Computer Science on Cambridge Core

Fix integers and and set . Let denote the complete -partite -uniform hypergraph with parts of size . We prove that the Zarankiewicz number provided . Previously this was known only for due to Pohoata and Zakharov. Our novel approach, which uses Behrend’s construction of sets with no 3-term arithmetic progression, also applies for small values of , for example, it gives where the exponent 11/4 is …

Direct collocation (DC) methods are utilized for addressing trajectory optimization challenges in robotics due to their ability to generate dynamically consistent solutions. However, in the cable-driven robotic systems, where tension constraints impose kinodynamic restrictions, maintaining accuracy becomes significantly complex. This article addresses robot tensionability and proposes a method to…

The distinction between the proofs that only certify the truth of their conclusion and those that also display the reasons why their conclusion holds has a long philosophical history. In the contemporary literature, the grounding relation—an objective, explanatory relation which is tightly connected with the notion of reason—is receiving considerable attention in several fields of philosophy. Whi…

Two salient notions of sameness of theories are synonymy , aka definitional equivalence , and bi-interpretability . Of these two definitional equivalence is the strictest notion. In which cases can we infer synonymy from bi-interpretability? We study this question for the case of sequential theories. Our result is as follows. Suppose that two sequential theories are bi-interpretable and that the …

Anselm described god as “something than which nothing greater can be thought” [1, p. 93], and Descartes viewed him as “a supreme being” [7, p. 122]. I first capture those characterizations formally in a simple language for monadic predicate logic. Next, I construct a model class inspired by Stoic and medieval doctrines of grades of being [8, 20]. Third, I prove the models sufficient for recoverin…