Understanding Robust Catalytic Computing

TL;DR

This paper extends the concept of lossy catalytic computing by defining and analyzing new models with various error allowances, providing a comprehensive characterization and implications for complexity classes.

Contribution

It introduces three natural extensions of catalytic computing with bounded or probabilistic errors and characterizes their relationships to classical complexity classes.

Findings

Complete characterization of the new catalytic models in general and logspace regimes.

Equivalences established between error models and classical complexity classes.

Under derandomization, catalytic classes collapse in the logspace regime.

Abstract

Catalytic computing concerns space bounded computation which starts with memory full of data that have to be restored by the end of the computation. Lossy catalytic computing, defined by Gupta et al. (2024) and fully characterized by Folkertsma et al. (ITCS 2025), is the study of allowing a small number of errors when resetting the catalytic tape at the end of a computation. Such a notion is useful when considering the robust use of catalytic techniques in the study of ordinary space-bounded algorithms. To that end however, defining and characterizing less strict notions of error was left open by Folkertsma et al. (ITCS 2025) and other works such as Mertz (B. EATCS, 2023). We expand the definition of possible resetting error in three natural ways: 1. randomized catalytic computation which can completely destroy the catalytic tape with some probability over the randomness 2. randomized catalytic computation which makes a bounded number of errors in expectation over the randomness 3. deterministic catalytic computation which makes a bounded number of errors in expectation over the initial catalytic tape itself We show a near complete characterization of the above models, both in the general case and in the logspace polynomial-time regime, by showing equivalences either between one another, to errorless catalytic space models, or to standard time or space complexity classes. Under a derandomization assumption, we show a near full collapse of all existing catalytic classes in the logspace regime.