Identifying left-right deterministic linear languages

Recently an algorithm to identify in the limit with polynomial time and data Left Deterministic Linear Languages (Left DLL) and, consequently Right DLL, was proposed. In this paper we show that the class of the Left-Right DLL formed by the union of both classes is also identifiable. To do that, we introduce the notion of n-negative characteristic sample, that is a sample that forces an inference algorithm to output an hypothesis of size bigger than n when strings from a non identifiable language are provided.This work was supported by the Spanish CICyT trough project TIC2003-08496-C04 and supported in part by the IST Programme of the European Community, under the Pascal Network of Excellence, IST-2002-506778

Identifying Left-Right Deterministic Linear Languages

Abstract. Recently an algorithm to identify in the limit with polynomial time and data Left Deterministic Linear Languages (Left DLL) and, consequently Right DLL, was proposed. In this paper we show that the class of the Left-Right DLLformed by the union of both classes is also identifiable. To do that, we introduce the notion of n-negative characteristic sample, that is a sample that forces an inference algorithm to output an hypothesis of size bigger than n when strings from a non identifiable language are provided. An important subclass of the linear languages is that of the Left Deterministic Linear Languages (Left DLL or LDLL) [1]. They are generated by Left Deterministic Linear Grammars such that the next rule to use in the parsing of a string is determined by observing the leftmost terminal in the unparsed part of the string. Regular languages, {a n b n | n ≥ 0} and {a m b n c n | n, m ≥ 0} are some examples of languages in the class, while {a n b n c m | n, m ≥ 0} is not. The class formed by the reversals of the languages in LDLL is called th