Efficient Pattern Matching in Python

Pattern matching is a powerful tool for symbolic computations. Applications include term rewriting systems, as well as the manipulation of symbolic expressions, abstract syntax trees, and XML and JSON data. It also allows for an intuitive description of algorithms in the form of rewrite rules. We present the open source Python module MatchPy, which offers functionality and expressiveness similar to the pattern matching in Mathematica. In particular, it includes syntactic pattern matching, as well as matching for commutative and/or associative functions, sequence variables, and matching with constraints. MatchPy uses new and improved algorithms to efficiently find matches for large pattern sets by exploiting similarities between patterns. The performance of MatchPy is investigated on several real-world problems

Abstract Canonical Inference

An abstract framework of canonical inference is used to explore how different proof orderings induce different variants of saturation and completeness. Notions like completion, paramodulation, saturation, redundancy elimination, and rewrite-system reduction are connected to proof orderings. Fairness of deductive mechanisms is defined in terms of proof orderings, distinguishing between (ordinary) "fairness," which yields completeness, and "uniform fairness," which yields saturation.Comment: 28 pages, no figures, to appear in ACM Trans. on Computational Logi

How well do meteorological indicators represent agricultural and forest drought across Europe?

Drought monitoring and early warning (M&EW) systems are an important component of agriculture/silviculture drought risk assessment. Many operational information systems rely mostly on meteorological indicators, a few incorporate vegetation state information. However, the relationships between meteorological drought indicators and agricultural/silvicultural drought impacts vary across Europe. The details of this variability have not been elucidated sufficiently on a continental scale in Europe to inform drought risk management at administrative scales. The objective of this study is to fill this gap and evaluate how useful the variety of meteorological indicators are to assess agricultural/silvicultural drought across Europe. The first part of the analysis systematically linked meteorological drought indicators to remote sensing based vegetation indices (VIs) for Europe at NUTs3 administrative regions scale using correlation analysis for crops and forests. In a second step, a stepwise multiple linear regression model was deployed to identify variables explaining the spatial differences observed. Finally, corn crop yield in Germany was chosen as a case study to verify VIs representativeness of agricultural drought impacts. Results show that short accumulation periods of SPI and SPEI are best linked to crop vegetation stress in most cases, which further validates the use of SPI3 in existing operational drought monitors. However, large regional differences in correlations are also revealed. Climate (temperature and precipitation) explained the largest proportion of variance, suggesting that meteorological indices are less informative of agricultural/silvicultural drought in colder/wetter parts of Europe. These findings provide important context for interpreting meteorological indices on widely used national to continental M&EW systems, leading to a better understanding of where/when such M&EW tools can be indicative of likely agricultural stress and impacts

Decidability of the Monadic Shallow Linear First-Order Fragment with Straight Dismatching Constraints

The monadic shallow linear Horn fragment is well-known to be decidable and has many application, e.g., in security protocol analysis, tree automata, or abstraction refinement. It was a long standing open problem how to extend the fragment to the non-Horn case, preserving decidability, that would, e.g., enable to express non-determinism in protocols. We prove decidability of the non-Horn monadic shallow linear fragment via ordered resolution further extended with dismatching constraints and discuss some applications of the new decidable fragment.Comment: 29 pages, long version of CADE-26 pape

Investigations on unconventional aspects in the quantum Hall regime of narrow gate defined channels

We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates on the surfaces of GaAs/AlGaAs heterostructures. In the low mobility regime the classical Hall resistance line is proportional to the magnetic field as measured in the high temperature limit and cuts through the center of each Hall plateau. For high mobility samples we observe in linear response measurements, that this symmetry is broken and the classical Hall line cuts the plateaus not at the center but at higher magnetic fields near the edges of the plateaus. These experimental results confirm the unconventional predictions of a model for the quantum Hall effect taking into account mutual screening of charge carriers within the Hall bar. The theory is based on solving the Poisson and Schr\"odinger equations in a self-consistent manner.Comment: EP2DS-17 Proceedings, 6 Pages, 2 Figure

