Proof Generation from Delta-Decisions

We show how to generate and validate logical proofs of unsatisfiability from delta-complete decision procedures that rely on error-prone numerical algorithms. Solving this problem is important for ensuring correctness of the decision procedures. At the same time, it is a new approach for automated theorem proving over real numbers. We design a first-order calculus, and transform the computational steps of constraint solving into logic proofs, which are then validated using proof-checking algorithms. As an application, we demonstrate how proofs generated from our solver can establish many nonlinear lemmas in the the formal proof of the Kepler Conjecture.Comment: Appeared in SYNASC'1

Chainspace: A Sharded Smart Contracts Platform

Chainspace is a decentralized infrastructure, known as a distributed ledger, that supports user defined smart contracts and executes user-supplied transactions on their objects. The correct execution of smart contract transactions is verifiable by all. The system is scalable, by sharding state and the execution of transactions, and using S-BAC, a distributed commit protocol, to guarantee consistency. Chainspace is secure against subsets of nodes trying to compromise its integrity or availability properties through Byzantine Fault Tolerance (BFT), and extremely high-auditability, non-repudiation and `blockchain' techniques. Even when BFT fails, auditing mechanisms are in place to trace malicious participants. We present the design, rationale, and details of Chainspace; we argue through evaluating an implementation of the system about its scaling and other features; we illustrate a number of privacy-friendly smart contracts for smart metering, polling and banking and measure their performance

Software safety : a definition and some preliminary thoughts

Software safety is the subject of a research project in its initial stages at the University of California Irvine. This research deals with critical real-time software where the cost of an error is high, e.g. human life. In this paper software techniques having a bearing on safety are described and evaluated. Initial definitions of software safety concepts are presented along with some preliminary thoughts and research questions

Affine functions and series with co-inductive real numbers

We extend the work of A. Ciaffaglione and P. Di Gianantonio on mechanical verification of algorithms for exact computation on real numbers, using infinite streams of digits implemented as co-inductive types. Four aspects are studied: the first aspect concerns the proof that digit streams can be related to the axiomatized real numbers that are already axiomatized in the proof system (axiomatized, but with no fixed representation). The second aspect re-visits the definition of an addition function, looking at techniques to let the proof search mechanism perform the effective construction of an algorithm that is correct by construction. The third aspect concerns the definition of a function to compute affine formulas with positive rational coefficients. This should be understood as a testbed to describe a technique to combine co-recursion and recursion to obtain a model for an algorithm that appears at first sight to be outside the expressive power allowed by the proof system. The fourth aspect concerns the definition of a function to compute series, with an application on the series that is used to compute Euler's number e. All these experiments should be reproducible in any proof system that supports co-inductive types, co-recursion and general forms of terminating recursion, but we performed with the Coq system [12, 3, 14]

KNOWLEDGE PRODUCTION, MULTIFUNCTIONALITY OF AGRICULTURE AND PUBLIC DECISIONS: CRITICAL ISSUES OF CONTEMPORARY CONTROVERSIES

Various theoretical models of public policy analysis are used to treat situations of decision-making in which public deciders have to take into account the multifunctionality of agriculture. For some, science-society relations are not really problematical. Others acknowledge the current attempts of these policy-makers to find adequate scientific knowledge, and the difficulties they encounter. These difficulties stem partly from the very content of knowledge produced by research. Could other modes of production be more efficient? The status of the knowledge produced by these approaches is a subject of debate. Bridging the divide between science and policy more effectively is not only a question of knowledge brokerage. Accessibility and reliability of the existing evidences are also problems to be addressed. The debates around evidence-based practices may provide some landmarks in this new situation although they also emphasize the limits of the tools that can be built for this purpose.Multifunctionality, Agriculture, Knowledge, Policy, Agribusiness, Community/Rural/Urban Development, Labor and Human Capital,

Forensic Fisheries Science: Literature Review and Research Suggestions

Recent years have seen a dramatic increase in litigation against the National Marine Fisheries Service, NOAA. Litigation may affect personnel throughout the agency, including scientists, whose work is often directly or indirectly influenced by complex legal requirements, but who may not be in a position to comment or engage in public dialogue. It may be helpful for scientists and other agency personnel to join the ongoing discussion in the legal community regarding the interface of science and law. This paper provides a starting point with a selected introduction to relevant legal literature in this area. It uses the phrase “forensic fisheries science” to describe the application of science to legal requirements in the fishery management context. It concludes with suggestions for future research that could assist NMFS scientists as they grapple with the challenge of using science to help the agency meet its complex legal requirements. Forensic: belonging to, used in, or suitable to courts of judicature or to public discussion and debate; argumentative, rhetorical; relating to or dealing with the application of scientific knowledge to legal problems (Merriam-Webster Online Dictionary