A Proof Strategy Language and Proof Script Generation for Isabelle/HOL

We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low memory usage. Upon success, PSL generates an efficient proof script, which bypasses a large part of the proof search. We also present PSL's monadic interpreter to show that the underlying idea of PSL is transferable to other ITPs.Comment: This paper has been submitted to CADE2

The exceptionally high diversity of small carnivorans from the Late Miocene hominid locality of Hammerschmiede (Bavaria, Germany)

The present study deals with new material of carnivorans (Mustelidae, Mephitidae, Ailuridae, Potamotheriinae and Viverridae) from the basal Tortonian (Late Miocene, late Astaracian) hominid-bearing locality of Hammerschmiede (Bavaria, Germany). The small carnivoran fauna includes 20 species belonging to nine different subfamilies (Guloninae, Lutrinae, Mellivorinae, Potamotheriinae, Leptarctinae, Mephitinae, Simocyoninae, Genettinae and Viverrinae). The identified forms include: “Martes” sansaniensis, “Martes” cf. munki, “Martes” sp., Circamustela hartmanni n. sp., Laphyctis mustelinus, Guloninae indet., Eomellivora moralesi, Vishnuonyx neptuni, Paralutra jaegeri, Lartetictis cf. dubia, Trocharion albanense, Palaeomeles pachecoi, Proputorius sansaniensis, Proputorius pusillus, Alopecocyon goeriachensis, Simocyoninae indet., Potamotherium sp., Semigenetta sansaniensis, Semigenetta grandis and Viverrictis modica. The new species Circamustela hartmanni n. sp. is differentiated from the other members of the genus by its small size and the morphology of its dental cusps in the upper and lower carnassials. This is one of the highest reported taxonomic diversities for fossil small carnivorans in the Miocene of Europe, including also first and last occurrences for several genera and species. Additionally, the assemblage comprises some rare taxa such as Palaeomeles pachecoi and Eomellivora moralesi. An ecomorphological comparison of the discovered taxa reveals possible cases of competition and niche partitioning. © 2022 Kargopoulos et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

XWeB: the XML Warehouse Benchmark

With the emergence of XML as a standard for representing business data, new decision support applications are being developed. These XML data warehouses aim at supporting On-Line Analytical Processing (OLAP) operations that manipulate irregular XML data. To ensure feasibility of these new tools, important performance issues must be addressed. Performance is customarily assessed with the help of benchmarks. However, decision support benchmarks do not currently support XML features. In this paper, we introduce the XML Warehouse Benchmark (XWeB), which aims at filling this gap. XWeB derives from the relational decision support benchmark TPC-H. It is mainly composed of a test data warehouse that is based on a unified reference model for XML warehouses and that features XML-specific structures, and its associate XQuery decision support workload. XWeB's usage is illustrated by experiments on several XML database management systems

Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697

Fragmentation transitions in multi-state voter models

Adaptive models of opinion formation among humans can display a fragmentation transition, where a social network breaks into disconnected components. Here, we investigate this transition in a class of models with arbitrary number of opinions. In contrast to previous work we do not assume that opinions are equidistant or arranged on a one-dimensional conceptual axis. Our investigation reveals detailed analytical results on fragmentations in a three-opinion model, which are confirmed by agent-based simulations. Furthermore, we show that in certain models the number of opinions can be reduced without affecting the fragmentation points.Comment: 11 pages, 8 figure

Mining State-Based Models from Proof Corpora

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will lead to a successful proof requires a significant amount of human intervention. This paper presents an automated technique that takes as input examples of successful proofs and infers an Extended Finite State Machine as output. This can in turn be used to generate proofs of new conjectures. Our preliminary experiments show that the inferred models are generally accurate (contain few false-positive sequences) and that representing existing proofs in such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201