Enforcing Termination of Interprocedural Analysis

Interprocedural analysis by means of partial tabulation of summary functions may not terminate when the same procedure is analyzed for infinitely many abstract calling contexts or when the abstract domain has infinite strictly ascending chains. As a remedy, we present a novel local solver for general abstract equation systems, be they monotonic or not, and prove that this solver fails to terminate only when infinitely many variables are encountered. We clarify in which sense the computed results are sound. Moreover, we show that interprocedural analysis performed by this novel local solver, is guaranteed to terminate for all non-recursive programs --- irrespective of whether the complete lattice is infinite or has infinite strictly ascending or descending chains

A representation theorem for MV-algebras

An {\em MV-pair} is a pair $(B,G)$ where $B$ is a Boolean algebra and $G$ is a subgroup of the automorphism group of $B$ satisfying certain conditions. Let $\sim_G$ be the equivalence relation on $B$ naturally associated with $G$. We prove that for every MV-pair $(B,G)$, the effect algebra $B/\sim_G$ is an MV- effect algebra. Moreover, for every MV-effect algebra $M$ there is an MV-pair $(B,G)$ such that $M$ is isomorphic to $B/\sim_G$

Quantitative Concept Analysis

Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.Comment: 16 pages, 3 figures, ICFCA 201

A Calculus of Space, Time, and Causality: its Algebra, Geometry, Logic

The calculus formalises human intuition and common sense about space, time, and causality in the natural world. Its intention is to assist in the design and implementation of programs, of programming languages, and of interworking by tool chains that support rational program development. The theses of this paper are that Concurrent Kleene Algebra (CKA) is the algebra of programming, that the diagrams of the Unified Modeling Language provide its geometry, and that Unifying Theories of Program- ming (UTP) provides its logic. These theses are illustrated by a fomalisation of features of the first concurrent object-oriented language, Simula 67. Each level of the calculus is a conservative extension of its predecessor. We conclude the paper with an extended section on future research directions for developing and applying UTP, CKA, and our calculus, and on how we propose to implement our algebra, geometry, and logic

Characterizations of the 00-distributive semilattice

summary:The $0$-distributive semilattice is characterized in terms of semiideals, ideals and filters. Some sufficient conditions and some necessary conditions for $0$-distributivity are obtained. Counterexamples are given to prove that certain conditions are not necessary and certain conditions are not sufficient

Seasonality and evaporation of water resources in Reynolds Creek Experimental Watershed and Critical Zone Observatory, Southwestern Idaho, USA

Abstract The Reynolds Creek Experimental Watershed (RCEW) and Critical Zone Observatory (CZO), located south of the western Snake River Plain in the Intermountain West of the United States, is the site of over 60 years of research aimed at understanding integrated earth processes in a semi‐arid climate to aid sustainable use of environmental resources. Meteoric water lines (MWLs) are used to interpret hydrologic processes, though equilibrium and nonequilibrium processes affect the linear function and can reveal seasonal and climatological effects, necessitating the development of local meteoric water lines (LMWLs). At RCEW‐CZO, an RCEW LMWL was developed using non‐volume‐weighted, orthogonal regression with assumed error in both predictor and response variables from several years of precipitation (2015, 2017, 2019, 2020, and 2021) primarily at three different elevations (1203, 1585, and 2043 m). As most precipitation is evaporated or intercepted by vegetation in the driest months, an RCEW LMWL for groundwater recharge (RCEW LMWL‐GWR) was also developed using precipitation from the wettest months (November through April). The RCEW LMWL (δ2H = 7.41 × δ18O – 3.09) is different from the RCEW LMWL‐GWR (δ2H = 8.21 × δ18O + 9.95) and compares favorably to other LMWLs developed for the region and climate. Comparative surface, spring, and subsurface water datasets within the RCEW‐CZO are more similar to precipitation during the wettest months than dry months, illustrating that some semi‐arid hydrologic systems may most appropriately be compared to MWLs developed from precipitation only from the wettest season