The Strategy Challenge in SMT Solving

Abstract. High-performance SMT solvers contain many tightly integrated, hand-crafted heuristic combinations of algorithmic proof methods. While these heuristic combinations tend to be highly tuned for known classes of problems, they may easily perform badly on classes of problems not anticipated by solver developers. This issue is becoming increasingly pressing as SMT solvers begin to gain the attention of practitioners in diverse areas of science and engineering. We present a challenge to the SMT community: to develop methods through which users can exert strategic control over core heuristic aspects of SMT solvers. We present evidence that the adaptation of ideas of strategy prevalent both within the Argonne and LCF theorem proving paradigms can go a long way towards realizing this goal. Prologue. Bill McCune, Kindness and Strategy, by Grant Passmore I would like to tell a short story about Bill, of how I met him, and one way his work and kindness impacted my life

Coalgebraic semantics for parallel derivation strategies in logic programming

Logic programming, a class of programming languages based on first-order logic, provides simple and efficient tools for goal-oriented proof-search. Logic programming supports recursive computations, and some logic programs resemble the inductive or coinductive definitions written in functional programming languages. In this paper, we give a coalgebraic semantics to logic programming. We show that ground logic programs can be modelled by either P f P f -coalgebras or P f List-coalgebras on Set. We analyse different kinds of derivation strategies and derivation trees (proof-trees, SLD-trees, and-or parallel trees) used in logic programming, and show how they can be modelled coalgebraically.</p

Algorithms, datastructures, and other issues in efficient automated deduction

Abstract. Algorithms and datastructures form the kernel of any efficient theorem prover. In this abstract we discuss research on algorithms and datastructures for efficient theorem proving based on our experience with the theorem prover Vampire. We also briefly overview other works related to algorithms and datastructures, and to efficient theorem proving in general.

Global relationships in tree functional traits

Due to massive energetic investments in woody support structures, trees are subject to unique physiological, mechanical, and ecological pressures not experienced by herbaceous plants. Despite a wealth of studies exploring trait relationships across the entire plant kingdom, the dominant traits underpinning these unique aspects of tree form and function remain unclear. Here, by considering 18 functional traits, encompassing leaf, seed, bark, wood, crown, and root characteristics, we quantify the multidimensional relationships in tree trait expression. We find that nearly half of trait variation is captured by two axes: one reflecting leaf economics, the other reflecting tree size and competition for light. Yet these orthogonal axes reveal strong environmental convergence, exhibiting correlated responses to temperature, moisture, and elevation. By subsequently exploring multidimensional trait relationships, we show that the full dimensionality of trait space is captured by eight distinct clusters, each reflecting a unique aspect of tree form and function. Collectively, this work identifies a core set of traits needed to quantify global patterns in functional biodiversity, and it contributes to our fundamental understanding of the functioning of forests worldwide.ISSN:2041-172