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Highlights • And-cross transitions are a useful abstraction that can make some constructs easier to specify for the modeler. • They can be transformed to and from alternative modeling solutions that require a greater number of transitions. • With fewer transitions, the time taken and memory required to certify a model to be deterministic using formal methods can be much reduced compared to other approaches. This is related to the time and memory required to compute the set of pairs of potentially conflicting transitions. Abstract In this paper, we present an approach to formally encode state machines expressed in Umple for symbolic verification. We illustrate this with a real-world modeling example that encodes and analyzes and-cross transitions. This paper discusses a formal description of our approach to represent state machine systems under analysis (SSUAs); a systematic approach to certifying that SSUAs are deterministic; and an evaluation of performance (memory usage and execution time) on the case study. Method We describe a formalization of state machines in Umple that enables their translation to model checking tools and also to code that is consistent with this. We present three alternative modeling solutions for a sample problem and a solution based on the use of and-cross transitions. State machine models corresponding to these solutions are represented in Umple, a model-oriented programming language. These are automatically transformed to SMV, the input language of the nuXmv (or NuSMV) model checker. By cleanly separating concerns, we systematically integrate components of hierarchical state systems as opposed to the traditional flattening approach, yet manage the complexity introduced by concurrency and and-crossing. We then compose and verify a set of requirements (e.g., correctness, safety, liveliness, etc.) on the resulting systems of all the modeling approaches to empirically compare the different modeling alternatives with the use of and-cross transitions. Results We can encode and formally analyse complex state machines with and-cross transition(s). We observed a large reduction in the number of required transitions for encoding the SSUA, as opposed to the alternative approaches. We asserted that solutions derived from the approaches are identical behavior-wise even though each approach models the SSUA differently. Each of the approaches yielded the same result for potentially conflicting pairs which is a false positive (i.e., the SSUAs are deterministic). We observe that each approach maintains the same global state-space irrespective of the variations in their number of transitions. Furthermore, we observe that it is untrue that a more abstract method applied to an SSUA outperforms its less abstract counterpart whenever parameters (such as execution time, memory usage and the number of Binary Decision Diagrams - BDDs) are the factors under consideration. Contributions A systematic approach to encode state machines with and-cross transitions (including unusual transitions). An enhanced but fully automated approach to discovering nondeterminism in state machines even in the presence of unbounded domains and multiple and-cross transitions within the same enclosing orthogonal state. An empirical study of the impact of abstraction on some performance parameters. We also present an extended formalization of Umple state machines. [ABSTRACT FROM AUTHOR]

• An approximately bisimilar symbolic model is constructed for a safe changeover process. • An automatic controller is designed for safe changeover process for the first time. • The synthesis of the proposed controller in a finite-state space is very fast and flexible. • The error bounds of the proposed controller are adjustable as design parameters. • The effectiveness of the symbolic controller is investigated via numerical simulation. Many process control problems with complex qualitative specifications cannot be addressed via conventional control design methods. Examples of such specifications include logic specifications expressed in the design of start-up, shut-down, changeover, and emergency shutdown operating procedures. In recent years, it has been shown in the control systems and computer science communities that symbolic models provide convenient and powerful mechanisms to synthesize controllers enforcing such qualitative specifications. The use of symbolic models reduces the synthesis of the controllers to a fixed-point computation problem over a finite-state abstract system. In this paper, after explaining the notion of approximate bisimulation for incrementally globally asymptotically stable (δ -GAS) nonlinear control systems, the construction of approximately bisimilar symbolic models for such systems is presented. Then synthesis of time-optimal symbolic controller for this class of systems is performed based on results from the computer science literature. As a benchmark chemical process control problem, an approximately bisimilar symbolic model is constructed for a safe changeover process. Then a symbolic controller is designed and it is refined to a controller to be applied to the original process. Simulation results show the effectiveness of the symbolic controller. Although the construction of the symbolic model may be complex, the synthesis of the controller in a finite-state space is fast and most importantly the error bounds are adjustable as design parameters. [ABSTRACT FROM AUTHOR]

The paper contributes to the topic of (purely) catalytic P systems. Catalytic P systems represent the original and likely the simplest class of membrane computing models. It is known that (purely) catalytic P systems with two (respectively three) catalysts and one membrane can simulate any Minsky register machine and, hence, they are computationally complete. However, the problem of minimal size of such a universal catalytic P system remains open for about ten years. We improve known results about small catalytic P systems simulating register machines in three different modes (generating, accepting, computing functions). Together with some specific universal register machine [7] , one could eventually construct a small universal catalytic P system. As a consequence, we also improve the previous construction of a minimal catalytic P system generating a non-semilinear set, diminishing the number of necessary rules from 29 to 24. [ABSTRACT FROM AUTHOR]