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We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Scaling large language models (LLMs) has driven significant advancements, yet it faces diminishing returns and escalating energy demands. This work explores how test-time compute (TTC) can serve as an energy-efficient complement to…
Neural reasoners such as Tiny Recursive Models (TRMs) solve complex problems by combining neural backbones with specialized inference schemes. Such inference schemes have been a central component of stochastic reasoning systems, where…
Large language models (LLMs) open up new horizons for sequential recommendations, owing to their remarkable language comprehension and generation capabilities. However, there are still numerous challenges that should be addressed to…
The compactness lemma in programming language theory states that any recursive function can be simulated by a finite unrolling of the function. One important use case it has is in the logical relations proof technique for proving properties…
Large Language Models (LLMs) have become increasingly capable of handling diverse tasks with the aid of well-crafted prompts and integration of external tools, but as task complexity rises, the workflow involving LLMs can be complicated and…
In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…
Enhancing the adaptive capabilities of large language models is a critical pursuit in both research and application. Traditional fine-tuning methods require substantial data and computational resources, especially for enhancing specific…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
To take full advantage of a specific hardware target, performance engineers need to gain control on compilers in order to leverage their domain knowledge about the program and hardware. Yet, modern compilers are poorly controlled, usually…
The cooperative Multi-A gent R einforcement Learning (MARL) with permutation invariant agents framework has achieved tremendous empirical successes in real-world applications. Unfortunately, the theoretical understanding of this MARL…
This paper establishes relative expressiveness results for several modal mu-calculi interpreted over timed automata. These mu-calculi combine modalities for expressing passage of (real) time with a general framework for defining formulas…
The ability of generative large language models (LLMs) to perform in-context learning has given rise to a large body of research into how best to prompt models for various natural language processing tasks. Machine Translation (MT) has been…
User defined recursive types are a fundamental feature of modern functional programming languages like Haskell, Clean, and the ML family of languages. Properties of programs defined by recursion on the structure of recursive types are…
For recursive functions general principles of induction needs to be applied. Instead of verifying them directly using the Vienna Development Method Specification Language (VDM-SL), we suggest a translation to Isabelle/HOL. In this paper,…
Although Multi-Agent Reinforcement Learning (MARL) is effective for complex multi-robot tasks, it suffers from low sample efficiency and requires iterative manual reward tuning. Large Language Models (LLMs) have shown promise in…
Although, many scientists and engineers use Octave or MATLAB as their preferred programming language, dynamic nature of these languages can lead to slower running-time of programs written in these languages compared to programs written in…
Formally reasoning about functional programs is supposed to be straightforward and elegant, however, it is not typically done as a matter of course. Reasoning in a proof assistant requires "reimplementing" the code in those tools, which is…
In Chapter 3 of his Notes on constructive mathematics, Martin-L{\"o}f describes recursively constructed ordinals. He gives a constructively acceptable version of Kleene's computable ordinals. In fact, the Turing definition of computable…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…