18008261
Optimization Complexity of Linear Logic Proof Games
A class of linear logic proof games is developed, each with a numeric score that depends on the number of preferred axioms used in a complete or partial proof tree. The complexity of these games is analyzed for the NP-complete multiplicative fragment (MLL) extended with additive constants and the PSPACE-complete multiplicative, additive fragment (MALL) of propositional linear logic. In each case, it is shown that it is as hard to compute an approximation of the best possible score as it is to determine the optimal strategy. Furthermore, it is shown that no efficient heuristics exist unless there is an unexpected collapse in the complexity hierarchy.
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.
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
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.
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...
1174606
Optimal covering tours with turn costs
We give the first algorithmic study of a class of “covering tour” problems related to the geometric Traveling Salesman Problem: Find a polygonal tour for a cutter so that it sweeps out a specified region (“pocket”), in order to minimize a cost that depends not only on the length of the tour but also on the number of turns. These problems arise naturally in manufacturing applications of computational geometry to automatic tool path generation and automatic inspection systems, as well as arc routing (“postman”) problems with turn penalties. We prove lower bounds (NP-completeness of minimum-turn milling) and give efficient approximation algorithms for several natural versions of the problem, including a polynomial-time approximation scheme based on a novel adaptation of the m-guillotine method.
16064699
Minimum-link watchman tours
We consider the problem of computing a watchman route in a polygon with holes. We show that the problem of finding a minimum-link watchman route is NP-complete, even if the holes are all convex. The proof is based on showing that the related problem of finding a minimum-link tour on a set of points in the plane is NP-complete. We provide a provably good approximation algorithm that achieves an approximation factor of O(log n ).
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.
9802380
Generating Random Polygons with Given Vertices
Abstract The problem of generating “random” geometric objects is motivated by the need to generate test instances for geometric algorithms. We examine the specific problem of generating a random x-monotone polygon on a given set of n vertices. Here, “random” is taken to mean that we select uniformly at random a polygon, from among all those x-monotone polygons having the given n vertices. We give an algorithm that generates a random monotone polygon in O(n) time and space after O(K) preprocessing time, where n
8879002
Status of clinical gene sequencing data reporting and associated risks for information loss
Clinical gene sequencing is growing in importance and cost-effectiveness. In the past two years, the number of genes associated with disease has grown by roughly 25%. Knowledge of genetic variations will soon guide drug selection and dosages, predict risks from toxin exposures, and inform nutritional needs. Despite the significance of sequencing, methods for reporting results are problematic. Frequent use of paper and infrequent use of naming standards impede data exchange and make incorporation into the electronic medical record difficult. Reports often describe only variations found, rather than all data (all patient bases sequenced). Also, reports frequently do not describe reference data used to define variations. These practices create risks for loss of both data and information. Standardized electronic reporting of all data (all bases sequenced and all reference data) and electronic record systems capable of storing these results would both prevent data loss and simplify the preservation of information those data provide.