Discrete Mathematics (Course 1 - Semester 2) Theory of Automata and Formal Languages (Course 2 - Semester 1)

Relevant contents: 1.- Cost of computational processes 2.- Recursive algorithms complexity 3.- Introduction to computability theory 4.- Introduction to computational complexity theory 5.- Spatial complexity 6.- Kolmogorov complexity 7.- Computation models 8.- Probabilistic algorithms Programme: 1. Computational Cost of Algorithms. 1.1 Computational Complexity and Computational Cost. 1.2 Computational Cost of Structured Programs 1.3 Computational Cost of Recursive Programs 1.4 Probabilistic Analysis 2. Introduction to Computability Theory 2.1 Definition of Problem. Decision Problems 2.2 Turing Machines and Decidability 2.3 Computability and Decidability 3. Introduction to Complexity Theory 3.1 Problem Reduction 3.2 Classes P, NP and NP-Complete. 3.3 Classes PSpace, NPSpace. 3.3 Classes NP-Hard, Exp, CoP, CoNP 4. Models of Computation 4.1 Turing Machines (Multi-tape, Non deterministic) 4.2 Cellular Automata 4.3 Lindenmayer Systems

THEORETICAL-PRACTICAL CLASSES. [44 hours with 100% classroom instruction, 1.67 ECTS] Knowledge and concepts students must acquire. Student receive course notes and will have basic reference texts to facilitate following the classes and carrying out follow up work. Students partake in exercises to resolve practical problems and participate in workshops and evaluation tests, all geared towards acquiring the necessary capabilities. TUTORING SESSIONS. [4 hours of tutoring with 100% on-site attendance, 0.15 ECTS] Individualized attendance (individual tutoring) or in-group (group tutoring) for students with a teacher. STUDENT INDIVIDUAL WORK OR GROUP WORK [98 hours with 0 % on-site, 3.72 ECTS] WORKSHOPS AND LABORATORY SESSIONS [8 hours with 100% on site, 0.3 ECTS] FINAL EXAM. [4 hours with 100% on site, 0.15 ECTS] Global assessment of knowledge, skills and capacities acquired throughout the course. METHODOLOGIES THEORY CLASS. Classroom presentations by the teacher with IT and audiovisual support in which the subject's main concepts are developed, while providing material and bibliography to complement student learning. PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group. TUTORING SESSIONS. Individualized attendance (individual tutoring sessions) or in-group (group tutoring sessions) for students with a teacher as tutor. LABORATORY PRACTICAL SESSIONS. Applied/experimental learning/teaching in workshops and laboratories under the tutor's supervision.