Related papers: Underapproximation of Procedure Summaries for Inte…
We consider functions mapping non-negative integers to non-negative real numbers such that a and a+n are mapped to values at least 1/n apart. In this paper we use a novel method to construct such a function. We conjecture that the supremum…
Abstractive summarization has been studied using neural sequence transduction methods with datasets of large, paired document-summary examples. However, such datasets are rare and the models trained from them do not generalize to other…
Trace slicing is a widely used technique for execution trace analysis that is effectively used in program debugging, analysis and comprehension. In this paper, we present a backward trace slicing technique that can be used for the analysis…
Elementary function calls are a common feature in numerical programs. While their implementions in library functions are highly optimized, their computation is nonetheless very expensive compared to plain arithmetic. Full accuracy is,…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
We present a randomized approximation scheme for the permanent of a matrix with nonnegative entries. Our scheme extends a recursive rejection sampling method of Huber and Law (SODA 2008) by replacing the upper bound for the permanent with a…
The aim of a probabilistic resource analysis is to derive a probability distribution of possible resource usage for a program from a probability distribution of its input. We present an automated multi- phase rewriting based method to…
In order to meet the precision requirements for the LHC and future colliders, next-to-next-to-leading order corrections to a wide range of processes are essential, making general automated tools highly desirable. Extending the strategy of…
There exist several approaches to infer runtime or resource bounds for integer programs automatically. In this paper, we study the subclass of periodic rational solvable loops (prs-loops), where questions regarding the runtime and the size…
Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…
Generating a readable summary that describes the functionality of a program is known as source code summarization. In this task, learning code representation by modeling the pairwise relationship between code tokens to capture their…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information…
We study termination time and recurrence time in programs with unbounded recursion, which are either randomized or operate on some statistically quantified inputs. As the underlying formal model for such programs we use probabilistic…
We propose an abstraction-based model checking method which relies on refinement of an under-approximation of the feasible behaviors of the system under analysis. The method preserves errors to safety properties, since all analyzed…
We propose a new approach to compute an interval over-approximation of the finite time reachable set for a large class of nonlinear systems. This approach relies on the notions of sensitivity matrices, which are the partial derivatives…
We describe some "unrestricted" algorithms which are useful for the computation of elementary and special functions when the precision required is not known in advance. Several general classes of algorithms are identified and illustrated by…
In this paper we show that the lengths of the approximating processes in epsilon substitution method are calculable by ordinal recursions in an optimal way.
An increasing sequence $(x_i)_{i=1}^n$ of positive integers is an $n$-term Egyptian underapproximation of $\theta \in (0,1]$ if $\sum_{i=1}^n \frac{1}{x_i} < \theta$. A greedy algorithm constructs an $n$-term underapproximation of $\theta$.…
Neural abstractive summarization has been widely studied and achieved great success with large-scale corpora. However, the considerable cost of annotating data motivates the need for learning strategies under low-resource settings. In this…