Agent-Alternation-Free Epistemic Metric Temporal Logic with Past: Model Checking and Complexity

2026-07-15

AI Summary

This work addresses verification problems for systems under partial observation—such as diagnosis and opacity—by studying a fragment of epistemic temporal logic that excludes agent alternation but supports past temporal operators and metric constraints. Under the assumption of synchronous perfect recall, the paper proposes a model-checking method combining temporal test automata with an observer mechanism, which handles historical indistinguishability by synchronously tracking the system and automaton states. The study establishes, for the first time, that the model-checking problem for this logic fragment is EXPSPACE-complete. Notably, this complexity lower bound holds even in a highly restricted setting featuring a single agent, a single occurrence of the knowledge operator, and no nontrivial metric constraints, thereby precisely delineating the computational complexity boundary for related verification tasks.

Abstract

We study model checking for an epistemic metric temporal logic with past, interpreted over finite Büchi automata under synchronous perfect recall. The logic is motivated by observation-based verification problems such as diagnosis and opacity, where an observer sees only a projection of an execution and reasons about events that may have occurred earlier. These requirements use no alternation between different agents' knowledge. We therefore consider the agent-alternation-free fragment, in which nested knowledge operators must refer to the same agent. We show that model checking for this fragment is EXPSPACE-complete. The lower bound already holds with one agent, one occurrence of the knowledge operator, and no non-trivial metric bounds. For the upper bound, we combine temporal test automata with perfect-recall observers. Because past formulas may have different truth values on indistinguishable histories ending in the same system state, the observer must track temporal automaton states in addition to system states.

Problem

• epistemic logic
• metric temporal logic
• model checking
• agent alternation
• past operators

Innovation

• agent-alternation-free
• epistemic metric temporal logic
• past operators
• model checking
• perfect recall