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Beyond Affine Loops: A Geometric Approach to Program Synthesis

Year: 2025

Type: conference-paper

Abstract: Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before and after each iteration. Generating polynomial invariants is a crucial task for loops, but it is an undecidable problem in the general case. Recently, an alternative approach to this problem has emerged, focusing on synthesizing loops from invariants. However, existing methods only synthesize affine loops without guard conditions from polynomial invariants. In this paper, we address a more general problem, allowing loops to have polynomial update maps with a given structure, inequations in the guard condition, and polynomial invariants of arbitrary form.

DOI: 10.1145/3735544.3735581

Authors: Erdenebayar Bayarmagnai, Fatemeh Mohammadi, Rémi Prébet

Institutions: KU Leuven, Lyon 1 Université, École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Laboratoire de l'Informatique du Parallélisme

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Funders: Agence Nationale de la Recherche, Fonds Wetenschappelijk Onderzoek, KU Leuven

Awards: Exploiting combinatorial structures for algebraic and geometric decompositions, Numerical Safety for Computer-Aided Proofs, Certified Numerics for Algebraic Curves with Singularities, G4869584417, Matroids in Applied and Combinatorial Commutative Algebra

OpenAlex ID: W4411266296

FWCI:

Cites: 34

Cited by:

Related to: 10