Formalization and Verification of PLC Timers in Coq

Programmable logic controllers (PLCs) are widely used in embedded systems. A timer plays a pivotal role in PLC real-time applications.The paper presents a formalization of TON-timers of PLC programs in the theorem proving system Coq. The behavior of a timer is characterized by a set of axioms at an abstract level. PLC programs with timers are modeled in Coq. As a case study, the quiz machine problem with timer is investigated. Relevant timing properties of practical interests are proposed and proven in Coq. This work unveils the hardness of timer modeling in embedded systems. It is an attempt of formally proving the correctness of PLC programs with timer control.