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 online with a discussion phase on June 28 - July 9. During the discussion feedback to selected exercises, special interest will be provided. See the organisational details on the TUWEL page. Supporting material, slides, recordings, as well exercises will be made available on TUWEL before June 14. Please register timely for the course, not later than March 21, so that the interest into the course can be properly anticipated.
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.
