Characterization of Context-Free Languages with Polynomially Bounded Ambiguity

Abstract. We prove that the class of context-free languages with polynomially bounded ambiguity (PCFL) is the closure of the class of unambiguous languages (UCFL) under projections which deletes Parikh bounded symbols only. A symbol a is Parikh bounded in a language L if there is a constant c such that no word of L contains more than c occurrences of a. Furthermore PCFL is closed under the formally stronger operation of Parikh bounded substitution, i.e., a substitution which is the identity for non Parikh bounded symbols. Finally we prove that the closure of UCFL under union and concatenation is a proper subset of PCFL.

• Type: Conference
• Year: 2001
• Where: MFCS
• Authors: Klaus Wich
• Keywords: Context-free Languages, MFCS 2001, Parikh Bounded Substitution, Parikh Bounded Symbols, Theoretical Computer Science