Collapsing Exact Arithmetic Hierarchies

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

Foundational and Mathematical Uses of Higher Types

In this paper we develop mathematically strong systems of analysis in higher types which, nevertheless, are proof-theoretically weak, i.e. conservative over elementary resp. primitive recursive arithmetic. These systems are based on non-collapsing hierarchies (Φn-WKL+, Ψn-WKL+) of principles which generalize (and for n = 0 coincide with) the so-called ‘weak’ König’s lemma WKL (which has been st...

Adaptive Collapsing on Bounding Volume Hierarchies for Ray-Tracing

Ray tracing is a computationally intensive process, several tree data structures and heuristics have been developed to optimize it. This paper presents a new heuristic in the area, based on collapsing some nodes in order to achieve a smaller expected number of node-tests. Two ways of using this heuristic in Bounding Volume Hierarchies are presented as well as the cost-model used to drive the he...

EGFC: An exact global fault collapsing tool for combinational circuits

Fault collapsing is the process of reducing the number of faults by using redundance and equivalence/dominance relationships among faults. Exact fault collapsing can be easily applied locally at the logic gates, however, it is often ignored for most circuits, due to its high demand of resources such as execution time and/or memory. In this paper, we present EGFC, an exact global fault collapsin...

Subshifts, MSO Logic, and Collapsing Hierarchies

We use monadic second-order logic to define two-dimensional subshifts, or sets of colorings of the infinite plane. We present a natural family of quantifier alternation hierarchies, and show that they all collapse to the third level. In particular, this solves an open problem of [Jeandel & Theyssier 2013]. The results are in stark contrast with picture languages, where such hierarchies are usua...