TY - JOUR
T1 - A complex measure for linear grammars
AU - Chattopadhyay, Ishanu
AU - Ray, Asok
N1 - Funding Information:
1991 Mathematics Subject Classification: 93A05. Key words and phrases: Language Measure; Discrete Event Supervisory Control; Linear Grammars. This work has been supported in part by the U.S. Army Research Laboratory and the U.S. Army Research Office (ARO) under Grant No. DAAD19-01-1-0646; and NASA Glenn Research Center under Grant No. NNC04GA49G.
Publisher Copyright:
© 2005 Warsaw University. All rights reserved.
PY - 2005/7
Y1 - 2005/7
N2 - 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. As a step toward achieving this goal, 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.
AB - 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. As a step toward achieving this goal, 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.
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U2 - 10.1515/dema-2005-0323
DO - 10.1515/dema-2005-0323
M3 - Article
AN - SCOPUS:34047228938
SN - 0420-1213
VL - 38
SP - 761
EP - 775
JO - Demonstratio Mathematica
JF - Demonstratio Mathematica
IS - 3
ER -