A Model-based Completeness Proof of Extended Narrowing And Resolution

We give a proof of refutational completeness for Extended Narrowing And Resolution (ENAR), a calculus introduced by Dowek, Hardin and Kirchner in the context of Theorem Proving Modulo. ENAR integrates narrowing with respect to a set of rewrite rules on propositions into automated first-order theorem proving by resolution. Our proof allows to impose ordering restriction- s on ENAR and provides general redundancy criteria, which are crucial for finding nontrivial proofs. On the other hand, it requires confluence and termination of the rewrite system, and in addition the existence of a well-founded ordering on propositions that is compatible with rewriting, compatible with ground inferences, total on ground clauses, and has some additional technical properties. Such orderings exist for hierarchical definitions of predicates. As an exampe we provide such an ordering for a fragment of set theory

A quantitative analysis to objectively appraise drought indicators and model drought impacts

Drought monitoring and early warning is an important measure to enhance resilience towards drought. While there are numerous operational systems using different drought indicators, there is no consensus on which indicator best represents drought impact occurrence for any given sector. Furthermore, thresholds are widely applied in these indicators but, to date, little empirical evidence exists as to which indicator thresholds trigger impacts on society, the economy, and ecosystems. The main obstacle for evaluating commonly used drought indicators is a lack of information on drought impacts. Our aim was therefore to exploit text-based data from the European Drought Impact report Inventory (EDII) to identify indicators that are meaningful for region-, sector-, and season-specific impact occurrence, and to empirically determine indicator thresholds. In addition, we tested the predictability of impact occurrence based on the best-performing indicators. To achieve these aims we applied a correlation analysis and an ensemble regression tree approach, using Germany and the UK (the most data-rich countries in the EDII) as test beds. As candidate indicators we chose two meteorological indicators (Standardized Precipitation Index, SPI, and Standardized Precipitation Evaporation Index, SPEI) and two hydrological indicators (streamflow and groundwater level percentiles). The analysis revealed that accumulation periods of SPI and SPEI best linked to impact occurrence are longer for the UK compared with Germany, but there is variability within each country, among impact categories and, to some degree, seasons. The median of regression tree splitting values, which we regard as estimates of thresholds of impact occurrence, was around −1 for SPI and SPEI in the UK; distinct differences between northern/northeastern vs. southern/central regions were found for Germany. Predictions with the ensemble regression tree approach yielded reasonable results for regions with good impact data coverage. The predictions also provided insights into the EDII, in particular highlighting drought events where missing impact reports may reflect a lack of recording rather than true absence of impacts. Overall, the presented quantitative framework proved to be a useful tool for evaluating drought indicators, and to model impact occurrence. In summary, this study demonstrates the information gain for drought monitoring and early warning through impact data collection and analysis. It highlights the important role that quantitative analysis with impact data can have in providing "ground truth" for drought indicators, alongside more traditional stakeholder-led approaches

Efficient Encodings of First-Order Horn Formulas in Equational Logic

We present several translations from first-order Horn formulas to equational logic. The goal of these translations is to allow equational theorem provers to efficiently reason about non-equational problems. Using these translations we were able to solve 37 problems of rating 1.0 (i.e. which had not previously been automatically solved) from the TPTP

Incompressible strips in dissipative Hall bars as origin of quantized Hall plateaus

We study the current and charge distribution in a two dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasi-local transport model, that includes non-linear screening effects on the conductivity via the self-consistently calculated density profile. The existence of ``incompressible strips'' with integer Landau level filling factor is investigated within a Hartree-type approximation, and non-local effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the longitudinal resistance as continuous functions of the magnetic field B, with plateaus of finite widths and the well-known, exactly quantized values. We emphasize the close relation between these plateaus and the existence of incompressible strips, and we show that for B values within these plateaus the potential variation across the Hall bar is very different from that for B values between adjacent plateaus, in agreement with recent experiments.Comment: 13 pages, 11 figures, All color onlin

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