460 research outputs found
Reasoning about Cardinal Directions between Extended Objects
Direction relations between extended spatial objects are important
commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model,
known as Cardinal Direction Calculus (CDC), for representing direction
relations between connected plane regions. CDC is perhaps the most expressive
qualitative calculus for directional information, and has attracted increasing
interest from areas such as artificial intelligence, geographical information
science, and image retrieval. Given a network of CDC constraints, the
consistency problem is deciding if the network is realizable by connected
regions in the real plane. This paper provides a cubic algorithm for checking
consistency of basic CDC constraint networks, and proves that reasoning with
CDC is in general an NP-Complete problem. For a consistent network of basic CDC
constraints, our algorithm also returns a 'canonical' solution in cubic time.
This cubic algorithm is also adapted to cope with cardinal directions between
possibly disconnected regions, in which case currently the best algorithm is of
time complexity O(n^5)
A very brief introduction to quantum computing and quantum information theory for mathematicians
This is a very brief introduction to quantum computing and quantum
information theory, primarily aimed at geometers. Beyond basic definitions and
examples, I emphasize aspects of interest to geometers, especially connections
with asymptotic representation theory. Proofs of most statements can be found
in standard references
Total Representations
Almost all representations considered in computable analysis are partial. We
provide arguments in favor of total representations (by elements of the Baire
space). Total representations make the well known analogy between numberings
and representations closer, unify some terminology, simplify some technical
details, suggest interesting open questions and new invariants of topological
spaces relevant to computable analysis.Comment: 30 page
Approximating values of generalized-reachability stochastic games
Simple stochastic games are turn-based 2½-player games with a reachability objective. The basic question asks whether one player can ensure reaching a given target with at least a given probability. A natural extension is games with a conjunction of such conditions as objective. Despite a plethora of recent results on the analysis of systems with multiple objectives, the decidability of this basic problem remains open. In this paper, we present an algorithm approximating the Pareto frontier of the achievable values to a given precision. Moreover, it is an anytime algorithm, meaning it can be stopped at any time returning the current approximation and its error bound
Robust Coin Flipping
Alice seeks an information-theoretically secure source of private random
data. Unfortunately, she lacks a personal source and must use remote sources
controlled by other parties. Alice wants to simulate a coin flip of specified
bias , as a function of data she receives from sources; she seeks
privacy from any coalition of of them. We show: If , the
bias can be any rational number and nothing else; if , the bias
can be any algebraic number and nothing else. The proof uses projective
varieties, convex geometry, and the probabilistic method. Our results improve
on those laid out by Yao, who asserts one direction of the case in his
seminal paper [Yao82]. We also provide an application to secure multiparty
computation.Comment: 22 pages, 1 figur
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