State space construction of timed automata models including difference constraints by LMNtal

Abstract

Realtime systems have realtime constraints on the behavior of the systems, and timed automata are one of the typical modeling methods for realtime systems. Since time is usually represented as continuous values, it is necessary to perform an appropriate abstraction of the state space and suppress the divergence of the number of states. The purpose of this study is to model realtime systems concisely and to construct state space with an appropriate abstraction. For modeling, we proposed framework for timed automata models using the language LMNtal, which makes it easy to represent multisets sets and hierarchical processes. We implemented the state space construction technique using LMNtal, and the number of states could be significantly reduced by managing time as a conjunction of constraint expressions. Additionally, we implemented Difference Bound Matrices in LMNtal, which is known as a data structure that enables efficient constraint processing for handling models including difference constraints.