# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics
**Teimuraz
Kutsia**, Research Institute for Symbolic Computation, JKU Linz,
will give a public talk (followed by a discussion) on **Wed, Oct. 13, 2010**
at **15:15 o'clock** at **HS 13**
on the topic of
"Symbolic Computation Techniques for Unranked Terms and Hedges"
. The organziers of the symposium,

Univ.-Prof. Dr. Gerhard Larcher

A.Univ.-Prof. Dr. Jürgen Maaß, and

die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series B - Mathematical Colloquium:

The intention is to present new mathematical results for an audience interested in general mathematics.

### Symbolic Computation Techniques for Unranked Terms and Hedges

In unranked terms (trees), symbols have no fixed arity. Hedges are finite sequences of such trees. They became an active subject of study in recent years because of various applications: These constructs are nearly ubiquitous in XML-related subjects. They model variadic procedures used in programming languages. They appear in rewriting, knowledge representation, program analysis and transformation, just to name a few. Most of the recent research on unranked terms and hedges has been focused on formal languages, automata, and logic.

Our contributions lie in developing new symbolic computation techniques in theories over unranked terms and hedges. We constructed solving procedures (unification, matching, disunification, constraint solving) in syntactic, equational, and order-sorted theories, proved their properties, addressed decidability issues, studied complexity, and established relations with some other solving problems. Besides, we extended equational proving methods (superposition with constraints, unfailing completion) and designed a calculus for conditional strategy-based hedge transformations. In this talk I will give an overview of some of these techniques and their applications.