### Simple Bounded MTLK Model Checking for Timed Interpreted Systems [chapter]

Agnieszka M. Zbrzezny, Andrzej Zbrzezny
2017 Smart Innovation, Systems and Technologies
We present a new translation of Metric Temporal Logic to the Linear Temporal Logic with a new set of the atomic propositions. We investigate a SAT-based bounded model checking method for Metric Temporal Logic that is interpreted over linear discrete infinite time models generated by discrete timed automata. We show how to implement the bounded model checking technique for Linear Temporal Logic with a new set of the atomic propositions and discrete timed automata, and as a case study we apply
more » ... technique in the analysis of the Timed Generic Pipeline Paradigm modelled by a network of discrete timed automata. We also present a comparison of the two translations of Metric Temporal Logic on common instances that can be scaled up to for performance evaluation. The theoretical description is supported by the experimental results that demonstrate the efficiency of the method. Introduction Bounded model checking [2, 3, 5] (BMC) is one of the symbolic model checking technique designed for finding witnesses for existential properties or counterexamples for universal properties. Its main idea is to consider a model reduced to a specific depth. The method works by mapping a bounded model checking problem to the satisfiability problem (SAT). For metric temporal logic (MTL) [4] and discrete time automata [1] the BMC method can by described as follows: given a model M for a discrete timed automaton , an MTL formula ϕ, and a bound k, a model checker creates a propositional formula [M, ϕ] k that is satisfiable if and only if the formula ϕ is true in the model M. The novelty of our paper lies in : 1. defining a translation of the existential model checking problem for MTL to the existential model checking problem for linear temporal logic with additional propositional variables q I . This logic is denoted by LTL q ; 2. defining bounded sematics for LTL q and defining the BMC algorithm; 3. implementing the new method. The translation from MTL to LTL q requires neither new clocks nor new transitions, whereas the translation to HLTL [7] requires as many new clocks as there are intervals in a given formula. It also requires an exponential number of resetting transitions.