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Title: 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:
 [1]
  1. 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}
}