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Collecting high-quality training data is essential for fine-tuning Large Language Models (LLMs). However, acquiring such data is often costly and time-consuming, especially for non-English languages such as Italian. Recently, researchers…

Large language models (LLMs) can translate natural language into optimization code, but silent failures pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations -- a…

We show a new simple algorithm that checks whether a given higher-order grammar generates a nonempty language of trees. The algorithm amounts to a procedure that transforms a grammar of order n to a grammar of order n-1, preserving…

A finite constraint language $\mathscr{R}$ is a finite set of relations over some finite domain $A$. We show that intractability of the constraint satisfaction problem $\operatorname{CSP}(\mathscr{R})$ can, in all known cases, be replaced…

The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…

We propose a new approach to automated theorem proving where an AlphaZero-style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to…

Large language models (LLMs) are increasingly adapted to downstream tasks via reinforcement learning (RL) methods like Group Relative Policy Optimization (GRPO), which often require thousands of rollouts to learn new tasks. We argue that…

The article surveys some decidability results for DPDAs on infinite words (omega-DPDA). We summarize some recent results on the decidability of the regularity and the equivalence problem for the class of weak omega-DPDAs. Furthermore, we…

Assuring the safety and trustworthiness of autonomous systems is particularly difficult when learning-enabled components and open environments are involved. Formal methods provide strong guarantees but depend on complete models and static…

The automatic generation of computer programs is one of the main applications with practical relevance in the field of evolutionary computation. With program synthesis techniques not only software developers could be supported in their…

Large Language Models (LLMs) exhibit remarkable proficiency in addressing a diverse array of tasks within the Natural Language Processing (NLP) domain, with various prompt design strategies significantly augmenting their capabilities.…

The integration of Formal Verification tools with Large Language Models (LLMs) offers a path to scale software verification beyond manual workflows. However, current methods remain unreliable: without a solid theoretical footing, the…

With the advent of neural language models, the performance of code generation has been significantly boosted. However, the problem of repetitions during the generation process continues to linger. Previous work has primarily focused on…

Large Language Models (LLMs) have demonstrated impressive capabilities across numerous fields, presenting an opportunity to revolutionize optimization problem-solving, a crucial, ubiquitous, and complex domain. This paper explores the…

Let \Gamma be a structure with a finite relational signature and a first-order definition in (R;*,+) with parameters from R, that is, a relational structure over the real numbers where all relations are semi-algebraic sets. In this article,…

Recent advances in large language models (LLMs) for code applications have demonstrated remarkable zero-shot fluency and instruction following on challenging code related tasks ranging from test case generation to self-repair.…

We consider variations on the following problem: given an NFA M and a pattern p, does there exist an x in L(M) such that p matches x? We consider the restricted problem where M only accepts a finite language. We also consider the variation…

Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…

We consider, as a means of making programming languages more flexible and powerful, a parsing algorithm in which the parser may freely modify the grammar while parsing. We are particularly interested in a modification of the canonical LR(1)…

This paper considers program synthesis in the context of computational hardness, asking the question: How hard is it to determine whether a given synthesis problem has a solution or not? To answer this question, this paper studies program…