Javier Esparza, Technical University München, Germany Title: Solving Fixed-Point Equations by Derivation Tree Analysis Abstract: Fixed-point equations over semirings are the mathematical foundation of program analysis, and have many other applications, e.g. in probability theory. These equations can be formally assigned context-free grammars in a natural way: for instance, the equation X = aXX + bX + c, where a, b, c are semiring elements, is assigned the grammar X -> aXX | bX | c with a, b, c as terminals. We show how by examining the derivation trees of this grammar we can obtain interesting algorithms for computing (or at least approximating) the least solution of the equation, when the semiring satisfies certian conditions. Joint work with Michael Luttenberger.
Gopal Gupta, University of Texas at Dallas, USA Title: Infinite Computation, Co-induction and Computational Logic Abstract: We give an overview of the coinductive logic programming paradigm. We discuss its applications to modeling \omega-automata, model checking, verification, non-monotonic reasoning, developing SAT solvers, etc. We also discuss future research directions. Joint work with Neda Saeedloei, Brian DeVries, Richard Min, Kyle Marple and Feliks Kluzniak.