Yukihide Takayama

Extraction of redundancy-free programs from constructive natural deduction proofs

Executable codes can be extracted from constructive proofs by using realizability interpretation. However, realizability also generates redundant codes that have no significant computational meaning. This redundancy causes heavy runtime overheads and is one of the obstacles in applying realizability to practical systems that realize the mathematical programming paradigm. This paper presents a method to eliminate redundancy by analysing proof trees as preprocessing of realizability interpretation. According to the declaration given to the theorem that is proved, each node of the proof tree is marked automatically to show which part of the realizer is needed. This procedure does not always work well. This paper also gives an analysis of the procedure and techniques to resolve critical cases. The method is studied in simple constructive logic with primitive types, mathematical induction and its q-realizability interpretation. As an example, the extraction of a prime number checker program is given.

Extraction of Concurrent Processes from Higher Dimensional Automata

We present an algorithm, called reverse interpretation, that extracts concurrent processes from labeled cubical complexes. E. Goubault and T. Jensen

STANLEY-REISNER IDEALS WHOSE POWERS HAVE FINITE LENGTH COHOMOLOGIES

We introduce a class of Stanley-Reisner ideals called generalized complete intersection, which is characterized by the property that all the residue class rings of powers of the ideal have FLC. We also give a combi- natorial characterization of such ideals.

Kodaira Type Vanishing Theorem for the Hirokado Variety

The Hirokado variety is a Calabi–Yau threefold in characteristic 3 that is not liftable either to characteristic 0 or the ring W 2 of the second Witt vectors. Although Deligne–Illusie–Raynaud type Kodaira vanishing cannot be applied, we show that H 1(X, L −1) = 0, for an ample line bundle such that L 3 has a non-trivial global section, holds for this variety.

Raynaud-Mukai construction and Calabi-Yau threefolds in positive characteristic

In this article, we study the possibility of producing a Calabi-Yau threefold in positive characteristic which is a counter-example to Kodaira vanishing. The only known method to construct the counter-example is so called inductive method such as the Raynaud-Mukai construction or Russel construction. We consider Mukais method and its modification. Finally, as an application of Shepherd-Barron vanishing theorem of Fano threefolds, we compute

NORMALITY OF AFFINE SEMIGROUP RINGS GENERATED BY 2-DIMENSIONAL CONE TYPE SIMPLICIAL COMPLEXES

H^1(X, H^{-1})

On Kodaira type vanishing for Calabi–Yau threefolds in positive characteristic

for any ample line bundle

Defining concurrent processes constructively

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Lifschitz's logic of calculable numbers and optimizations in program extraction

on a Calabi-Yau threefold

Resolutions by mapping cones

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