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Prime normal form and equivalence of simple grammars

Cédric Bastien, Jurek Czyzowicz, Wojciech Fraczak, Wojciech Rytter
2006 Theoretical Computer Science  
Our algorithm computes a canonical representation of a simple language, converting its arbitrary simple grammar into prime normal form (PNF); a simple grammar is in PNF if all its nonterminals define primes  ...  We also improve the complexity of testing the equivalence of simple grammars. The best previously known algorithm for this problem worked in O(n 13 ) time.  ...  Acknowledgment The research of the first three authors was supported by NSERC and the research of the fourth author was supported by the Grants KBN 4T11C04425 and ITR-CCR-0313219.  ... 
doi:10.1016/j.tcs.2006.07.021 fatcat:x5smhvnbzfbgfd4n7dbv2bucmm

Prime Normal Form and Equivalence of Simple Grammars [chapter]

Cédric Bastien, Jurek Czyzowicz, Wojciech Fraczak, Wojciech Rytter
2006 Lecture Notes in Computer Science  
Our algorithm computes a canonical representation of a simple language, converting its arbitrary simple grammar into prime normal form (PNF); a simple grammar is in PNF if all its nonterminals define primes  ...  We also improve the complexity of testing the equivalence of simple grammars. The best previously known algorithm for this problem worked in O(n 13 ) time.  ...  Acknowledgment The research of the first three authors was supported by NSERC and the research of the fourth author was supported by the Grants KBN 4T11C04425 and ITR-CCR-0313219.  ... 
doi:10.1007/11605157_7 fatcat:qg2sll637rg7fkmyzk3ijpqu4e

Decidability results in automata and process theory [chapter]

Yoram Hirshfeld, Faron Moller
1996 Lecture Notes in Computer Science  
simple if the grammar is in Greibach normal form. / \ Example 1 Consider the grammar G = ({X,Y}, {a,b},P,X) where P con-% / sists of the rules This guarded grammar generates the (context-free) language  ...  A grammar is guarded iff each of its production rules is of the form X --+ ac~ where a E T. If moreover each c~ E V* then the grammar is in Greibach normal form (GNF).  ...  We would like to thank the organiser of the worksho p series Graham Birtwistle for allowing us the opportunity and the motivation for producing the notes, as well as a forum in which to present the material  ... 
doi:10.1007/3-540-60915-6_4 fatcat:zoxvo4dlergqdfkugtlypihd5i

A Note on the Generative Power of Some Simple Variants of Context-Free Grammars Regulated by Context Conditions [chapter]

Tomáš Masopust
2009 Lecture Notes in Computer Science  
Finally, this paper also presents some normal form results, an overview of known results, and unsolved problems.  ...  forbidding strings) where permitting and forbidding strings of each production are of length no more than one, and of simple semi-conditional grammars where, in addition, no production has attached both  ...  Specifically, it has proved that In addition, it has also presented some normal form results and an overview of known results, demonstrated the generative power of simple semi-conditional grammars of degree  ... 
doi:10.1007/978-3-642-00982-2_47 fatcat:ioduiodgzndoxi4oqqyrgs2uha

A polynomial-time algorithm for deciding bisimulation equivalence of normed Basic Parallel Processes

Yoram Hirshfeld, Mark Jerrum, Faron Moller
1996 Mathematical Structures in Computer Science  
A polynomial-time algorithm is presented for deciding bisimulation equivalence of so-called Basic Parallel Processes: multisets of elementary processes combined by a commutative parallelcomposition operator  ...  Theorem 2 Suppose the set Mon V of processes is de ned by a normed, context-free grammar in Greibach normal form.  ...  Notation and basic facts Let be a context-free grammar in Greibach normal form with variables V = fX 1 ; : : : ; X n g and terminals A. 1 For reasons that will become apparent presently, we sometimes  ... 
doi:10.1017/s0960129500000992 fatcat:tqtfyn5prfcndcw34w7lnq2egq

A polynomial algorithm for deciding bisimilarity of normed context-free processes

Yoram Hirshfeld, Mark Jerrum, Faron Moller
1996 Theoretical Computer Science  
As a corollary, we have a polynomial algorithm for the equivalence problem for simple grammars. 4 Recall that a grammar is in Greibach normal form if the right-hand side of every production consists of  ...  a proof of equivalence and validates this proof in polynomial time using oracles freely answering questions which are in NP.  ...  A simple gr~mur is a context-free grammar in Greibach normal form such that for any pair (X,a) consisting of a variable X and terminal a, there is at most one production of the form X + aa.  ... 
doi:10.1016/0304-3975(95)00064-x fatcat:5vln2w27gfcbfedxln5zxxexb4

Balanced Grammars and Their Languages [chapter]

Jean Berstel, Luc Boasson
2002 Lecture Notes in Computer Science  
Next, the set of right-hand sides of productions may be an infinite regular language. XML-grammars are a special kind of balanced grammars. This paper studies balanced grammars and their languages.  ...  It is shown that there exists a unique minimal balanced grammar equivalent to a given one. Next, balanced languages are characterized through a property of their syntactic congruence.  ...  Corollary 4. 2 . 2 If a context-free grammar is balanced (pure balanced, in Greibach normal form, in two-sided Greibach normal form, is finite), there exists an equivalent codeterministic grammar that  ... 
doi:10.1007/3-540-45711-9_1 fatcat:n3k5xev62beslascwxvengli5e

