# The Cost of Monitoring Alone

## TL;DR

This paper analyzes the size complexity involved in transforming parallel monitors into regular and deterministic monitors for infinite trace properties, revealing tight double and triple-exponential bounds.

## Contribution

It establishes tight bounds on the exponential blowup in monitor size when converting between different monitoring systems and logic fragments.

## Key findings

- Transforming parallel to regular monitors incurs double-exponential size increase.
- Deterministic monitor translation causes a triple-exponential blowup.
- Bounds are proven to be tight for these transformations.

## Abstract

We compare the succinctness of two monitoring systems for properties of infinite traces, namely parallel and regular monitors. Although a parallel monitor can be turned into an equivalent regular monitor, the cost of this transformation is a double-exponential blowup in the syntactic size of the monitors, and a triple-exponential blowup when the goal is a deterministic monitor. We show that these bounds are tight and that they also hold for translations between corresponding fragments of Hennessy-Milner logic with recursion over infinite traces.