A Theory and Calculus for Reasoning about Sequential Behavior
<|reference_start|>A Theory and Calculus for Reasoning about Sequential Behavior: Basic results in combinatorial mathematics provide the foundation for a theory and calculus for reasoning about sequential behavior. A key concept of the theory is a generalization of Boolean implicant which deals with statements of the form:   A sequence of Boolean expressions alpha is an implicant of a set of sequences of Boolean expressions A   This notion of a generalized implicant takes on special significance when each of the sequences in the set A describes a disallowed pattern of behavior. That is because a disallowed sequence of Boolean expressions represents a logical/temporal dependency, and because the implicants of a set of disallowed Boolean sequences A are themselves disallowed and represent precisely those dependencies that follow as a logical consequence from the dependencies represented by A. The main result of the theory is a necessary and sufficient condition for a sequence of Boolean expressions to be an implicant of a regular set of sequences of Boolean expressions. This result is the foundation for two new proof methods. Sequential resolution is a generalization of Boolean resolution which allows new logical/temporal dependencies to be inferred from existing dependencies. Normalization starts with a model (system) and a set of logical/temporal dependencies and determines which of those dependencies are satisfied by the model.<|reference_end|>
@article{furtek2007a,
    title={A Theory and Calculus for Reasoning about Sequential Behavior},
    author={Frederick Furtek},
    journal={arXiv preprint arXiv:cs/0701088},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0701088},
    primaryClass={cs.LO cs.DM}
}