Automata-less Monitoring via Trace-Checking (Extended Version)

TL;DR

This paper introduces a trace-checking approach for runtime verification of certain formulas, avoiding automaton construction and reducing complexity, especially for LTLf and specific LTL fragments.

Contribution

It identifies conditions for automaton-less monitoring using trace-checking for safe and cosafe formulas, improving efficiency and complexity bounds.

Findings

Monitoring of safe and cosafe formulas can be done via trace-checking with polynomial complexity.

All formulas in LTLf safety and cosafety fragments are inherently safe and cosafe, removing the need for checks.

The complexity of recognizing safe and cosafe formulas in LTL is in PSPACE, better than previous EXPSPACE bounds.

Abstract

In runtime verification, monitoring consists of analyzing the current execution of a system and determining, on the basis of the observed finite trace, whether all its possible continuations satisfy or violate a given specification. This is typically done by synthesizing a monitor--often a Deterministic Finite State Automaton (DFA)--from logical specifications expressed in Linear Temporal Logic (LTL) or in its finite-word variant (LTLf). Unfortunately, the size of the resulting DFA may incur a doubly exponential blow-up in the size of the formula. In this paper, we identify some conditions under which monitoring can be done without constructing such a DFA. We build on the notion of intentionally safe and cosafe formulas, introduced in [Kupferman & Vardi, FMSD, 2001], to show that monitoring of these formulas can be carried out through trace-checking, that is, by directly evaluating them on the current system trace, with a polynomial complexity in the size of both the trace and the formula. In addition, we investigate the complexity of recognizing intentionally safe and cosafe formulas for the safety and cosafety fragments of LTL and LTLf. As for LTLf, we show that all formulas in these fragments are intentionally safe and cosafe, thus removing the need for the check. As for LTL, we prove that the problem is in PSPACE, significantly improving over the EXPSPACE complexity of full LTL.