A Tale of Conjunctive Grammars

Conjunctive grammars are an extension of ordinary (“context-free”) grammars with a conjunction operator, which can be used in any rules to specify a substring that satisfies several syntactic conditions simultaneously. This family has been systematically studied since the turn of the century, and is a subject of current studies. This paper gives an overview of the current state of the art in the research on conjunctive grammars.

[1]  Masaru Tomita,et al.  An Efficient Augmented-Context-Free Parsing Algorithm , 1987, Comput. Linguistics.

[2]  Alexander Okhotin,et al.  Linear-space recognition for grammars with contexts , 2017, Theor. Comput. Sci..

[3]  Panos Rondogiannis,et al.  Well-founded semantics for Boolean grammars , 2009, Inf. Comput..

[4]  Pierre Boullier,et al.  A Cubic Time Extension of Context-Free Grammars , 2000, Grammars.

[5]  Alexander Okhotin.  LR Parsing for Conjunctive Grammars , 2002, Grammars.

[6]  Stepan Kuznetsov,et al.  Conjunctive Grammars in Greibach Normal Form and the Lambek Calculus with Additive Connectives , 2013, FG.

[7]  Artur Jez,et al.  Computational completeness of equations over sets of natural numbers , 2014, Inf. Comput..

[8]  Alexander Okhotin,et al.  An extension of context-free grammars with one-sided context specifications , 2014, Inf. Comput..

[9]  Alexander Okhotin,et al.  Two-sided context specifications in formal grammars , 2015, Theor. Comput. Sci..

[10]  Weiping Shi,et al.  Single Tree Grammars , 1992, Theoretical Studies in Computer Science.

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

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

[13]  Michael Kaminski,et al.  Conjunctive grammars and alternating pushdown automata , 2013, Acta Informatica.

[14]  William C. Rounds,et al.  LFP A Logic for Linguistic Descriptions and an Analysis of its Complexity , 1988, Comput. Linguistics.

[15]  Alexander Okhotin,et al.  Conjunctive grammars with restricted disjunction , 2010, Theor. Comput. Sci..

[16]  Alexander Okhotin,et al.  Boolean Grammars and GSM Mappings , 2010, Int. J. Found. Comput. Sci..

[17]  Jelle Hellings,et al.  Conjunctive Context-Free Path Queries , 2014, ICDT.

[18]  Alexander Okhotin,et al.  Conjunctive and Boolean grammars: The true general case of the context-free grammars , 2013, Comput. Sci. Rev..

[19]  Artur Jez,et al.  On the Number of Nonterminal Symbols in Unambiguous Conjunctive Grammars , 2012, DCFS.

[20]  Daniel J. Rosenkrantz,et al.  Properties of Deterministic Top-Down Grammars , 1970, Inf. Control..

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

[22]  Alexander Okhotin,et al.  Conjunctive Categorial Grammars , 2017, MOL.

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

[24]  Alexander Okhotin,et al.  Generalized LR Parsing Algorithm for Grammars with One-Sided Contexts , 2017, Theory of Computing Systems.

[25]  Alexander Okhotin.  Conjunctive Grammars and Systems of Language Equations , 2004, Programming and Computer Software.

[26]  Artur Jez,et al.  Conjunctive Grammars over a Unary Alphabet: Undecidability and Unbounded Growth , 2008, Theory of Computing Systems.

[27]  Véronique Terrier.  Some Computational Limits of Trellis Automata , 2017, AUTOMATA.

[28]  Zhendong Su,et al.  Context-sensitive data-dependence analysis via linear conjunctive language reachability , 2017, POPL.

[29]  Alexander Okhotin,et al.  Underlying Principles and Recurring Ideas of Formal Grammars , 2018, LATA.

[30]  Max Rabkin,et al.  Recognizing Two-Sided Contexts in Cubic Time , 2014, CSR.

[31]  Amaury Habrard,et al.  Using Contextual Representations to Efficiently Learn Context-Free Languages , 2010, J. Mach. Learn. Res..

[32]  Alexander Okhotin.  Notes on Dual Concatenation , 2007, Int. J. Found. Comput. Sci..

