The determination of integral closures and geometric applications

We express explicitly the integral closures of some ring extensions; this is done for all Bring-Jerrard extensions of any degree as well as for all general extensions of degree < 6; so far such an explicit expression is known only for degree < 4 extensions. As a geometric application we present explicitly the structure sheaf of every Bring-Jerrard covering space in terms of coefficients of the equation defining the covering; in particular, we show that a degree-3 morphism f : Y --> X is quasi-etale if and only if the first Chern class of the sheaf f_*(O_Y) is trivial (details in Theorem 5.3). We also try to get a geometric Galoisness criterion for an arbitrary degree-n finite morphism; this is successfully done when n = 3 and less satifactorily done when n = 5.Comment: Advances in Mathematics, to appear (no changes, just add this info

The Geometry of Synchronization (Long Version)

We graft synchronization onto Girard's Geometry of Interaction in its most concrete form, namely token machines. This is realized by introducing proof-nets for SMLL, an extension of multiplicative linear logic with a specific construct modeling synchronization points, and of a multi-token abstract machine model for it. Interestingly, the correctness criterion ensures the absence of deadlocks along reduction and in the underlying machine, this way linking logical and operational properties.Comment: 26 page

Non-termination using Regular Languages

We describe a method for proving non-looping non-termination, that is, of term rewriting systems that do not admit looping reductions. As certificates of non-termination, we employ regular (tree) automata.Comment: Published at International Workshop on Termination 201

Proving Looping and Non-Looping Non-Termination by Finite Automata

A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the language by a tree automaton with a fixed number of states, and expressing the mentioned requirements in a SAT formula. Satisfiability of this formula implies non-termination. Our approach succeeds for many examples where all earlier techniques fail, for instance for the S-rule from combinatory logic