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Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in…
We study the existence of polynomial kernels for the problem of deciding feasibility of integer linear programs (ILPs), and for finding good solutions for covering and packing ILPs. Our main results are as follows: First, we show that the…
Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and…
Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly…
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
Runtime efficiency and termination are crucial properties in the studies of program verification. Instead of dealing with these issues in an ad hoc manner, it would be useful to develop a robust framework in which such properties are…
We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…
Program verification offers a framework for ensuring program correctness and therefore systematically eliminating different classes of bugs. Inferring loop invariants is one of the main challenges behind automated verification of real-world…
In this work, we consider adaptive linear programming (ALP) decoding of linear codes over the finite field $\mathbb{F}_p$ of size $p$ where $p$ is a prime. In particular, we provide a general construction of valid inequalities for the…
We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…
Behavioral synthesis involves compiling an Electronic System-Level (ESL) design into its Register-Transfer Level (RTL) implementation. Loop pipelining is one of the most critical and complex transformations employed in behavioral synthesis.…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
Because loops execute their body many times, compiler developers place much emphasis on their optimization. Nevertheless, in view of highly diverse source code and hardware, compilers still struggle to produce optimal target code. The sheer…
The rise of large language models (LLMs) has sparked interest in coding assistants. While general-purpose programming languages are well supported, generating code for domain-specific languages remains a challenging problem for LLMs. In…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
In this paper, we investigate the verification of quantized Graph Neural Networks (GNNs), where some fixed-width arithmetic is used to represent numbers. We introduce the linear-constrained validity (LVP) problem for verifying GNNs…
Automatic parallelization remains a challenging problem in software engineering, particularly in identifying code regions where loops can be safely executed in parallel on modern multi-core architectures. Traditional static analysis…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties. In this work, we show that any low complexity affine-invariant property of…