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The undecidability of form equivalence for context-free and E0L forms

Valtteri Niemi
1984 Theoretical Computer Science  
We prove that the form equivalence problem is undecidable for (a) context-free grammar forms, and (b) EOL forms. The proofs of these results are based on our investigations concerning language forms.  ...  This paper studies the decidability status of various equivalence problems in form theory. Most of our discussions concern the notion of a language form. We compare the form equivalence problem be!  ...  for a context-free grammar G, and a right-linear grammar Gz to the form equivalence problem for context-free forms. Here 'L( G,) c L( t%)?  ... 
doi:10.1016/0304-3975(84)90045-8 fatcat:dxldpzae6fcpfmuxtdbo42ty2e

Decidability of EDT0L structural equivalence

Kai Salomaa, Sheng Yu
2002 Theoretical Computer Science  
In this way we reduce the structural equivalence problem for EDT0L grammars to deciding emptiness of the tree language recognized by a tree pushdown automaton, i.e., to the emptiness problem for context-free  ...  Thus we establish that structural equivalence for EDT0L grammars can be decided e ectively. The result contrasts the known undecidability result for ET0L structural equivalence.  ...  Both syntax and structural equivalence are decidable for context-free and E0L grammars [8, 13, 15, 16, 19, 26] .  ... 
doi:10.1016/s0304-3975(01)00197-9 fatcat:2mahst2kkvduhamm7pg6g5uu4u

On fixed, terminal fixed and nonterminal fixed interpretations of E0L forms

G. Rozenberg, R. Verraedt
1981 Information and Control  
It is also proved that for each of the new defined interpretation mechanisms the form equivalence problem is undecidable.  ...  This paper presents a systematic investigation of the basic axioms of the theory of E0L forms, in particular it continues the research from Rozenberg and Verraedt.  ...  It is easily seen that all the E0L forms used in proofs of our undecidability results of this section were essentially linear context free forms under strict interpretations (see Maurer et al., 1980)  ... 
doi:10.1016/s0019-9958(81)90639-2 fatcat:tv6vqbqsufdxfhaggo52dqs5pm

Synchronized, desynchronized and coordinated E0L systems

G. Rozenberg, R. Verraedt
1980 Information and Control  
By abstracting various essential features of derivations in those systems the notions of a coordinated E0L system and a desynchronized E0L system are formulated and properties of the classes of languages  ...  This paper presents a systematic study of the phenomenon of synchronization in E0L systems.  ...  ACKNOWLED GMENTS The authors are very much indebted to the referee for very detailed and valuable comments regarding the first version of this paper.  ... 
doi:10.1016/s0019-9958(80)90708-1 fatcat:rzfasw23zzc6jhmfw5fd2eqsaq

Cumulative subject index

1978 Information and Control  
, 37, 182 Forms normal, chain free: propagation for E0L systems, 36, 309 Fourier transforms multivariate, plain and covariant, 39, 73 Function cost, finite automata with, 37, 40 entropy, and polymatroid  ...  , existence in stratified tessellation automata, 36, 234 Context-dependent tree automata new family of tree automata, 38, 81 Context free grammar forms, context sensitive lan- guages and, 39, 135  ... 
doi:10.1016/s0019-9958(78)90707-6 fatcat:3g6qa5hi2zc2lgyyvndbar65di

Decidability of structural equivalence of E0L grammars

Kai Salomaa, Sheng Yu
1991 Theoretical Computer Science  
Unfortunately, the equivalence problems for both context-free and EOL grammars are undecidable (cf. [8,9,1 a]).  ...  We say that EOL grammars G, and G2 are equivalent if L( G,) -L( G,). It is well known that equivalence is undecidable even for context-free grammars.  ... 
doi:10.1016/0304-3975(91)90176-3 fatcat:dw75hztgxzdhjguf62dp2kv3ru

L Systems [chapter]

Lila Kari, Grzegorz Rozenberg, Arto Salomaa
1997 Handbook of Formal Languages  
The equivalence problem is undecidable for P0L languages and so are the context-freeness, regularity and 0L-ness problems for E0L languages. 2 Because even simple subfamilies of IL contain nonrecursive  ...  For instance, equivalence is undecidable for context-free grammars, whereas structural equivalence, where also the derivation structures of the two grammars have to be the same, is decidable.  ... 
doi:10.1007/978-3-642-59136-5_5 fatcat:5evlmahr75dadkiqepxf7rqkf4

