5553551
Decision Problems for Propositional Linear Logic
Abstract Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. This accounting is made possible by removing the ‘structural’ rules of contraction and weakening, adding a modal operator and adding finer versions of the propositional connectives. Linear logic has fundamental logical interest and applications to computer science, particularly to Petri nets, concurrency, storage allocation, garbage collection and the control structure of logic programs. In addition, there is a direct correspondence between polynomial-time computation and proof normalization in a bounded form of linear logic. In this paper we show that unlike most other propositional (quantifier-free) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes PSPACE-complete. We also establish membership in NP for the multiplicative fragment, NP-completeness for the multiplicative fragment extended with unrestricted weakening, and undecidability for fragments of noncommutative propositional linear logic.
9031501
Design of a role-based trust-management framework
We introduce the RT framework, a family of role-based trust management languages for representing policies and credentials in distributed authorization. RT combines the strengths of role-based access control and trust-management systems and is especially suitable for attribute-based access control. Using a few simple credential forms, RT provides localized authority over roles, delegation in role definition, linked roles, and parameterized roles. RT also introduces manifold roles, which can be used to express threshold and separation-of-duty policies, and delegation of role activations. We formally define the semantics of credentials in the RT framework by presenting a translation from credentials to Datalog rules. This translation also shows that this semantics is algorithmically tractable.
16397953
Parametricity and Variants of Girard's J Operator
Abstract The Girard–Reynolds polymorphic λ -calculus is generally regarded as a calculus of parametric polymorphism in which all well-formed terms are strongly normalizing with respect to β -reductions. Girard demonstrated that the addition of a simple “non-parametric” operation, J , to the calculus allows the definition of a non-normalizing term. Since the type of J is not inhabited by any closed term, one might suspect that this may play a role in defining a non-normalizing term using it. We demonstrate that this is not the case by giving a simple variant, J′ , of J whose type is otherwise inhabited and which causes normalization to fail. It appears that impredictivity is essential to the argument; predictive variants of the polymorphic λ -calculus admit non-parametric operations without sacrificing normalization.
3062362
Managing Digital Rights using Linear Logic
Digital music players protect songs by enforcing licenses that convey specific rights for individual songs or groups of songs. For licenses specified in industry, we show that deciding whether a license authorizes a sequence of actions is NP-complete, with a restricted version of the problem solvable efficiently using a reduction to maximum network flow. The authorization algorithm used in industry is online, deciding which rights to exercise as actions occur, but we show that all online algorithms are necessarily non-monotonic: each allows actions under one license that it does not allow under a more flexible license. In one approach to achieving monotonicity, we exhibit the unique maximal set of licenses on which there exists a monotonic online algorithm. This set of well-behaved licenses induces an approximation algorithm by replacing each license with a well-behaved license. In a second approach, we consider allowing the player to revise its past decisions about which rights to exercise while still ensuring compliance with the license. We propose an efficient algorithm based on linear logic, with linear negation used to revise past decisions. We prove our algorithm monotonic, live, and sound with respect to the semantics of licenses
18708753
Unification and ML-Type Reconstruction
We study the complexity of type reconstruction for a core fragment of ML with lambda abstraction, function application, and the polymorphic let declaration. We derive exponential upper and lower bounds on recognizing the typable core ML expressions. Our primary technical tool is uniication of succinctly represented type expressions. After observing that core ML expressions, of size n, can be typed in DTIME(2 n), we exhibit two diierent families of programs whose principal types grow exponentially. We show how to exploit the expressiveness of the let-polymorphism in these constructions to derive lower bounds on deciding typability: one leads naturally to NP-hardness and the other to DTIME(2 n k)-hardness for each integer k 1. Our generic simulation of any exponential time Turing Machine by ML type reconstruction may be viewed as a nonstandard way of computing with types. Our worst-case lower bounds stand in contrast to practical experience, which suggests that commonly used algorithms for type reconstruction do not slow compilation substantially.
215952437
Beyond proof-of-compliance: security analysis in trust management
Trust management is a form of distributed access control that allows one principal to delegate some access decisions to other principals. While the use of delegation greatly enhances flexibility an...
11133086
Query-sensitive ray shooting
Ray shooting is the problem of determining the first intersection of a ray with a set of obstacies. We assume that obstacles are modeled as polygons in the plane, or generally polyhedra in higher dimensions. Since many ray shooting queries may be applied to a given set of obstacles, it is desirable to preprocess the obstacles so that query processing is as efficient as possible. The problem of ray shooting in a simple polygon with n vertices haa been studied by [7, 6, 10]. In all cases, with linear space, ray shooting queries can be answered in O(log n) time. Ray shooting amidst a set of polygonal obstacles has been considered by [1, 6, 8, 10, 15]. In all these cases, space is within a polylogarithmic factor of linear, and the best query time is O(fi log n) query time. One of the shortcomings of these approaches is that they fail to account for the geometric structure of the obstacle set and query ray. Analyses based solely upon input size cannot account for the fact that, for a fixed in-
7753820
Approximate Geometric Pattern Matching Under Rigid Motions
We present techniques for matching point-sets in two and three dimensions under rigid-body transformations. We prove bounds on the worst-case performance of these algorithms to be within a small constant factor of optimal and conduct experiments to show that the average performance of these matching algorithms is often better than that predicted by the worst-case bounds.
16007270
Point Probe Decision Trees for Geometric Concept Classes
A fundamental problem in model-based computer vision is that of identifying to which of a given set of concept classes of geometric models an observed model belongs. Considering a “probe” to be an oracle that tells whether or not the observed model is present at a given point in an image, we study the problem of computing efficient strategies (“decision trees”) for probing an image, with the goal to minimize the number of probes necessary (in the worst case) to determine in which class the observed model belongs. We prove a hardness result and give strategies that obtain decision trees whose height is within a log factor of optimal.
37648029
Folding flat silhouettes and wrapping polyhedral packages: New results in computational origami
Abstract We show a remarkable fact about folding paper: from a single rectangular sheet of paper, one can fold it into a flat origami that takes the (scaled) shape of any connected polygonal region, even if it has holes. This resolves a long-standing open problem in origami design. Our proof is constructive, utilizing tools of computational geometry, resulting in efficient algorithms for achieving the target silhouette. We show further that if the paper has a different color on each side, we can form any connected polygonal pattern of two colors. Our results apply also to polyhedral surfaces, showing that any polyhedron can be “wrapped” by folding a strip of paper around it. We give three methods for solving these problems: the first uses a thin strip whose area is arbitrarily close to optimal; the second allows wider strips to be used; and the third varies the strip width to optimize the number or length of visible “seams” subject to some restrictions.
18575731
Classifying the World Anti-Doping Agency's 2005 Prohibited List Using the Chemistry Development Kit Fingerprint
We used the freely available Chemistry Development Kit (CDK) fingerprint to classify 5235 representative molecules taken from ten banned classes in the 2005 World Anti-Doping Agency’s (WADA) prohibited list, including molecules taken from the corresponding activity classes in the MDL Drug Data Report (MDDR). We used both Random Forest and k-Nearest Neighbours (kNN) algorithms to generate classifiers. The kNN classifiers withk = 1 gave a very slightly better Matthews Correlation Coefficient than the Random Forest classifiers; the latter, however, predicted fewer false positives. The performance of kNN classifiers tended to decline with increasing k. The performance of the CDK fingerprint is essentially equivalent to that of Unity 2D. Our results suggest that it will be possible to use freely available chemoinformatics tools to aid the fight against drugs in sport, while minimising the risk of wrongfully penalising innocent athletes.