Abstract. Let X d,n be an n-element subset of {0, 1}d chosen uniformly at random, and denote by P d,n := conv X d,n its convex hull. Let ∆ d,n be the density of the graph of P d,n (i.e., the number of one-dimensional faces of P d,n divided by n 2 ). Our main result is that, for any function
In the futile questioning problem, one must decide whether acquisition of additional information can possibly lead to the proof of a conclusion. Solution of that problem demands evaluation of a quantified Boolean formula at the second level of the polynomial hierarchy. The same evaluation problem, called Q-ALL SAT, arises in many other applications. In this paper, we introduce a special subclass of Q-ALL SAT that is at the first level of the polynomial hierarchy. We develop a solution algorithm for the general case that uses a backtracking search and a new form of learning of clauses. Results are reported for two sets of instances involving a robot route problem and a game problem. For these instances, the algorithm is substantially faster than state-of-the-art solvers for quantified Boolean formulas.
Although the satisfiability problem (SAT) is NP-complete, state-of-the-art solvers for SAT can solve instances that are considered to be very hard. Emerging applications demand to solve even more complex problems residing at the second or higher levels of the polynomial hierarchy. We identify such a problem, called Q-ALL SAT, that arises in a variety of applications. We have designed a solution algorithm for Q-ALL SAT that employs a SAT solver and thus exploits the recent advances of SAT solvers. In addition, a heuristic is applied to reduce the number of instances that are to be solved by the SAT solver. A learning scheme improves the performance of that heuristic. Test results of a first implementation of the proposed algorithm confirm that this is a very promising approach.
This paper explores the use of the two contextualized learning tools, animations and educational robots, in an introductory computer science course. We describe our experience when supplementing Greenfoot animation exercises with robotic exercises using the Scribbler and Finch robot, and compare the impact of the different learning tools on students' engagement and performance. We also outline practical considerations concerning the use of Greenfoot animations, Scribbler robots, and Finch robots.
This paper describes learning in a compiler for algorithms solving classes of the logic minimization problem MINSAT, where the underlying propositional formula is in conjunctive normal form (CNF) and where costs are associated with the True/False values of the variables. Each class consists of all instances that may be derived from a given propositional formula and costs for True/False values by fixing or deleting variables, and by deleting clauses. The learning step begins once the compiler has constructed a solution algorithm for a given class. The step applies that algorithm to comparatively few instances of the class, analyses the performance of the algorithm on these instances, and modifies the underlying propositional formula, with the goal that the algorithm will perform much better on all instances of the class.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.