Bounded Model Checking for Metric Temporal Logic Properties of Timed Automata with Digital Clocks

Abstract

Metric temporal logic (MTL) is a popular real-time extension of linear temporal logic (LTL). This paper presents a new simple SAT-based bounded model-checking (SAT-BMC) method for MTL interpreted over discrete infinite timed models generated by discrete timed automata with digital clocks. We show a new translation of the existential part of MTL to the existential part of linear temporal logic with a new set of atomic propositions and present the details of the new translation. We compare the new method’s advantages to the old method based on a translation of the hard reset LTL (HLTL). Our method does not need new clocks or new transitions. It uses only one path and requires a smaller number of propositional variables and clauses than the HLTL-based method. We also implemented the new method, and as a case study, we applied the technique to analyze several systems. We support the theoretical description with the experimental results demonstrating the method’s efficiency.

Keywords

• bounded model checking
• timed automata
• digital clocks
• metric temporal logic
• satisfiability problem