A Note on the Proper ties of the Supremal Controllable Sublanguage in Pushdown Systems.
Abstract
Consider an event alphabet $$\Sigma$$. The Supervisory Control Theory of Ramadge and Wonham asks the question, given a plant model $$G$$ with language $$\LanM(G) \subseteq \Sigma^{*}$$ and another language $$K \subseteq \LanM(G)$$, is there a supervisor $$\varphi$$ such that $$\LanM(\varphi/G)=K$$? Ramadge and Wonham showed that a necessary condition for this to be true is the so called \textit{controllability} of $$K$$ with respect to $$\LanM(G)$$. They showed that when $$G$$ is a finite state automaton and $$K$$ is a regular language (also generated by a finite state automaton), then there is a regular \textit{supremal controllable sublanguage} $$\supC(K) \subseteq K$ that is is effectively constructable from generators of $$K$$ and $$G$$. In this paper, we show: (i) There is an algorithm to compute the supremal controllable sublanguage of a prefix closed $$K$$ accepted by a deterministic pushdown automaton when the plant language is also prefix closed and accepted by a finite state automaton. (ii) In this case, we show this supremal controllable sublanguage is also accepted by a DPDA.
- Authors:
-
- ORNL
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- ORNL other overhead
- OSTI Identifier:
- 939933
- DOE Contract Number:
- DE-AC05-00OR22725
- Resource Type:
- Journal Article
- Journal Name:
- IEEE Transactions on Automatic Control
- Additional Journal Information:
- Journal Volume: 53; Journal Issue: 3
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; ALGORITHMS; CONTROL THEORY; MACHINERY; Discrete Event Control; Supremal Controllable Sublanguage; Pushdown machine; Algorithm
Citation Formats
Griffin, Christopher H. A Note on the Proper ties of the Supremal Controllable Sublanguage in Pushdown Systems.. United States: N. p., 2008.
Web. doi:10.1109/TAC.2008.919519.
Griffin, Christopher H. A Note on the Proper ties of the Supremal Controllable Sublanguage in Pushdown Systems.. United States. https://doi.org/10.1109/TAC.2008.919519
Griffin, Christopher H. 2008.
"A Note on the Proper ties of the Supremal Controllable Sublanguage in Pushdown Systems.". United States. https://doi.org/10.1109/TAC.2008.919519.
@article{osti_939933,
title = {A Note on the Proper ties of the Supremal Controllable Sublanguage in Pushdown Systems.},
author = {Griffin, Christopher H},
abstractNote = {Consider an event alphabet $\Sigma$. The Supervisory Control Theory of Ramadge and Wonham asks the question, given a plant model $G$ with language $\LanM(G) \subseteq \Sigma^{*}$ and another language $K \subseteq \LanM(G)$, is there a supervisor $\varphi$ such that $\LanM(\varphi/G)=K$? Ramadge and Wonham showed that a necessary condition for this to be true is the so called \textit{controllability} of $K$ with respect to $\LanM(G)$. They showed that when $G$ is a finite state automaton and $K$ is a regular language (also generated by a finite state automaton), then there is a regular \textit{supremal controllable sublanguage} $\supC(K) \subseteq K$ that is is effectively constructable from generators of $K$ and $G$. In this paper, we show: (i) There is an algorithm to compute the supremal controllable sublanguage of a prefix closed $K$ accepted by a deterministic pushdown automaton when the plant language is also prefix closed and accepted by a finite state automaton. (ii) In this case, we show this supremal controllable sublanguage is also accepted by a DPDA.},
doi = {10.1109/TAC.2008.919519},
url = {https://www.osti.gov/biblio/939933},
journal = {IEEE Transactions on Automatic Control},
number = 3,
volume = 53,
place = {United States},
year = {Tue Jan 01 00:00:00 EST 2008},
month = {Tue Jan 01 00:00:00 EST 2008}
}