Nach positiver Absolvierung der Lehrveranstaltung sind Studierende in der Lage die Grundlagen der Termersetzung, sowie ausgewählte Kapitel dazu zu verstehen. Die Grundlagen umfassen zumindest (i) Abstract Rewrite Systems; (ii) (First-Order) Term Rewrite Systems; (iii) Completion, Complexity, Confluence and Termination. Die ausgewählten Kapitel werden im Vorfeld geklärt werden.
The following topics are discussed:
Foundations.
(i) Abstract Rewrite Systems: definitions, properties, Newman's Lemma, commutation, strategies; (ii) (First-Order) Term Rewrite Systems: definitions, properties, equational reasoning, word problem; (iii) Completion, Complexity, Confluence and Termination: critical pair lemma, Gröbner basis, derivational complexity, connection to subrecursive hierarchies, (beyond) orthogonality, decreasing diagrams, polynomial and matrix interpretations, dependency pairs.
Advanced Topics (one or two of these, depending on interest).
(i) Mathematical Foundations; (ii) Automated Resource Analysis; (iii) Probabilistic Term Rewriting; (iv) Tree Automata; (v) Strategies.
The course is taught in English and will be held blocked with from July 10 to July 14 (tentaive). During the lecture, selected exercises will be discussed and further information to topics of special interest will be provided. Supporting material, slides, recordings, as well exercises will be made available on TUWEL. Please register timely for the course.
Die Vorlesung wird teilweise auf das folgende Skriptum aufbauen:
- Term Rewrite Systems, Aart Middeldorp, lecture notes, University of Innsbruck.
Zusätzliches Material ist auf der LVA Homepage zu finden.