Towards Understanding and Harnessing the Potential of Clause Learning

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its importance, little is known of the ultimate strengths and limitations of the technique. This paper presents the first precise characterization of clause learning as a proof system (CL), and begins the task of understanding its power by relating it to the well-studied resolution proof system. In particular, we show that with a new learning scheme, CL can provide exponentially shorter proofs than many proper refinements of general resolution (RES) satisfying a natural property. These include regular and Davis-Putnam resolution, which are already known to be much stronger than ordinary DPLL. We also show that a slight variant of CL with unlimited restarts is as powerful as RES itself. Translating these analytical results to practice, however, presents a challenge because of the nondeterministic nature of clause learning algorithms. We propose a novel way of exploiting the underlying problem structure, in the form of a high level problem description such as a graph or PDDL specification, to guide clause learning algorithms toward faster solutions. We show that this leads to exponential speed-ups on grid and randomized pebbling problems, as well as substantial improvements on certain ordering formulas

Public and Private Interests in Copyright Law: Creativity, Science and Democracy vs. Property and Market

Copyright law in USA has a utilitarian objective, which has to be fulfilled through economic incentives given to authors. Creative works produce social and cultural benefits for society. Often the market power of the copyright owner, combined with property aspirations prevents the free flow of information and impedes learning. Restrictions of copyright owner’s monopoly such as the doctrine of fair use are inevitable. Free speech values in the Copyright Clause are consistent with broad public interest of information and are justified by the notion of liberty. The idea-expression dichotomy reconciles the conflict between the Copyright Clause and the First Amendment. Ideas are important components of the public domain. Public domain is reward for the grant of copyright. Challenges of the new information society require a respect and better understanding of the public purpose of copyright. Democratic goals of Copyright Law cannot be obscured by market and property considerations

Designing effective contracts within the buyer-seller context: a DEMATEL and ANP study

This study examines the factors that contribute to effective contract design within the context of buyer-seller relationship. Research streams on contract factors, supply chain factors, environmental factors, and competitive factors were reviewed to arrive at 18 contract factors. A hybrid model of Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Analytic Hierarchy Process (ANP) analysed empirical data collected from 17 experts to weight the importance of contract factors. It was found that most important factors are, in order of significance: policies, supplier technology, force majeure, formality, relationship learning, buyer power, legal actions, liquidated damages, supplier power and partnership

Learning to Reason: Leveraging Neural Networks for Approximate DNF Counting

Weighted model counting (WMC) has emerged as a prevalent approach for probabilistic inference. In its most general form, WMC is #P-hard. Weighted DNF counting (weighted #DNF) is a special case, where approximations with probabilistic guarantees are obtained in O(nm), where n denotes the number of variables, and m the number of clauses of the input DNF, but this is not scalable in practice. In this paper, we propose a neural model counting approach for weighted #DNF that combines approximate model counting with deep learning, and accurately approximates model counts in linear time when width is bounded. We conduct experiments to validate our method, and show that our model learns and generalizes very well to large-scale #DNF instances.Comment: To appear in Proceedings of the Thirty-Fourth AAAI Conference on Artificial Intelligence (AAAI-20). Code and data available at: https://github.com/ralphabb/NeuralDNF

The Original Understanding of the New Hampshire Constitution’s Education Clause

[Excerpt] “In 1993, the New Hampshire Supreme Court held that “part II, article 83 [of the state constitution] imposes a duty on the State to provide a constitutionally adequate education to every educable child in the public schools in New Hampshire and to guarantee adequate funding,” and that this duty is enforceable by the judiciary. This decision, known as Claremont I, was the wellspring of a line of decisions that has radically changed both the manner in which public education is funded in New Hampshire and the respective roles of the judicial branch and the representative branches in formulating education policy. Since the adoption of the state constitution in 1784, public education in New Hampshire had been funded primarily with local taxes. The Claremont decisions flatly rejected this long tradition of local control of the funding of public education: “Whatever the State identifies as comprising constitutional adequacy it must pay for. None of that financial obligation can be shifted to local school districts, regardless of their relative wealth or need.”

Conditional Spending After \u3ci\u3eNFIB v. Sebelius\u3c/i\u3e: The Example of Federal Education Law

In NFIB v. Sebelius, the Supreme Court’s recent case addressing the constitutionality of the Affordable Care Act, the Court concluded that the expansion of Medicaid in that Act was unconstitutionally coercive and therefore exceeded the scope of Congress’s authority under the Spending Clause. This was the first time that the Court treated coercion as an issue of more than mere theoretical possibility under the Spending Clause. In the wake of the Court’s decision, commentators have expressed either the concern or the hope that NFIB’s coercion analysis may lead to the undoing of much of the federal regulatory state, which substantially relies on the spending power. This article argues that both this concern and this hope are misplaced. Taking federal education law as a test case for future coercion analysis—since federal funding given to the states for elementary and secondary education is second only to federal funding for Medicaid—the article concludes that NFIB’s coercion inquiry is unlikely to lead to much else being found unconstitutional. The major federal education laws, and by implication other conditional spending laws, will not likely find their demise under the Court’s analysis. Nonetheless, NFIB will likely have some effect on the future of federal education law. It should put a damper on calls to dramatically increase federal education funding; encourage the trend towards smaller grants of limited duration, especially those that bypass the states; result in some structural changes both in funding and enforcement; and, somewhat paradoxically for a decision that found the Medicaid enforcement regime coercive, may lead to greater federal enforcement of conditional spending laws