# On Symbolic Analysis of Discrete Event Systems Modeled as Automata with Variables

Sammanfattning: In benefit of the current revolution in computer technology, nowadays, society is dependent on dedicated computer-aided systems more than ever to assist us in every aspect of daily life. Thereby, designing reliable control logic of those systems to avoid malfunctioning behavior is of importance. At some certain level of abstraction, the dynamics of many computer-aided systems can be characterized by a set of states and the state evolution depends entirely on the occurrence of discrete events. Such dynamic systems are referred to as discrete event systems (DES), which is the main subject of this thesis. Supervisory Control Theory (SCT) is a formal methodology for generating control function for DESs based on a model of an uncontrolled plant and speci- fications that the closed-loop system must fulfill. SCT makes it easier to handle changes for the system to be controlled. This is, for example, important for man- ufacturing systems where both the products to be produced and the production equipment may change frequently. With such a model-based framework, it is possible to use algorithms to generate large parts of the control logic. Although SCT shows great promise to assist control engineers to create cor- rect control functions, industrial acceptance has been limited so far. One of the main obstacles with SCT is the state-space explosion problem which arises from the failure of explicit enumerating and storing large number of states due to lack of memory. To alleviate this problem, a well-known strategy is to utilize compact data structures such Binary Decision Diagrams (BDDs) to efficiently represent set of states. By encoding system models, the computation of control functions can be carried out implicitly (symbolically). In this thesis, DESs are modeled as Extended Finite Automata (EFAs), which are ordinary automata augmented with variables. By taking advantage of the EFA structure, this thesis presents a set of BDD-based algorithms and formal analysis for exploring the state-space of large-scale DESs. Specifically, by using one of the partitioning techniques, the algorithms partition the state-space of a considered DES into a set of BDDs according to the included events and explore them in an efficient and structural manner. The work presented in this thesis has been implemented and integrated into the SCT tool Supremica and the algorithm efficiency is demonstrated on a set of academic and industrial examples.

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