Let P be a simple polygon. We define a witness set W to be a set of points such that if any (prospective) guard set G guards W , then it is guaranteed that G guards P . We show that not all polygons admit a finite witness set. If a finite minimal witness set exists, then it cannot contain any witness in the interior of P ; all witnesses must lie on the boundary of P , and there can be at most o...

Abstract interpretation-based proof carrying code uses postfixpoints of abstract interpretations to witness that a program respects a safety policy. Some witnesses carry more information than needed and are therefore unnecessarily large. We introduce a notion of size of a witness and propose techniques for reducing the size of such certificates. For distributive analyses, we show that a smalles...

Given a set C of binary n-tuples and c ∈ C, how many bits of c suffice to distinguish it from the other elements in C ? We shed new light on this old combinatorial problem and improve on previously known bounds.

The studies apply a Bayesian source credibility model to a legal setting to test epistemic influence of witness testimonies. The model amalgamates perceived witness trustworthiness and access to accurate information as independent elements that describe and predict the impact of the testimony of that particular witness. Across two studies, the model enjoys a good fit with observed posterior rat...

The dilution effect occurs when the introduction of nondiagnostic information lessens the impact on reasoning of diagnostic information despite having no relevance to the hypothesis in question. While the effect has been reproduced in several studies, the psychological basis of the effect remains unclear. Some believe it to be conversational while others believe it to be cognitive and social. T...

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

We propose a new cryptographic primitive called witness pseudorandom functions (witness PRFs). Witness PRFs are related to witness encryption, but appear strictly stronger: we show that witness PRFs can be used for applications such as multi-party key exchange without trsuted setup, polynomially-many hardcore bits for any one-way function, and several others that were previously only possible u...