Related papers: The computability path ordering
In [arXiv:1006.4939] the enumeration order reducibility is defined on natural numbers. For a c.e. set A, [A] denoted the class of all subsets of natural numbers which are co-order with A. In definition 5 we redefine co-ordering for rational…
Proof theory provides a foundation for studying and reasoning about programming languages, most directly based on the well-known Curry-Howard isomorphism between intuitionistic logic and the typed lambda-calculus. More recently, a…
Machine unlearning has gained increasing attention in recent years, as a promising technique to selectively remove unwanted privacy or copyrighted information from Large Language Models that are trained on a massive scale of human data.…
Ranking systems used in decision-support settings should not only order candidates but also expose evidence that can be independently checked. We study evidence-certified candidate ranking: given an intent_id, a predefined plan skeleton, a…
Data-driven approaches to predict-then-optimize decision-making problems seek to mitigate the risk of uncertainty region misspecification in safety-critical settings. Current approaches, however, suffer from considering overly conservative…
Direct Preference Optimization (DPO) often struggles with long-chain mathematical reasoning. Existing approaches, such as Step-DPO, typically improve this by focusing on the first erroneous step in the reasoning chain. However, they…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
The univalence axiom expresses the principle of extensionality for dependent type theory. However, if we simply add the univalence axiom to type theory, then we lose the property of canonicity - that every closed term computes to a…
Automatic prompt optimization has recently emerged as a strategy for improving the quality of prompts used in Large Language Models (LLMs), with the goal of generating more accurate and useful responses. However, most prior work focuses on…
Large reasoning models have achieved remarkable performance through extended chain-of-thought sequences, yet this computational freedom leads to excessive token generation even for simple problems. We present Length-Adaptive Policy…
This paper introduces a new kind of propositional encoding for reasoning about partial orders. The symbols in an unspecified partial order are viewed as variables which take integer values and are interpreted as indices in the order. For a…
Four new variants of the Computational Order of Convergence (COC) of a one-point iterative method with memory for solving nonlinear equations are presented. Furthermore, the way to approximate the new variants to the local order of…
Chain-of-Thought (CoT) prompting enables large language models to solve complex reasoning problems by generating intermediate steps. However, confined by its inherent single-pass and sequential generation process, CoT heavily relies on the…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
The Higher-Order $\Psi$-calculus framework (HO$\Psi$) is a generalisation of many first- and higher-order extensions of the $\pi$-calculus. It was proposed by Parrow et al. who showed that higher-order calculi such as HO$\pi$ and CHOCS can…
DPO (Direct Preference Optimization) has become a widely used offline preference optimization algorithm due to its simplicity and training stability. However, DPO is prone to overfitting and collapse. To address these challenges, we propose…
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of…
Primitive recursion is a mature, well-understood topic in the theory and practice of programming. Yet its dual, primitive corecursion, is underappreciated and still seen as exotic. We aim to put them both on equal footing by giving a…
Recursive coalgebras provide an elegant categorical tool for modelling recursive algorithms and analysing their termination and correctness. By considering coalgebras over categories of suitably indexed families, the correctness of the…