A Verification Framework for Obstruction, Probability, and Time

Wissal DAHANI, Jean Leneutre, Vadim Malvone, James Ortiz, Axel Oscar

Keywords: Strategic reasoning, Cybersecurity, Model checking, Quantitative verification, Security games, Moving Target Defense mechanisms

TL;DR: PTOTL a probabilistic real-time logic with cost-bounded edge disabling and a PSPACE model checker, used to verify MTD policies that bound time and breach probability in automotive CPS use case.

Abstract: Verifying strategic behaviour in real-time multi-agent systems under uncertainty is vital for safety- and security-critical domains.Existing obstruction logics treat either adversarial timing (TOL) or probabilistic risk (POTL), but real scenarios require both. We introduce Probabilistic Timed Obstruction Temporal Logic (PTOTL), which unifies dense time, probabilities, and cost-bounded obstruction for real-time security games. Interpreted over Weighted Probabilistic Timed Automaton (WPTA), PTOTL models attacker–defender interactions where discrete actions and time elapse evolve, and the defender may disable transitions under a per-step budget. We give syntax and semantics, and a symbolic model-checking procedure on a probabilistic zone graph. Despite added strategic and probabilistic features, verification remains PSPACE, not highter than PTCTL or PTATL while offering greater temporal expressiveness. An automotive Moving Target Defense (MTD) case study demonstrates practicality as a specification and verification language.

Area: Representation and Reasoning (RR)

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Submission Number: 1252