TY - GEN
T1 - Pumping lemma for higher-order languages
AU - Asada, Kazuyuki
AU - Kobayashi, Naoki
N1 - Publisher Copyright:
© Kazuyuki Asada and Naoki Kobayashi;.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal's tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages.
AB - We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal's tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages.
KW - Higher-order grammars
KW - Kruskal's tree theorem
KW - Pumping lemma
UR - http://www.scopus.com/inward/record.url?scp=85027285764&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85027285764&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ICALP.2017.97
DO - 10.4230/LIPIcs.ICALP.2017.97
M3 - Conference contribution
AN - SCOPUS:85027285764
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017
A2 - Muscholl, Anca
A2 - Indyk, Piotr
A2 - Kuhn, Fabian
A2 - Chatzigiannakis, Ioannis
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 44th International Colloquium on Automata, Languages, and Programming, ICALP 2017
Y2 - 10 July 2017 through 14 July 2017
ER -