CERTIFYING CONFLUENCE PROOFS VIA RELATIVE TERMINATION AND RULE LABELING

The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule labeling in the theorem prover Isabelle. Moreover, we report on the integration of this result into the certifier CeTA, facilitating the checking of confluence certificates based on decreasing diagrams. The power of the method is illustrated by an experimental evaluation on a (standard) collection of confluence problems

Propositional Encoding of Constraints over Tree-Shaped Data

We present a functional programming language for specifying constraints over tree-shaped data. The language allows for Haskell-like algebraic data types and pattern matching. Our constraint compiler CO4 translates these programs into satisfiability problems in propositional logic. We present an application from the area of automated analysis of (non-)termination of rewrite systems

Certified rule labeling

© Julian Nagele and Harald Zankl. The rule labeling heuristic aims to establish confluence of (left-)linear term rewrite systems via decreasing diagrams. We present a formalization of a confluence criterion based on the interplay of relative termination and the rule labeling in the theorem prover Isabelle. Moreover, we report on the integration of this result into the certifier CeTA, facilitating the checking of confluence certificates based on decreasing diagrams for the first time. The power of the method is illustrated by an experimental evaluation on a (standard) collection of confluence problems

AC-KBO Revisited

Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In this paper we consider various definitions of AC-compatible Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are revisited. The former is enhanced to a more powerful version, and we modify the latter to amend its lack of monotonicity on non-ground terms. We further present new complexity results. An extension reflecting the recent proposal of subterm coefficients in standard Knuth-Bendix orders is also given. The various orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming (TPLP) special issue for the 12th International Symposium on Functional and Logic Programming (FLOPS 2014

Cops and CoCoWeb: Infrastructure for Confluence Tools

In this paper we describe the infrastructure supporting confluence tools and competitions: Cops, the confluence problems database, and CoCoWeb, a convenient web interface for tools that participate in the annual confluence competition

Rabl's model of the interphase chromosome arrangement tested in Chinise hamster cells by premature chromosome condensation and laser-UV-microbeam experiments

In 1885 Carl Rabl published his theory on the internal structure of the interphase nucleus. We have tested two predictions of this theory in fibroblasts grown in vitro from a female Chinese hamster, namely (1) the Rabl-orientation of interphase chromosomes and (2) the stability of the chromosome arrangement established in telophase throughout the subsequent interphase. Tests were carried out by premature chromosome condensation (PCC) and laser-UV-microirradiation of the interphase nucleus. Rabl-orientation of chromosomes was observed in G1 PCCs and G2 PCCs. The cell nucleus was microirradiated in G1 at one or two sites and pulse-labelled with 3H-thymidine for 2h. Cells were processed for autoradiography either immediately thereafter or after an additional growth period of 10 to 60h. Autoradiographs show unscheduled DNA synthesis (UDS) in the microirradiated nuclear part(s). The distribution of labelled chromatin was evaluated in autoradiographs from 1035 cells after microirradiation of a single nuclear site and from 253 cells after microirradiation of two sites. After 30 to 60h postincubation the labelled regions still appeared coherent although the average size of the labelled nuclear area fr increased from 14.2% (0h) to 26.5% (60h). The relative distance dr, i.e. the distance between two microirradiated sites divided by the diameter of the whole nucleus, showed a slight decrease with increasing incubation time. Nine metaphase figures were evaluated for UDS-label after microirradiation of the nuclear edge in G1. An average of 4.3 chromosomes per cell were labelled. Several chromosomes showed joint labelling of both distal chromosome arms including the telomeres, while the centromeric region was free from label. This label pattern is interpreted as the result of a V-shaped orientation of these particular chromosomes in the interphase nucleus with their telomeric regions close to each other at the nuclear edge. Our data support the tested predictions of the Rabl-model. Small time-dependent changes of the nuclear space occupied by single chromosomes and of their relative positions in the interphase nucleus seem possible, while the territorial organization of interphase chromosomes and their arrangement in general is maintained during interphase. The present limitations of the methods used for this study are discussed

Confluence Competition 2018

We report on the 2018 edition of the Confluence Competition, a competition of software tools that aim to (dis)prove confluence and related properties of rewrite systems automatically

The application of FLUKA to dosimetry and radiation therapy

The FLUKA Monte Carlo code has been evolving over the last several decades and is now widely used for radiation shielding calculations. In order to facilitate the use of FLUKA in dosimetry and therapy applications, supporting software has been developed to allow the direct conversion of the output files from standard CT-scans directly into a voxel geometry for transport within FLUKA. Since the CT-scan information essentially contains only the electron density information over the scanned volume, one needs the specific compositions for each voxel individually. We present here the results of a simple algorithm to assign tissues in the human body to one of four categories: soft-tissue, hard-bone, trabecular-bone and porous-lung. In addition, we explore the problem of the pathlength distributions in porous media such as trabecular bone. A mechanism will be implemented within FLUKA to allow for variable multipal fixed density materials to accommodate the pathlength distributions discovere