Related papers: Inferring Lower Runtime Bounds for Integer Program…

Recursive list decoding is considered for Reed-Muller (RM) codes. The algorithm repeatedly relegates itself to the shorter RM codes by recalculating the posterior probabilities of their symbols. Intermediate decodings are only performed…

Large language models (LLMs) have demonstrated strong performance on coding tasks such as generation, completion and repair, but their ability to handle complex symbolic reasoning over code still remains underexplored. We introduce the task…

Neural code intelligence (CI) models are opaque black-boxes and offer little insight on the features they use in making predictions. This opacity may lead to distrust in their prediction and hamper their wider adoption in safety-critical…

We study the problem of programmatic reinforcement learning, in which policies are represented as short programs in a symbolic language. Programmatic policies can be more interpretable, generalizable, and amenable to formal verification…

We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…

One of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation…

Time complexity in rewriting is naturally understood as the number of steps needed to reduce terms to normal forms. Establishing complexity bounds to this measure is a well-known problem in the rewriting community. A vast majority of…

We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…

We consider the problem of inference in higher-order undirected graphical models with binary labels. We formulate this problem as a binary polynomial optimization problem and propose several linear programming relaxations for it. We compare…

For any pair $(X,Z)$ of correlated random variables we can think of $Z$ as a randomized function of $X$. Provided that $Z$ is short, one can make this function computationally efficient by allowing it to be only approximately correct. In…

We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…

We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…

We propose a new method for proving lower bounds on quantum query algorithms. Instead of a classical adversary that runs the algorithm with one input and then modifies the input, we use a quantum adversary that runs the algorithm with a…

In many sequence learning tasks, such as program synthesis and document summarization, a key problem is searching over a large space of possible output sequences. We propose to learn representations of the outputs that are specifically…

With the advancement of large language models (LLMs), solving complex reasoning tasks has gained increasing attention. Inference-time computation methods (e.g., Best-of-N, beam search, et al.) are particularly valuable as they can enhance…

The inference-time resource costs of large language and vision models present a growing challenge in production deployments. We propose the use of foundation model programs, i.e., programs that can invoke foundation models with varying…

We propose an automated verification technique for hypersafety properties, which express sets of valid interrelations between multiple finite runs of a program. The key observation is that constructing a proof for a small representative set…

The safety of our day-to-day life depends crucially on the correct functioning of embedded software systems which control the functioning of more and more technical devices. Many of these software systems are time-critical. Hence,…

Memory corruption is a serious class of software vulnerabilities, which requires careful attention to be detected and removed from applications before getting exploited and harming the system users. Symbolic execution is a well-known method…

A first step towards more reliable software is to execute each statement and each control-flow path in a method once. In this paper, we present a formal method to automatically compute test cases for this purpose based on the idea of a…