Paper Info
Title
A Theory and Calculus for Reasoning about Sequential Behavior
Abstract
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.
Year
Venue
Keywords
2007
Clinical Orthopaedics and Related Research
regular expressions,inference,finite state automata,implicants,additional key words and phrases: regular sets,de morgan algebras,kripke structures,resolution,regular expression,satisfiability
Field
DocType
Volume
Boolean network,Discrete mathematics,Algorithm,Product term,Standard Boolean model,Implicant,Boolean expression,Mathematics,Calculus,Boolean analysis,Dependency theory (database theory),Two-element Boolean algebra
Journal
abs/cs/070
Citations
PageRank
References
0
0.34
10
Authors
1
Name
Order
Citations
PageRank
Frederick C Furtek193.43