Interactive L systems with almost interactionless behaviour

Karel Culik, J. Karhumäki
1979 Information and Control  
Some interesting properties of e-GD2L systems are established, the main result being the decidability of the sequence equivalence problem for them. I.  ...  For this reason the most important systems for a biologist are I)0L and DIL sy'stems, the deterministic vcrsions of the basic interactionlcss and interactive systems.  ...  So the abbreviation a ~ c~ for the context-free production (x, a, y) --+ a can be used. The production of G, which arc not context-free, arc called context-sensitive.  ... 
doi:10.1016/s0019-9958(79)90094-9 fatcat:4camr7hpuze2rntpxpcjv7cbea

Decidability of operation problems for T0L languages and subclasses

Henning Bordihn, Markus Holzer, Martin Kutrib
2011 Information and Computation  
We show that for all of the above mentioned language operations, except for the Kleene closure, the corresponding operation problems of 0L and T0L languages and their propagating variants are not even  ...  We investigate the decidability of the operation problem for T0L languages and subclasses. Fix an operation on formal languages.  ...  Introduction Elementary undecidable questions for formal language families appeared first in [1] , where it was shown that the family of languages defined by context-free grammars is too wide to admit  ... 
doi:10.1016/j.ic.2010.11.008 fatcat:mxblm63rgbbb3jemgn3joozl6a

Complexity of E0L structural equivalence

Kai Salomaa, Derick Wood, Sheng Yu
1995 RAIRO - Theoretical Informatics and Applications  
Contrasting the results for context-free (CF) and EOL grammars it was shown recently [17] that the structural équivalence problem for ETOL (tabled EOL) grammars is undecidable.  ...  While it is well known that language équivalence of context-free grammars is undecidable, it was shown by McNaughton [10] , and, Paull and Unger [14] that structural équivalence can be decided effectively  ... 
doi:10.1051/ita/1995290604711 fatcat:srktc66sznel7k73r674kxevhy

Watson–Crick D0L systems: generative power and undecidable problems

Petr Sosík
2003 Theoretical Computer Science  
Finally, we show that the graph reachability problem, equivalence problems and some other problems of standard Watson-Crick D0L systems are undecidable.  ...  The model incorporates the iterated D0L-like morphism and the DNA complementarity principle represented by a letter-to-letter morphism.  ...  The growth, sequence and language equivalence problem for given standard Watson-Crick D0L systems G 1 and G 2 are all undecidable. Proof.  ... 
doi:10.1016/s0304-3975(03)00214-7 fatcat:dikvxkgfired5c226fkbjl7xqq

Iterated sequential transducers as language generating devices

Henning Bordihn, Henning Fernau, Markus Holzer, Vincenzo Manca, Carlos Martín-Vide
2006 Theoretical Computer Science  
The corresponding language families are related to the families of languages generated by Lindenmayer systems and Chomsky grammars.  ...  The hierarchy induced by the size of the state alphabet is proved to collapse to the fourth level.  ...  Acknowledgments The authors are grateful towards Gheorghe Pȃun for sharing his ideas about IFT's with us and for his support of this paper project that summarizes all previously obtained results.  ... 
doi:10.1016/j.tcs.2006.07.059 fatcat:altxtilpojaftmeso5liep6c6i

Theory of L systems: From the point of view of formal language theory [chapter]

G. Rozenberg
1974 Lecture Notes in Computer Science  
Thus the only real difference (from the language generation point of view) between (the classes of) EIL, ETOL and E0L systems on the one hand and (the classes of) type-0, context-sensitive and context-free  ...  hand is the absolutely parallel fashion of rewriting in E0L and EIL systems and the absolutely sequential fashion of rewriting in context-free and type-0 grammars. 2.3.  ... 
doi:10.1007/3-540-06867-8_1 fatcat:pymonbceyra37o37dymgntem6u

EOL and ETOL forms [chapter]

1980 Lecture Notes in Computer Science  
The major distinction between the study of L forms and grammar forms is that the natural mode of interpretation for L forms is the s-interpretation. some ~j V# ~j i J m. for in such that = -l(mj), 0 ~  ...  This chapter is devoted to the study of EOL and ETOL forms, that is L forms.  ...  The question of which context-free grammatical families are E0L form families, is partially answered.  ... 
doi:10.1007/3-540-10233-7_3 fatcat:d5ble7uzyfd4dd2fnox23qrkue

Defining families of trees with E0L grammars

Thomas Ottmann, Derick Wood
1991 Discrete Applied Mathematics  
Height equivalence is solved completely, weight equivalence remains open, and structural equivalence is solved for two special cases.  ...  We characterize EOL grammars with two nonterminals that generate exactly the sets of l-2 and 2-3 trees.  ...  The importance of this concept for context-free grammars is that structural equivalence is decidable [5] , while language equivalence is undecidable.  ... 
doi:10.1016/0166-218x(91)90100-b fatcat:fml7quvum5h4vpprscin5ieqle
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