10533033
On the Sequential Nature of Unification
Abstract The problem of unification of terms is log-space complete for P. In deriving this lower bound no use is made of the potentially concise representation of terms by directed acyclic graphs. In addition, the problem remains complete even if infinite substitutions are allowed. A consequence of this result is that parallelism cannot significantly improve on the best sequential solutions for unification. However, we show that for the problem of term matching, an important subcase of unification, there is a good parallel algorithm using O ( log 2 n ) time and n O(1) processors on a PRAM. For the O ( log 2 n ) parallel time upper bound we assume that the terms are represented by directed acyclic graphs; if the longer string representation is used we obtain an O ( log n ) parallel time bound.
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
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.
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.
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.
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...
11557966
An algorithmic study of manufacturing paperclips and other folded structures
We study algorithmic aspects of bending wires and sheet metal into a specified structure. Problems of this type are closely related to the question of deciding whether a simple non-self-intersecting wire structure (a carpenter's ruler) can be straightened, a problem that was open for several years and has only recently been solved in the affirmative. If we impose some of the constraints that are imposed by the manufacturing process, we obtain quite different results. In particular, we study the variant of the carpenter's ruler problem in which there is a restriction that only one joint can be modified at a time. For a linkage that does not self-intersect or self-touch, the recent results of Connelly et al. and Streinu imply that it can always be straightened, modifying one joint at a time. However, we show that for a linkage with even a single vertex degeneracy, it becomes NP-hard to decide if it can be straightened while altering only one joint at a time. If we add the restriction that each joint can be altered at most once, we show that the problem is NP-complete even without vertex degeneracies. In the special case, arising in wire forming manufacturing, that each joint can be altered at most once, and must be done sequentially from one or both ends of the linkage, we give an efficient algorithm to determine if a linkage can be straightened.
992845
The Lazy Sweep Ray Casting Algorithm for Rendering Irregular Grids
Lazy sweep ray casting is a fast algorithm for rendering general irregular grids. It is based on the sweep-plane paradigm, and it is able to accelerate ray casting for rendering irregular grids, including disconnected and nonconvex unstructured irregular grids (even with holes) with a rendering cost that decreases as the "disconnectedness" decreases. The algorithm is carefully tailored to exploit spatial coherence even if the image resolution differs substantially from the object space resolution. Lazy sweep ray casting has several desirable properties, including its generality, (depth-sorting) accuracy, low memory consumption, speed, simplicity of implementation and portability (e.g. no hardware dependencies). We establish the practicality of our method through experimental results based on our implementation, which is shown to be substantially faster (by up to two orders of magnitude) than other algorithms implemented in software. We also provide theoretical results, both lower and upper bounds, on the complexity of ray casting of irregular grids.
12359075
Geometric knapsack problems
We study a variety of geometric versions of the classical knapsack problem. In particular, we consider the following “fence enclosure” problem: given a setS ofn points in the plane with valuesvi ≥ 0, we wish to enclose a subset of the points with a fence (a simple closed curve) in order to maximize the “value” of the enclosure. The value of the enclosure is defined to be the sum of the values of the enclosed points minus the cost of the fence. We consider various versions of the problem, such as allowingS to consist of points and/or simple polygons. Other versions of the problems are obtained by restricting the total amount of fence available and also allowing the enclosure to consist of at mostM connected components. When there is an upper bound on the length of fence available, we show that the problem is NP-complete. We also provide polynomial-time algorithms for many versions of the fence problem when an unrestricted amount of fence is available.
16824358
On Minimum-Area Hulls
Abstract. We study some minimum-area hull problems that generalize the notion of convex hull to star-shaped and monotone hulls. Specifically, we consider the minimum-area star-shaped hull problem: Given an n -vertex simple polygon P , find a minimum-area, star-shaped polygon P* containing P . This problem arises in lattice packings of translates of multiple, nonidentical shapes in material layout problems (e.g., in clothing manufacture), and has been recently posed by Daniels and Milenkovic. We consider two versions of the problem: the restricted version, in which the vertices of P* are constrained to be vertices of P , and the unrestricted version, in which the vertices of P* can be anywhere in the plane. We prove that the restricted problem falls in the class of ``3sum-hard'' (sometimes called ``n2 -hard'') problems, which are suspected to admit no solutions in o(n2) time. Further, we give an O(n2) time algorithm, improving the previous bound of O(n5) . We also show that the unrestricted problem can be solved in O(n2 p(n)) time, where p(n) is the time needed to find the roots of two equations in two unknowns, each a polynomial of degree O(n) . We also consider the case in which P* is required to be monotone, with respect to an unspecified direction; we refer to this as the minimum-area monotone hull problem. We give a matching lower and upper bound of Θ(n log n) time for computing P* in the restricted version, and an upper bound of O(n q(n)) time in the unrestricted version, where q(n) is the time needed to find the roots of two polynomial equations in two unknowns with degrees 2 and O(n) .
20253449
Approximating Polygons and Subdivisions with Minimum Link Paths
We study several variations on one basic approach to the task of simplifying a plane polygon or subdivision: Fatten the given object and construct an approximation inside the fattened region. We investigate fattening by convolving the segments or vertices with disks and attempt to approximate objects with the minimum number of line segments, or with near the minimum, by using efficient greedy algorithms. We give some variants that have linear or O(n log n) algorithms approximating polygonal chains of n segments. We also show that approximating subdivisions and approximating with chains with. no self-intersections are NP-hard.