[33]  Alexander Okhotin.  Top-Down Parsing of Conjunctive Languages , 2002, Grammars.

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

[35]  Donald E. Knuth,et al.  On the Translation of Languages from Left to Right , 1965, Inf. Control..

[36]  Robert Wall,et al.  Intersective context-free languages , 1993 .

[37]  Leslie G. Valiant,et al.  General Context-Free Recognition in Less than Cubic Time , 1975, J. Comput. Syst. Sci..

[38]  Alexander Okhotin.  The Hardest Language for Conjunctive Grammars , 2016, CSR.

[39]  Artur Jez,et al.  One-Nonterminal Conjunctive Grammars over a Unary Alphabet , 2011, Theory of Computing Systems.

[40]  Martin Lange.  Alternating Context-Free Languages and Linear Time mu-Calculus with Sequential Composition , 2002, EXPRESS.

[41]  Mikhail Barash,et al.  Programming language specification by a grammar with contexts , 2013, NCMA.

[42]  Sheila A. Greibach,et al.  A New Normal-Form Theorem for Context-Free Phrase Structure Grammars , 1965, JACM.

[43]  Alexander Okhotin,et al.  On the number of nonterminals in linear conjunctive grammars , 2004, Theor. Comput. Sci..

[44]  Alexander Okhotin.  Unambiguous Boolean grammars , 2007, Inf. Comput..

[45]  Lothar Schmitz,et al.  An Efficient Recognizer for the Boolean Closure of Context-Free Languages , 1991, Theor. Comput. Sci..

[46]  Michael Kaminski,et al.  LR(0) conjunctive grammars and deterministic synchronized alternating pushdown automata , 2016, J. Comput. Syst. Sci..

[47]  Makoto Kanazawa.  The Lambek calculus enriched with additional connectives , 1992, J. Log. Lang. Inf..

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

[49]  Alexander Okhotin,et al.  Improved normal form for grammars with one-sided contexts , 2013, Theor. Comput. Sci..

[50]  Alexander Okhotin,et al.  Linear grammars with one-sided contexts and their automaton representation , 2015, RAIRO Theor. Informatics Appl..

[51]  Noam Chomsky,et al.  Three models for the description of language , 1956, IRE Trans. Inf. Theory.

[52]  Alexander Okhotin,et al.  The dual of concatenation , 2005, Theor. Comput. Sci..

[53]  Detlef Wotschke,et al.  The Boolean Closures of the Deterministic and Nondeterministic Context-Free Languages , 1973, GI Jahrestagung.

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

[55]  Alexander Okhotin,et al.  Formal Languages over GF(2) , 2018, LATA.

[56]  Alexander Okhotin.  Parsing by matrix multiplication generalized to Boolean grammars , 2014, Theor. Comput. Sci..

[57]  Jean Berstel,et al.  Context-Free Languages and Pushdown Automata , 1997, Handbook of Formal Languages.

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

[59]  Artur Jez,et al.  Unambiguous conjunctive grammars over a one-symbol alphabet , 2017, Theor. Comput. Sci..

[60]  Alexander Okhotin,et al.  On the expressive power of univariate equations over sets of natural numbers , 2012, Inf. Comput..

[61]  Artur Jez,et al.  Complexity of Equations over Sets of Natural Numbers , 2009, Theory of Computing Systems.

[62]  Alexander Okhotin,et al.  On Language Equations XXK = XXL and XM = N over a Unary Alphabet , 2010, Developments in Language Theory.

[63]  Alexander Okhotin.  Expressive power of LL(k) Boolean grammars , 2011, Theor. Comput. Sci..

[64]  Michael Kaminski,et al.  Linear Conjunctive Grammars and One-turn Synchronized Alternating Pushdown Automata , 2014, Int. J. Found. Comput. Sci..

[65]  S. Arumugam,et al.  Probabilistic Conjunctive Grammar , 2016, ICTCSDM.

[66]  Ryo Yoshinaka.  Learning Conjunctive Grammars and Contextual Binary Feature Grammars , 2015, LATA.

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

[68]  Alexander Okhotin,et al.  Parsing Boolean grammars over a one-letter alphabet using online convolution , 2012, Theor. Comput. Sci..