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We present a new method for inferring complexity properties for a class of programs in the form of flowcharts annotated with loop information. Specifically, our method can (soundly and completely) decide if computed values are polynomially…
Discrete statistical models supported on labelled event trees can be specified using so-called interpolating polynomials which are generalizations of generating functions. These admit a nested representation. A new algorithm exploits the…
We present the Polar framework for fully automating the analysis of classical and probabilistic loops using algebraic reasoning. The central theme in Polar comes with handling algebraic recurrences that precisely capture the loop semantics.…
A C# package is presented that allows a user for an input quantum circuit to generate a set of multivariate polynomials over the finite field Z_2 whose total number of solutions in Z_2 determines the output of the quantum computation…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
Protein retrieval, which targets the deconstruction of the relationship between sequences, structures and functions, empowers the advancing of biology. Basic Local Alignment Search Tool (BLAST), a sequence-similarity-based algorithm, has…
The remarkable growth and significant success of machine learning have expanded its applications into programming languages and program analysis. However, a key challenge in adopting the latest machine learning methods is the representation…
Tokenization is the task of chopping it up into pieces, called tokens, perhaps at the same time throwing away certain characters, such as punctuation. A token is an instance of token a sequence of characters in some particular document that…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We consider private polynomial computation (PPC) over noncolluding coded databases. In such a setting a user wishes to compute a multivariate polynomial of degree at most $g$ over $f$ variables (or messages) stored in multiple databases…
The detailed analysis of molecular structures and properties holds great potential for drug development discovery through machine learning. Developing an emergent property in the model to understand molecules would broaden the horizons for…
We present a neural network verification toolbox to 1) assess the probability of satisfaction of a constraint, and 2) synthesize a set expansion factor to achieve the probability of satisfaction. Specifically, the tool box establishes with…
Providing examples is one of the most common way for end-users to interact with program synthesizers. However, program synthesis systems assume that examples consistent with the program are chosen at random, and do not exploit the fact that…
This paper describes a method to efficiently retrieve protein database sequences similar to a query sequence, while allowing for significant numbers of mutations. We call this method SEQR for SEQuence Retrieval. This approach increases the…
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
The matrix chain problem consists in finding the parenthesization of a matrix product $M := A_1 A_2 \cdots A_n$ that minimizes the number of scalar operations. In practical applications, however, one frequently encounters more complicated…
Context: Experiment replications play a central role in the scientific method. Although software engineering experimentation has matured a great deal, the number of experiment replications is still relatively small. Software engineering…
Humans perform co-saliency detection by first summarizing the consensus knowledge in the whole group and then searching corresponding objects in each image. Previous methods usually lack robustness, scalability, or stability for the first…
A key challenge in example-based program synthesis is the gigantic search space of programs. To address this challenge, various work proposed to use abstract interpretation to prune the search space. However, most of existing approaches…
Efficient characteristic set methods for computing solutions of polynomial equation systems in a finite field are proposed. The concept of proper triangular sets is introduced and an explicit formula for the number of solutions of a proper…