Unambiguous Boolean grammars

Boolean grammars are an extension of context-free grammars, in which conjunction and negation may be explicitly used in the rules. In this paper, the notion of ambiguity in Boolean grammars is defined. It is shown that the known transformation of a Boolean grammar to the binary normal form preserves unambiguity, and that every unambiguous Boolean language can be parsed in time O(n^2). Linear conjunctive languages are shown to be unambiguous, while the existence of languages inherently ambiguous with respect to Boolean grammars is left open.

[1]  Wojciech Rytter,et al.  Oberservation on log(n) Time Parallel Recognition of Unambiguous cfl's , 1992, Inf. Process. Lett..

[2]  Artur Jez.  Conjunctive Grammars Can Generate Non-regular Unary Languages , 2007, Developments in Language Theory.

[3]  Sheila A. Greibach,et al.  The Undecidability of the Ambiguity Problem for Minimal Linear Grammars , 1963, Inf. Control..

[4]  Robert W. Floyd,et al.  On ambiguity in phrase structure languages , 1962, CACM.

[5]  Alexander Okhotin,et al.  Recursive descent parsing for Boolean grammars , 2007, Acta Informatica.

[6]  Jay Earley,et al.  An efficient context-free parsing algorithm , 1970, Commun. ACM.

[7]  Alexander Okhotin.  The hardest linear conjunctive language , 2003, Inf. Process. Lett..

[8]  Wojciech Rytter.  Parallel Time O(log n) Recognition of Unambiguous Context-free Languages , 1987, Inf. Comput..

[9]  Alexander Okhotin.  Expressive Power of LL(k) Boolean Grammars , 2007, FCT.

[10]  Alexander Okhotin.  Boolean grammars , 2004, Inf. Comput..

[11]  Oscar H. Ibarra,et al.  Characterizations and Computational Complexity of Systolic Trellis Automata , 1984, Theor. Comput. Sci..

[12]  Véronique Terrier,et al.  On Real Time One-Way Cellular Array , 1995, Theor. Comput. Sci..

[13]  Klaus Wich.  Sublogarithmic ambiguity , 2005, Theor. Comput. Sci..

[14]  Alexander Okhotin,et al.  On the equivalence of linear conjunctive grammars and trellis automata , 2004, RAIRO Theor. Informatics Appl..

[15]  Michael A. Harrison,et al.  Introduction to formal language theory , 1978 .

[16]  Seymour Ginsburg,et al.  Two Families of Languages Related to ALGOL , 1962, JACM.

[17]  Carme Àlvarez,et al.  A Very Hard log-Space Counting Class , 1993, Theor. Comput. Sci..

[18]  William F. Ogden,et al.  A helpful result for proving inherent ambiguity , 1968, Mathematical systems theory.

[19]  Alexander Okhotin,et al.  Conjunctive Grammars , 2001, J. Autom. Lang. Comb..

[20]  Joseph S. Ullian,et al.  Ambiguity in context free languages , 1966, JACM.

[21]  Panos Rondogiannis,et al.  Well-founded semantics for Boolean grammars , 2006, Inf. Comput..

[22]  Tadao Kasami,et al.  A Syntax-Analysis Procedure for Unambiguous Context-Free Grammars , 1969, J. ACM.

[23]  Alexander Okhotin,et al.  Generalized Lr Parsing Algorithm for Boolean Grammars , 2006, Int. J. Found. Comput. Sci..

[24]  Arto Salomaa,et al.  Systolic trellis automatat , 1984 .