2021/10/03 by Gianluca Curzi, Anupam Das, Curzi, Gianluca +1 · 1 citation
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2110.01114
openalex publication_date 2021/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have been proposed. However, little is known about the complexity theoretic aspects of circular proofs, which exhibit sophisticated loop structures atypical of more common `recursion schemes'. This paper attempts to bridge the gap between circular proofs and implicit computational complexity (ICC). Namely we introduce a circular proof system based on Bellantoni and Cook's famous safe-normal function algebra, and we identify proof theoretical constraints, inspired by ICC, to characterise the polynomial-time and elementary computable functions. Along the way we introduce new recursion theoretic implicit characterisations of these classes that may be of interest in their own right.