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Automated verification of all members of a (potentially infinite) set of programs has the potential to be useful in program synthesis, as well as in verification of dynamically loaded code, concurrent code, and language properties. Existing…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
For large-scale simulation codes with huge and complex code bases, where bit-for-bit comparisons are too restrictive, finding the source of statistically significant discrepancies (e.g., from a previous version, alternative hardware or…
Solving problems through tool use under explicit constraints constitutes a highly challenging yet unavoidable scenario for large language models (LLMs), requiring capabilities such as function calling, instruction following, and…
Probabilistic programming languages (PPLs) are receiving widespread attention for performing Bayesian inference in complex generative models. However, applications to science remain limited because of the impracticability of rewriting…
Large language models (LLMs) have demonstrated remarkable capabilities across diverse tasks. However, the truthfulness of their outputs is not guaranteed, and their tendency toward overconfidence further limits reliability. Uncertainty…
Code large language models (LLMs) enhance programming by understanding and generating code across languages, offering intelligent feedback, bug detection, and code updates through reflection, improving development efficiency and…
We study a novel language model architecture that is capable of scaling test-time computation by implicitly reasoning in latent space. Our model works by iterating a recurrent block, thereby unrolling to arbitrary depth at test-time. This…
Deploying large language models (LLMs) on edge devices is crucial for delivering fast responses and ensuring data privacy. However, the limited storage, weight, and power of edge devices make it difficult to deploy LLM-powered applications.…
Scaling training compute, measured in FLOPs, has long been shown to improve the accuracy of large language models, yet training remains resource-intensive. Prior work shows that increasing test-time compute (TTC)-for example through…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
Automated analysis of recursive derivations in logic programming is known to be a hard problem. Both termination and non-termination are undecidable problems in Turing-complete languages. However, some declarative languages offer a…
Counters that hold natural numbers are ubiquitous in modeling and verifying software systems; for example, they model dynamic creation and use of resources in concurrent programs. Unfortunately, such discrete counters often lead to…
Understanding a program's runtime reasoning behavior, meaning how intermediate states and control flows lead to final execution results, is essential for reliable code generation, debugging, and automated reasoning. Although large language…
Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model…
The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it…
We present a new procedure to infer size bounds for integer programs automatically. Size bounds are important for the deduction of bounds on the runtime complexity or in general, for the resource analysis of programs. We show that our…
This paper extends prior work on the connections between logics from finite model theory and propositional/algebraic proof systems. We show that if all non-isomorphic graphs in a given graph class can be distinguished in the logic…
It is well-known, and often a topic of heated debates, that programs in some programming languages are more concise than in others. This is a relevant factor when comparing or aggregating volume-impacted metrics on source code written in a…