 Syntax and semantics of behavioral operators.
      07.03 Trace based equivalence.
      07.04 Bisimulation based equivalence.

08. Languages for the specification of software architectures:
      08.01 Components, connectors, and architectural styles.
      08.02 Syntax of an architectural language based on process algebra.
      08.03 Semantics of an architectural language based on process algebra.

09. Functional programming in Haskell:
      09.01 Introduction to Haskell.
      09.02 Functions, recursion, and polymorphism.
      09.03 Complex structures and higher-order functions.
      09.04 Datatypes,

10. Laboratory activity:
      10.01 Specification of systems through Kripke models.
      10.02 Model checking of systems specified through Kripke models.
      10.03 Practice on Haskell
 

Although there are no mandatory prerequisites for this exam, students are strongly recommended to take it after Object Oriented Programming and Software Engineering, and Operating Systems, by respecting the prerequisites of these two courses.

Knowledge and understanding: the student will be able to understand the semantics of the most used programming languages and the methodological principles behind the formal methods for design and verification of software systems that are illustrated in the program; the student will be also able to apply the principles of the functional programming in the specific case of the language Haskell.

Applying knowledge and understanding: the student will be able to design the base modules of the compilers for programming languages and to specify and verify formally software systems through the tools used in the classrooms; the student will be also able to develop small functional programs in Haskell.

Making judgements: the student will be able to evaluate the correctness of syntax and semantics of any programming language and to represent and compare formally the several specifications of a software system under design and development.

Communication skills: the student will be able to illustrate in a proper way the semantic features of the programming languages and to describe formally the functionalities and the properties of a software system by using the modeling and verification tools used in the classrooms.

Learning skills: the student will learn how to describe formally syntax and semantics of programming languages and how to model and check software systems; the student wil be also able to understand and use the functional programming tools made available by the modern programming languages.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Teaching

Theory lectures and laboratory exercises, both face-to-face and on-line.

Attendance

Although recommended, course attendance is not mandatory.

Course books

Hopcroft, Motwani, Ullman, "Automi, Linguaggi e Calcolabilità", Addison-Wesley, 2009 or Aiello, Pirri, "Strutture, logica, linguaggi", Pearson, 2005 to cover the sections 02 and 03 of the program. The original version of the former book is Hopcroft, Motwani, Ullman, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, 2007.

Sections 04 and 05 are inspired by Nielson, Nielson, "Semantics with Applications: An Appetizer", Springer, 2007.
 
Section 06 is covered by Clarke, Grumberg, Peled, "Model Checking", MIT Press, 1999, while sections 07 and 08 are taken from Aldini, Bernardo, Corradini, "A Process Algebraic Approach to Software Architecture Design", Springer, 2010.

For Haskell, a reference book is O'Sullivan, Stewart, and Goerzen, "Real World Haskell", O'Reilly, 2008.

Assessment

Individual project, written exam, and oral exam.

The individual project consists of modeling and verifying a software system with NuSMV. The project specification, one per session and the same for everybody, is published online at least one month before the beginning of every session, with delivery deadline by the noon of two days before the date of the written exam of interest. The project, even if passed, is valid only within the related session. The project text is given by the specification of a real system to model and verify. The student can freely choose the abstraction level of the system, the variants and configurations under analysis, and the properties to verify. Delivery is by email with subject LPVS: consegna progetto name_surname and must include source files with specifications and analysis results, each part adequately commented. The project mark is at most 10/30. The aim of the project is to check the capability of the student in the practical and autonomous use of the acquired skills about the modeling and verification of software.

The written exam can be given only after the delivery of the project related to the same session. Its duration is 90 minutes and it consists of practical exercises. Notes and didactical material can be used. The written exam mark is at most 20/30. In the winter session a partial written exam can be given to be integrated with another partial written exam in the summer session. In such a case, the two written exams are associated with the project of the summer session. The aim of the written exam is to verify the understanding skills about the theoretical topics of the program and checking the use skills concerning the functional paradigm.

The oral exam is mandatory about the individual project and is optional about the course program. The optional oral exam yields a positive or negative adjustment (at most 5 points) to the final mark. The objective of the oral exam is to estimate making judgements as well as communication and learning skills.

For texts of projects and written exams, see this link.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

The course offers additional e-learning facilities on the Moodle platform > elearning.uniurb.it