Reducing Simple Grammars: Exponential Against Highly-Polynomial Time in Practice [chapter]

Cédric Bastien, Jurek Czyzowicz, Wojciech Fraczak, Wojciech Rytter
2006 Lecture Notes in Computer Science  
We present a comparison and experimental analysis of the best-known algorithms for the grammar reduction.  ...  The simple grammar reduction is an important component in the implementation of Concatenation State Machines (a hardware version of stateless pushdown automata designed for wire-speed network packet classification  ...  A grammar G = (Σ, N, P ) is a simple grammar if G is a Greibach Normal Form grammar such that whenever A → a α 1 and A → a α 2 , for a same a ∈ Σ, then α 1 = α 2 .  ... 
doi:10.1007/11812128_10 fatcat:dzfsb5wh2vchfiebs24lb45ujm

Page 3211 of Mathematical Reviews Vol. , Issue 80H [page]

1980 Mathematical Reviews  
Various well-known families of languages are obtained (for example, the context sensitive, the EOL, and ETOL). Some normal form results are derived, and closure and decidability results established.  ...  From the introduction: “The aim of this paper is to prove that the system of simple graph grammars described in notes of E. Denent and H. Ehrig is complete.  ... 

Fast equivalence-checking for normed context-free processes

Wojciech Czerwinski, Slawomir Lasota, Marc Herbstritt
2010 Foundations of Software Technology and Theoretical Computer Science  
It also improves the previously known complexity O(n 6 polylog(n)) of the equality problem for simple grammars.  ...  Bisimulation equivalence is decidable in polynomial time over normed graphs generated by a context-free grammar.  ...  We are very grateful to Wojtek Rytter and Sibylle Fröschle for many helpful discussions.  ... 
doi:10.4230/lipics.fsttcs.2010.260 dblp:conf/fsttcs/CzerwinskiL10 fatcat:itqdcepqnrfa7eejwh36ngbo2m

Learning executable semantic parsers for natural language understanding

Percy Liang
2016 Communications of the ACM  
We will see that semantic parsing is a rich fusion of the logical and the statistical world, and that this fusion will play an integral role in the future of natural language understanding systems.  ...  Semantic parsers map natural language into logical forms, the classic representation for many important linguistic phenomena.  ...  Formally, the grammar is a set of rules of the form α ⇒ β. 1 Here is a simple grammar for our running example: (R1) prime ⇒ NP[primes] (R2) 10 ⇒ NP[10] (R3) less than NP[z] ⇒ QP[(−∞, z)] (R4) NP[z1]  ... 
doi:10.1145/2866568 fatcat:lcl6pogzmfazdma4wmt5rnebai

New evidence of a rhythmic priming effect that enhances grammaticality judgments in children

Alexander Chern, Barbara Tillmann, Chloe Vaughan, Reyna L. Gordon
2018 Journal of Experimental Child Psychology  
No such effect of rhythmic priming was found in two non-linguistic control tasks, suggesting a neural overlap between rhythm processing and mechanisms recruited during grammar processing.  ...  The present study aimed to understand the potential influence of musical rhythmic priming on subsequent spoken grammar task performance in children with typical development who were native speakers of  ...  Use of REDCap was made possible by Vanderbilt CTSA grant UL1 TR000445 from NCATS/NIH.  ... 
doi:10.1016/j.jecp.2018.04.007 pmid:29778278 pmcid:PMC5986615 fatcat:m3cymnekfjae7i6mx4heoqd3pm

Learning Executable Semantic Parsers for Natural Language Understanding [article]

Percy Liang
2016 arXiv   pre-print
We will see that semantic parsing is a rich fusion of the logical and the statistical world, and that this fusion will play an integral role in the future of natural language understanding systems.  ...  Semantic parsers map natural language into logical forms, the classic representation for many important linguistic phenomena.  ...  Formally, the grammar is a set of rules of the form α ⇒ β. 1 Here is a simple grammar for our running example: (R1) prime ⇒ NP[primes] (R2) 10 ⇒ NP[10] (R3) less than NP[z] ⇒ QP[(−∞, z)] (R4) NP[z1]  ... 
arXiv:1603.06677v1 fatcat:p4dwgeh5onfr7kd6mk53mls7au

Concatenation State Machines and Simple Functions [chapter]

Wojciech Debski, Wojciech Fraczak
2005 Lecture Notes in Computer Science  
We introduce a class of deterministic push-down transducers called concatenation state machine (CSM) and we study its semantic domain which is a class of parial mappings over finitely generated free monoids  ...  , called simple functions.  ...  The resulting system of equations corresponds to a context-free grammar which is a simple grammar (i.e., LL(1) grammar under Greibach normal form, [1] [2] [3] ).  ... 
doi:10.1007/978-3-540-30500-2_11 fatcat:y3x2uy5vefhznfhl7756wk4or4

Even linear simple matrix languages: formal language properties and grammatical inference

Henning Fernau
2002 Theoretical Computer Science  
even linear simple matrix grammars as basic and uniform learning target.  ...  Moreover, we investigate formal language properties of even linear simple matrix languages and related language classes.  ...  Stephan, and Y. Takada. The talk at COCOON'99 conference [19] (presenting the grammatical inference part of this paper) was given by K. Reinhardt.  ... 
doi:10.1016/s0304-3975(01)00313-9 fatcat:mylev7nygnct7curhqp5nccl4e
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