Properties of UTxO Ledgers and Programs Implemented on Them

2025-06-06

Electronic Proceedings in Theoretical Computer Science

AI Summary

UTxO ledger models lack a formal trace semantics, hindering rigorous verification of smart contracts. Method: We model valid execution traces of UTxO smart contracts as infinite paths in the category of simple graphs and equip them with a hypermetric structure; we introduce an on-chain program representation based on non-expansive mappings, enabling rigorous embedding of stateful semantics into the stateless UTxO model. By integrating category theory, graph theory, topology, and trace semantics, we construct a unified analytical framework that formally relates execution traces to stateful program behavior. Contribution/Results: We prove key safety properties—including trace consistency and abstraction soundness—and establish a verifiable state abstraction mechanism. This work provides a solid mathematical foundation for high-assurance formal verification of UTxO-based smart contracts.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Cryptocurrency and smart contracts
• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Trace-based properties are the gold standard for program behaviour analysis. One of the domains of application of this type of analysis is cryptocurrency ledgers, both for the purpose of analyzing the behaviour of the ledger itself, and any user-defined programs called by it, known as smart contracts. The (extended) UTxO ledger model is a kind of ledger model where all smart contract code is stateless, and additional work must be done to model stateful programs. We formalize the application of trace-based analysis to UTxO ledgers and contracts, expressing it in the languages of topology, as well as graph and category theory. To describe valid traces of UTxO ledger executions, and their relation to the behaviour of stateful programs implemented on the ledger, we define a category of simple graphs, infinite paths in which form an ultra-metric space. Maps in this category are arbitrary partial sieve-define homomorphisms of simple graphs. Programs implemented on the ledger correspond to non-expanding maps out of the graph of valid UTxO execution traces. We reason about safety properties in this framework, and prove properties of valid UTxO ledger traces.

Problem

• Formalize trace-based analysis for UTxO ledgers and contracts
• Model stateful programs on stateless UTxO ledger systems
• Define safety properties of UTxO ledger execution traces

Innovation

• Trace-based analysis for UTxO ledgers
• Category theory for stateful program modeling
• Ultra-metric space for execution traces