12005506
Kripke-Style Models for Typed lambda Calculus
The semantics of typed lambda calculus is usually described using Henkin models, consisting of functions over some collection of sets, or concrete cartesian closed categories, which are essentially equivalent. We describe a more general class of Kripte-style models. In categorical terms, our Kripke lambda models are cartesian closed subcategories of the presheaves over a poset. While the traditional lambda calculus proof system is not complete for Henkin models that may have empty types, we prove strong completeness for Kripke models. In fact, every set of equations that is closed under implication is the theory of a single Kripke model. We develop some properties of logical relations over Kripke structures, showing that every theory if the theory of a model determined by a Kripke equivalence relation over a Henkin model
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...
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.
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.
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.
16356321
Decision trees for geometric models
A fundamental problem in model-based computer vision is that ofidentifying which of a given set of geometric models is present in animage. Considering a “probe” to be an oracle that tells uswhether or not a model is present at a given point, we study the problemof computing efficient strategies (“decision trees”) forprobing an image, with the goal to minimize the number of probesnecessary (in the worst case) to determine which single model ispresent. We show that a <inline-equation><f><fen lp="ceil">lgk<rp post="ceil"></fen></f></inline-equation> height binary decision tree always exists for<?Pub Fmt italic>k<?Pub Fmt /italic> polygonal models (in fixedposition), provided (1) they are non-degenerate (do not shareboundaries) and (2) they share a common point of intersection. Further,we give an efficient algorithm for  constructing such decision treeswhen the models are given as a set of polygons in the plane. We showthat constructing a minimum height tree is NP-complete if either of thetwo assumptions is omitted. We provide an efficient greedy heuristicstrategy and show that, in the general case, it yields a decision treewhose height is at most <inline-equation><f><fen lp="ceil">lgn<rp post="ceil"></fen></f><?Pub Caret></inline-equation> times that of an optimal tree. Finally,we discuss some restricted cases whose special structure allows forimproved results.
24130262
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 set S of n points in the plane with values v i ≥ 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 allowing S 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 up to K connected components. When there is an upper bound on the length of fence available, we show that the problem is N P-complete. Additionally we provide polynomial-time algorithms for many versions of the fence problem when an unrestricted amount of fence is available.
42803318
File Servers
This chapter discusses file servers that are accessible via some form of local network or internetwork. It characterizes file services from the client point of view along a number of dimensions; distributivity of the service itself, the network environment of the service, the file model supported by the service, the kind(s) of atomic update provided by the service, the techniques used for controlling the allocation of files. It then describes the client interfaces to three existing file services. Finally, the impact of these features on design and implementation is discussed. An appendix contains characterizations of a variety of existing network-based file services using the criteria developed in the chapter.
8247618
An efficiently computable metric for comparing polygonal shapes
Abstract : Model-based recognition is concerned with comparing a shape A, which is stored as a model for some particular object, with a shape B, which is found to exist in an image. If A and B are close to being the same shape, then a vision system should report a match and return a measure of how good that match is. To be useful this measure should satisfy a number of properties, including: (1) it should be a metric, (2) it should be invariant under translation, rotation, and change-of-scale, (3) it should be reasonably easy to compute, and (4) it should match our intuition (i.e., answers should be similar to those that a person might give). We develop a method for comparing polygons that has these properties. The method works for both convex and nonconvex polygons and runs in time O(mn log mn) where m is the number of vertices in one polygon and n is the number of vertices in the other. Some examples are presented that show the method produces answers that are intuitively reasonable.