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 (mainly) online with a discussion phase on July 13-17. See the organisational details on the TUWEL page. At the moment it is unclear, whether regulations allow to hold the discussion phase in attendance. Supporting material, slides, recordings, as well exercises have been made available on TUWEL. During the discussion the feedback to selected exercises, special interest will be provided.
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.
