A Theory and Calculus for Reasoning about Sequential Behavior
| dc.creator | Furtek, Frederick | |
| dc.date | 2007-01-15 | |
| dc.date | 2007-03-29 | |
| dc.date.accessioned | 2026-07-07T07:54:48Z | |
| dc.date.available | 2026-07-07T07:54:48Z | |
| dc.description | 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. | |
| dc.description | 102 double-spaced pages, 17 figures. Abstract and introduction revised 29 March 2007 to improve readability | |
| dc.identifier | https://arxiv.org/abs/cs/0701088 | |
| dc.identifier | http://arxiv.org/abs/cs/0701088 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126752 | |
| dc.subject | Logic in Computer Science | |
| dc.subject | Discrete Mathematics | |
| dc.subject | F.4.1; D.2.4; G.2.1 | |
| dc.title | A Theory and Calculus for Reasoning about Sequential Behavior | |
| dc.type | text |