It is shown that the class of left-to-right regular languages coincides with the class of languages that are accepted by monotone deterministic RL-automata, in this way establishing a close correspondence between a classical parsing algorithm and a certain restricted type of analysis by reduction.
@article{ITA_2009__43_3_653_0, author = {Otto, Friedrich}, title = {Left-to-right regular languages and two-way restarting automata}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, volume = {43}, year = {2009}, pages = {653-665}, doi = {10.1051/ita/2009013}, mrnumber = {2541135}, zbl = {1176.68107}, language = {en}, url = {http://dml.mathdoc.fr/item/ITA_2009__43_3_653_0} }
Otto, Friedrich. Left-to-right regular languages and two-way restarting automata. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) pp. 653-665. doi : 10.1051/ita/2009013. http://gdmltest.u-ga.fr/item/ITA_2009__43_3_653_0/
[1] Extending lookahead for LR parsers. J. Comput. System. Sci. 22 (1981) 243-259. | MR 624880 | Zbl 0472.68049
,[2] Practical arbitrary lookahead LR parsing. J. Comput. System. Sci. 41 (1990) 230-250. | MR 1072043 | Zbl 0698.68070
and ,[3] Growing context-sensitive languages and Church-Rosser languages. Inform. Comput. 141 (1998) 1-36. | MR 1604216 | Zbl 0894.68093
and ,[4] LR-regular grammars - an extension of LR() grammars. J. Comput. System. Sci. 7 (1973) 66-96. | MR 319413 | Zbl 0253.68014
and ,[5] A bounded graph-connect construction for LR-regular parsers, in Proc. Compiler Construction, CC 2001. Lect. Notes Comput. Sci. 2027 (2001) 244-258. | Zbl 0977.68570
and ,[6] A metatheorem for undecidable properties of formal languages and its application to LRR and LLR grammars and languages. Theoret. Comput. Sci. 23 (1983) 49-68. | MR 693068 | Zbl 0507.68044
,[7] Restarting automata, in Proc. FCT 1995. Lect. Notes Comput. Sci. 965 (1995) 283-292. | MR 1459184
, , and ,[8] On monotonic automata with a restart operation. J. Autom. Lang. Comb. 4 (1999) 287-311. | MR 1737858 | Zbl 0942.68064
, , and ,[9] Church-Rosser languages vs. UCFL, in Proc. ICALP 2002. Lect. Notes Comput. Sci. 2380 (2002) 147-158. | MR 2062454 | Zbl 1056.68095
and ,[10] Shrinking restarting automata. Int. J. Found. Comput. Sci. 18 (2007) 361-385. | MR 2311139 | Zbl 1112.68087
and ,[11] Monotone deterministic RL-automata don't need auxiliary symbols, in Proc. DLT 2005. Lect. Notes Comput. Sci. 3572 (2005) 284-295. | MR 2187270 | Zbl 1132.68450
, , and ,[12] Degrees of non-monotonicity for restarting automata. Theoret. Comput. Sci. 369 (2006) 1-34. | Zbl 1142.68423
, , and ,[13] When Church-Rosser becomes context-free. Int. J. Found. Comput. Sci. 18 (2007) 1293-1302. | MR 2363809 | Zbl pre05664844
and ,[14] One pushdown and a small tape, in Dirk Siefkes zum 50. Geburtstag, edited by K.W. Wagner, Technische Universität Berlin and Universität Augsburg (1988) 42-47.
,[15] Church-Rosser Thue systems and formal languages. J. ACM 35 (1988) 324-344. | MR 935255 | Zbl 0652.68093
, and ,[16] CD-Systems of Restarting Automata. Doctoral Dissertation, Fachbereich Elektrotechnik/Informatik, Universität Kassel (2008).
,[17] On nonforgetting restarting automata that are deterministic and/or monotone, in Proc. CSR 2006. Lect. Notes Comput. Sci. 3967 (2006) 247-258. | MR 2260999 | Zbl pre05148731
and ,[18] Restart-Automaten mit mehreren Restart-Zuständen, in Proc. Workshop “Formale Methoden in der Linguistik” und 14. Theorietag “Automaten und Formale Sprachen”, edited by H. Bordihn, Institut für Informatik, Universität Potsdam (2004) 111-116.
and ,[19] Church-Rosser and Related Thue Systems. Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, New York (1984).
,[20] Further results on restarting automata, in Proc. Words, Languages and Combinatorics III, edited by M. Ito and T. Imaoka, World Scientific, Singapore (2003) 353-369. | MR 2028887
and ,[21] The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages. Inform. Comput. 197 (2005) 1-21. | MR 2126360 | Zbl 1075.68046
and ,[22] Restarting automata and their relations to the Chomsky hierarchy, in Proc. DLT 2003. Lect. Notes Comput. Sci. 2710 (2003) 55-74. | MR 2053874 | Zbl 1037.68088
,[23] Restarting automata, in Recent Advances in Formal Languages and Applications, edited by Z. Ésik, C. Martin-Vide and V. Mitrana. Studies in Computational Intelligence 25 (2006) 269-303.
,[24] Two-way restarting automata and j-monotonicity, in Proc. SOFSEM 2001. Lect. Notes Comput. Sci. 2234 (2001) 316-325. | Zbl 1052.68628
,[25] A YACC extension for LRR grammar parsing. Theoret. Comput. Sci. 52 (1987) 91-143. | MR 918115 | Zbl 0627.68070
,[26] Noncanonical extensions of bottom-up parsing techniques. SIAM J. Comput. 5 (1976) 231-250. | MR 408349 | Zbl 0373.68048
and ,