A logic-based approach to program flow analysis

A formalism is presented for tracking assertions which hold universally, i.e., at the end of all the execution paths to a given program point, and assertions which hold existentially, i.e., at the end of some execution paths. In the formalism, the assertions which hold at a given execution path are uniformly defined by an entry environment which contains the assertions which hold when the execution of the program begins and an environment transformer for every program construct. The novel aspect of our formalism is that Horn clauses are used to specify the consistent environments and the meaning of program constructs. The best iterative algorithm (a notion defined by P. Cousot and R. Cousot) for tracking universal and existential assertions simultaneously is given. Conditions are presented under which the best iterative algorithm can be efficiently implemented. The formalism is applied to the pointer equality problem in Pascal. It is shown that universal pointer equalities may be used to reduce the number of superfluous existential equalities, and that existential equalities may be used to obtain more universal equalities. Recent empirical results indicate that tracking the combination of may and must equalities leads to substantial improvements in the result of the analysis. For programs without recursively defined records, the best iterative algorithm can be effectively implemented. These results apply to multiple levels of pointers and can be extended to handle possibly recursive procedures. However, for programs with recursively defined data types further approximations are necessary, e.g., by using a finite graph to model all the possible pointer equalities. For simplicity, this paper does not present an analysis algorithm for this case. Received: 2 September 1991 / 25 June 1997     

Similarity preservation in default logic

The paper identifies a problem in default reasoning in Reiter’s Default Logic and related systems: elements which are similar given the axioms only, become distinguishable in extensions. We explain why, sometimes, this is considered undesirable. Two approaches are presented for guaranteeing similarity preservation: One approach formalizes a way of uniformly applying the defaults to all similar elements by introducing generic extensions, which depend only on similarity types of objects. According to the second approach, for a restricted class of default theories, a default theory is viewed as a “shorthand notation” to what is “really meant” by its formulation. In this approach we propose a rewriting of defaults in a form that guarantees similarity preservation of the modified theory. It turns out that the above two approaches yield the same result. This revised version was published online in June 2006 with corrections to the Cover Date.     

Bounds on the sample complexity for private learning and private data release

Learning is a task that generalizes many of the analyses that are applied to collections of data, in particular, to collections of sensitive individual information. Hence, it is natural to ask what can be learned while preserving individual privacy. Kasiviswanathan et al. (in SIAM J. Comput., 40(3):793–826, 2011) initiated such a discussion. They formalized the notion of private learning, as a combination of PAC learning and differential privacy, and investigated what concept classes can be learned privately. Somewhat surprisingly, they showed that for finite, discrete domains (ignoring time complexity), every PAC learning task could be performed privately with polynomially many labeled examples; in many natural cases this could even be done in polynomial time. While these results seem to equate non-private and private learning, there is still a significant gap: the sample complexity of (non-private) PAC learning is crisply characterized in terms of the VC-dimension of the concept class, whereas this relationship is lost in the constructions of private learners, which exhibit, generally, a higher sample complexity. Looking into this gap, we examine several private learning tasks and give tight bounds on their sample complexity. In particular, we show strong separations between sample complexities of proper and improper private learners (such separation does not exist for non-private learners), and between sample complexities of efficient and inefficient proper private learners. Our results show that VC-dimension is not the right measure for characterizing the sample complexity of proper private learning. We also examine the task of private data release (as initiated by Blum et al. in STOC, pp. 609–618, 2008), and give new lower bounds on the sample complexity. Our results show that the logarithmic dependence on size of the instance space is essential for private data release.     

Reconsideration of polymorphic transformations in cocoa butter using the DSC

Cocoa butter was crystallized in the differential scanning calorimeter (DSC) in the presence and the absence of sorbitan monostearate at different cooling rates. The solidification and fusion curves were recorded. It was found that cooling rate affects enthalpies and temperatures of phase transitions. The very slow cooling rate causes a significant decrease in crystallization enthalpy, suggesting that fractionation of glycerides occurs under these conditions. In the presence of sorbitan monostearate 5%, cooling and heating curves of cocoa butter are sharper, the solidification point is higher and the fusion point is slightly lower. Further, in the presence of sorbitan monostearate both crystallization and fusion enthalpies are lower than in pure cocoa butter. The presence of the emulsifier seems mainly to promote the fractional crystallization. Fusion curves after different periods of isothermal crystallization suggest that higher polymorphic forms differ in chemical composition from lower ones, and that the presence of sorbitan monostearate affects the fractionation in the fat.     

In vivo oxidation of [13C]galactose in patients with galactose-1-phosphate uridyltransferase deficiency

We developed an intravenous and oral [13C]galactose breath test for the in vivo study of galactose metabolism. Following an intravenous bolus of 7 mg/kg of [1-13C]galactose in the fasting state, normal children and adults eliminated 3-6% and 21-47% of the bolus as 13CO2 in expired air collected over 1 and 5 h, respectively. Comparable fractional elimination was seen when the dose was given orally. Patients with galactosemia who have barely detectable or absent galactose-1-phosphate uridyltransferase (GALT) activity in erythrocytes and are homoallelic for the Q188R gene mutation, when given a 7 mg/kg intravenous bolus had barely detectable 13CO2 in air samples in the first hour, but eventually eliminated as much as 3.6% of the dose in 5 h. A galactosemia/Duarte (Q188R/N314D) compound heterozygote and a homozygous Duarte subject, as well as a subject with one normal allele and one Q188R allele, showed normal in vivo oxidation. An assessment of whole body galactose metabolism can be made with this procedure. Further use of this in vivo modality in patients with different genetic backgrounds should increase our understanding of genotype-phenotype relationships in hereditary galactosemia.