415,929 research outputs found
The Algebraic Intersection Type Unification Problem
The algebraic intersection type unification problem is an important component
in proof search related to several natural decision problems in intersection
type systems. It is unknown and remains open whether the algebraic intersection
type unification problem is decidable. We give the first nontrivial lower bound
for the problem by showing (our main result) that it is exponential time hard.
Furthermore, we show that this holds even under rank 1 solutions (substitutions
whose codomains are restricted to contain rank 1 types). In addition, we
provide a fixed-parameter intractability result for intersection type matching
(one-sided unification), which is known to be NP-complete.
We place the algebraic intersection type unification problem in the context
of unification theory. The equational theory of intersection types can be
presented as an algebraic theory with an ACI (associative, commutative, and
idempotent) operator (intersection type) combined with distributivity
properties with respect to a second operator (function type). Although the
problem is algebraically natural and interesting, it appears to occupy a
hitherto unstudied place in the theory of unification, and our investigation of
the problem suggests that new methods are required to understand the problem.
Thus, for the lower bound proof, we were not able to reduce from known results
in ACI-unification theory and use game-theoretic methods for two-player tiling
games
Linear Rank Intersection Types
Non-idempotent intersection types provide quantitative information about typed programs, and have been used to obtain time and space complexity measures. Intersection type systems characterize termination, so restrictions need to be made in order to make typability decidable. One such restriction consists in using a notion of finite rank for the idempotent intersection types. In this work, we define a new notion of rank for the non-idempotent intersection types. We then define a novel type system and a type inference algorithm for the ?-calculus, using the new notion of rank 2. In the second part of this work, we extend the type system and the type inference algorithm to use the quantitative properties of the non-idempotent intersection types to infer quantitative information related to resource usage
The Intersection Type Unification Problem
The intersection type unification problem is an important component in
proof search related to several natural decision problems in
intersection type systems. It is unknown and remains open whether the
unification problem is decidable. We give the first nontrivial lower
bound for the problem by showing (our main result) that it is
exponential time hard. Furthermore, we show that this holds even under
rank 1 solutions (substitutions whose codomains are restricted to
contain rank 1 types). In addition, we provide a fixed-parameter
intractability result for intersection type matching (one-sided
unification), which is known to be NP-complete.
We place the intersection type unification problem in the context of
unification theory. The equational theory of intersection types can
be presented as an algebraic theory with an ACI (associative,
commutative, and idempotent) operator (intersection type) combined
with distributivity properties with respect to a second operator
(function type). Although the problem is algebraically natural and
interesting, it appears to occupy a hitherto unstudied place in the
theory of unification, and our investigation of the problem suggests
that new methods are required to understand the problem. Thus, for the
lower bound proof, we were not able to reduce from known results in
ACI-unification theory and use game-theoretic methods for two-player
tiling games
GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces
We present a detailed study of the generalized hypergeometric system
introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in
the context of toric geometry. GKZ systems arise naturally in the moduli theory
of Calabi-Yau toric varieties, and play an important role in applications of
the mirror symmetry. We find that the Gr\"obner basis for the so-called toric
ideal determines a finite set of differential operators for the local solutions
of the GKZ system. At the special point called the large radius limit, we find
a close relationship between the principal parts of the operators in the GKZ
system and the intersection ring of a toric variety. As applications, we
analyze general three dimensional hypersurfaces of Fermat and non-Fermat types
with Hodge numbers up to . We also find and analyze several non
Landau-Ginzburg models which are related to singular models.Comment: 55 pages, 3 Postscript figures, harvma
Row and Bounded Polymorphism via Disjoint Polymorphism
Polymorphism and subtyping are important features in mainstream OO languages. The most common way to integrate the two is via ?_{< :} style bounded quantification. A closely related mechanism is row polymorphism, which provides an alternative to subtyping, while still enabling many of the same applications. Yet another approach is to have type systems with intersection types and polymorphism. A recent addition to this design space are calculi with disjoint intersection types and disjoint polymorphism. With all these alternatives it is natural to wonder how they are related.
This paper provides an answer to this question. We show that disjoint polymorphism can recover forms of both row polymorphism and bounded polymorphism, while retaining key desirable properties, such as type-safety and decidability. Furthermore, we identify the extra power of disjoint polymorphism which enables additional features that cannot be easily encoded in calculi with row polymorphism or bounded quantification alone. Ultimately we expect that our work is useful to inform language designers about the expressive power of those common features, and to simplify implementations and metatheory of feature-rich languages with polymorphism and subtyping
Vehicle-Infrastructure Cooperative Systems for Intersection Collision Avoidance: Driver Assessment Challenges
According to National Highway Traffic Safety Administration (NHTSA, 1998) data, there were 37,280 crashes that involved fatalities in 1997. Of these crashes, 8,571 were related to intersections. The fatal crashes at intersection were about evenly divided among noncontrolled intersections, signal controlled intersections, and stop sign controlled intersection. In addition to fatal crashes, almost 1 million injury crashes occur at intersections annually, and there are about 1.7 million police reported crashes at intersection each year. Various programs have proposed alternative countermeasures to reduce the number of crashes and fatalities at intersections. Conventional countermeasures such as protected left turn signals are effective and fairly well understood. However, these countermeasures alone will not eliminate intersection crashes because they do not address factors such as willful and unintentional red-light and stop sign violations, gap acceptance problems associated with older drivers, and sight distance problems at intersections that may not warrant traffic signals. The Federal Highway Administration is pursuing infrastructure based ITS solutions to address crashes at intersections. Initially these solutions will not require changes to vehicles. It is anticipated that in the future, some of these solutions could be integrated into in-vehicle ITS systems to enable either in-vehicle warnings or automated crash avoidance systems. Four types of intersection-infrastructure systems are envision: (1) traffic signal violation warning, (2) stop sign violation warning, (3) traffic signal left turn assistances, and (4) stop sign movement assistance. Each of these systems is described briefly, and a preliminary list of the driver behavior issues associated with each is identified. The challenge for the design of these systems is similar to that for other areas of highway and vehicle design – how to assess driver performance and behavior with these systems before the systems are fielded. Various assessment techniques are discussed in association with the advantages and disadvantages of each. The FHWA human-centered research approach for intersection-infrastructure solutions is presented
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