Abstract
The signed real measure of regular languages, introduced and validated in recent literature, has been the driving force for quantitative analysis and synthesis of discrete-event supervisory (DES) control systems dealing with finite state automata (equivalently, regular languages). However, this approach relies on memoryless state-based tools for supervisory control synthesis and may become inadequate if the transitions in the plant dynamics cannot be captured by finitely many states. From this perspective, the measure of regular languages needs to be extended to that of non-regular languages, such as Petri nets or other higher level languages in the Chomsky hierarchy. Measures for non-regular languages has not apparently been reported in open literature and is an open area of research. This paper introduces a complex measure of linear context free grammars (LCFG) that belong to the class of non-regular languages. The proposed complex measure becomes equivalent to the signed real measure, reported in recent literature, if the LCFG is degenerated to a regular grammar.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
