Proving acceptability properties of relaxed nondeterministic approximate programs

Approximate program transformations such as skipping tasks [29, 30], loop perforation [21, 22, 35], reduction sampling [38], multiple selectable implementations [3, 4, 16, 38], dynamic knobs [16], synchronization elimination [20, 32], approximate function memoization [11],and approximate data types [34] produce programs that can execute at a variety of points in an underlying performance versus accuracy tradeoff space. These transformed programs have the ability to trade accuracy of their results for increased performance by dynamically and nondeterministically modifying variables that control their execution. We call such transformed programs relaxed programs because they have been extended with additional nondeterminism to relax their semantics and enable greater flexibility in their execution. We present language constructs for developing and specifying relaxed programs. We also present proof rules for reasoning about properties [28] which the program must satisfy to be acceptable. Our proof rules work with two kinds of acceptability properties: acceptability properties [28], which characterize desired relationships between the values of variables in the original and relaxed programs, and unary acceptability properties, which involve values only from a single (original or relaxed) program. The proof rules support a staged reasoning approach in which the majority of the reasoning effort works with the original program. Exploiting the common structure that the original and relaxed programs share, relational reasoning transfers reasoning effort from the original program to prove properties of the relaxed program. We have formalized the dynamic semantics of our target programming language and the proof rules in Coq and verified that the proof rules are sound with respect to the dynamic semantics. Our Coq implementation enables developers to obtain fully machine-checked verifications of their relaxed programs.National Science Foundation (U.S.). (Grant number CCF-0811397)National Science Foundation (U.S.). (Grant number CCF-0905244)National Science Foundation (U.S.). (Grant number CCF-1036241)National Science Foundation (U.S.). (Grant number IIS-0835652)United States. Defense Advanced Research Projects Agency (Grant number FA8650-11-C-7192)United States. Defense Advanced Research Projects Agency (Grant number FA8750-12-2-0110)United States. Dept. of Energy. (Grant Number DE-SC0005288

Targeted Automatic Integer Overflow Discovery Using Goal-Directed Conditional Branch Enforcement

We present a new technique and system, DIODE, for auto- matically generating inputs that trigger overflows at memory allocation sites. DIODE is designed to identify relevant sanity checks that inputs must satisfy to trigger overflows at target memory allocation sites, then generate inputs that satisfy these sanity checks to successfully trigger the overflow. DIODE works with off-the-shelf, production x86 binaries. Our results show that, for our benchmark set of applications, and for every target memory allocation site exercised by our seed inputs (which the applications process correctly with no overflows), either 1) DIODE is able to generate an input that triggers an overflow at that site or 2) there is no input that would trigger an overflow for the observed target expression at that site.United States. Defense Advanced Research Projects Agency (Grant FA8650-11-C-7192

Index Mapping for Fibers with Symmetric and Asymmetric Refractive Index Profiles

The application of phase imaging to refractive index profiling of an optical fiber slice is described. It is shown that the refractive index profile of axially symmetric and asymmetric optical fibers can be obtained from quantitative phase image of thin transverse optical fiber slices. Although this method requires careful and time consuming sample preparation, one advantage of this technique is that it can be applied to a wide range of optical fibers. In this paper results for both symmetric and non-symmetric fibers are presented and good agreement with the industrystandard refracted near-field technique demonstrated