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Defining families of trees with E0L grammars

Thomas Ottmann, Derick Wood
1991 Discrete Applied Mathematics  
Wood, Defining families of trees with EOL grammars, Discrete Applied Mathematics 32 (1991) 195-209. We consider EOL grammars as tree-generating mechanisms.  ...  We characterize EOL grammars with two nonterminals that generate exactly the sets of l-2 and 2-3 trees.  ...  Introduction We initiate the study of "context-free" rewriting systems that define well-known families of trees such as l-2 trees, 2-3 trees, brother trees, etc.  ... 
doi:10.1016/0166-218x(91)90100-b fatcat:fml7quvum5h4vpprscin5ieqle

How to get rid of pseudoterminals

W. Ainhirn
1980 Information and Control  
We investigate the role of pseudoterminals of E0L forms. This leads us to the definition of m-interpretation which avoids the introduction of additional pseudoterminals via interpretation.  ...  Finally, we consider the validity of some basic results on E0L forms under minterpretation.  ...  However, when working with E0L families, it turns out that terminal productions indeed lead to additional language families as shown in Maureretal. (1977) .  ... 
doi:10.1016/s0019-9958(80)90515-x fatcat:6lmrqwtlnfht5jibshbf62lhu4

Two collapsing hierarchies of subregularly tree controlled languages

Jürgen Dassow, Ralf Stiebe, Bianca Truthe
2009 Theoretical Computer Science  
Tree controlled grammars are context-free grammars where the associated language only contains those terminal words which have a derivation where the word of any level of the corresponding derivation tree  ...  We show that the corresponding hierarchy of tree controlled languages collapses already at the second level.  ...  To construct a tree-controlled grammar with a control language with a fixed number of states, we modify the grammar as follows.  ... 
doi:10.1016/j.tcs.2009.03.005 fatcat:nrevoac4wfalbhadob66gdrixi

Membrane Systems Using Noncooperative Rules with Unconditional Halting [chapter]

Markus Beyreder, Rudolf Freund
2009 Lecture Notes in Computer Science  
consisting of terminal objects only.  ...  The computational power of (tissue) P systems using non-cooperative rules turns out to be equivalent to that of (E)0L systems.  ...  The authors gratefully acknowledge the interesting discussions with Miguel Gutiérrez-Naranjo and Mario Pérez-Jiménez on the ideas presented in their paper [3] .  ... 
doi:10.1007/978-3-540-95885-7_10 fatcat:qf7iva3vtjhndndhgcwghieray

Complexity of E0L structural equivalence

Kai Salomaa, Derick Wood, Sheng Yu
1995 RAIRO - Theoretical Informatics and Applications  
The set of z-syntax trees, z G {s, p} of the grammar G is defined by where S f is the tree with a single node labeled by the initial nonterminal S.  ...  It is well known that context-free syntax trees can be recognized by finite tree automatons. Conversely, the family of sets of syntax trees clearly does not contain all recognizable tree languages.  ... 
doi:10.1051/ita/1995290604711 fatcat:srktc66sznel7k73r674kxevhy

Decidability of structural equivalence of E0L grammars

Kai Salomaa, Sheng Yu
1991 Theoretical Computer Science  
The set of syntax trees S(G) of an EOL grammar G = ( V, 2, S, P) is defined inductively as follows. If X E Vu 2, then the tree -with one node labeled by X belongs to S(G).  ...  Our main result is that structural equivalence of EOL grammars is decidable. To this end we define a tree automaton model that is able to recognize the structures of syntax trees of an EOL grammar.  ... 
doi:10.1016/0304-3975(91)90176-3 fatcat:dw75hztgxzdhjguf62dp2kv3ru

Parallel Hyperedge Replacement Grammars [article]

Graham Campbell
2021 arXiv   pre-print
generated by various families of parallel hyperedge replacement grammars, laying the foundations for future work in this area.  ...  In 2018, it was shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is still an open problem as to where to precisely place the word problems of  ...  I am also grateful to the anonymous reviewers for their comments on the earlier TERMGRAPH workshop proceedings version of this paper.  ... 
arXiv:2101.02310v1 fatcat:qivtxhs2eje5vclhhnq2iohfji

Applications of scheduling theory to formal language theory

Jakob Gonczarowski, Manfred K. Warmuth
1985 Theoretical Computer Science  
We approach the study of these families by investigating their computational complexity.  ...  Context-free grammars are extended to the case where it is required that at each derivation step, a fixed number k of nonterminals must be rewritten in parallel.  ...  There may, however, be a family of possible derivation forests for a given word, as defined by the grammar.  ... 
doi:10.1016/0304-3975(85)90092-1 fatcat:3r2kay6gkvetnm6iqrorxazyku

On ambiguity in E0L systems

A. Ehrenfeucht, G. Rozenberg
1980 Theoretical Computer Science  
It is demonstrated that the degree of ambiguity of a context free language K in the class of EOL systems is not larger than the degree of ambiguity of K in the class of context free grammars.  ...  A language K is said to have the negative prefix property if no word K catenated with a nonempty prefix of a word from K+ yields an element of K.  ...  Salomaa for useful comments on the first draft of this paper. They gratefully acknowledge the financial support of NSF grant number MCS79-03838.  ... 
doi:10.1016/0304-3975(80)90025-0 fatcat:kdns7ocztzaofjy7uedi7bo7dq

Structured OL-systems [chapter]

K. Čulík
1974 Lecture Notes in Computer Science  
The systems, also called developmental systems, were introduced in connection with a theory proposed to model the development of filamentous organisms.  ...  The stages of development are represented by strings of symbols correspondings to states of individual cells of an organism. The developmental instructions are modelled by grammar-like productions.  ...  A derivation in a context-free grammar can be represented as a derivation-tree which describes the structure of a string with respect to this derivation.  ... 
doi:10.1007/3-540-06867-8_17 fatcat:mgdfyaseqnhtpnai4ei3auapji

Beginnings [chapter]

1980 Lecture Notes in Computer Science  
A number of the families of context-free grammars define proper sub-families of,~(CF).  ...  Let Tree(G) = {~(y): y:S ~ x in G with x in Z*}, that is all derivation trees of G with terminal frontiers.  ... 
doi:10.1007/3-540-10233-7_1 fatcat:m57ng67jsjez3prkivij34zaaq

Nonterminal complexity of tree controlled grammars

S. Turaev, J. Dassow, M. Selamat
2011 Theoretical Computer Science  
It is proved that the number of nonterminals in tree controlled grammars without erasing rules leads to an infinite hierarchy of families of tree controlled languages, while every recursively enumerable  ...  language can be generated by a tree controlled grammar with erasing rules and at most nine nonterminals.  ...  languages (which we have taken in this paper) which led to a reduction of the number of nonterminals from fifteen to nine.  ... 
doi:10.1016/j.tcs.2011.06.033 fatcat:7zhugq7fmngmzdz6ufkhmza4vq

Complexity of EOL structural equivalence [chapter]

Kai Salomaa, Derick Wood, Sheng Yu
1994 Lecture Notes in Computer Science  
The set of z-syntax trees, z G {s, p} of the grammar G is defined by where S f is the tree with a single node labeled by the initial nonterminal S.  ...  It is well known that context-free syntax trees can be recognized by finite tree automatons. Conversely, the family of sets of syntax trees clearly does not contain all recognizable tree languages.  ... 
doi:10.1007/3-540-58338-6_105 fatcat:dmgvqskxynao7hpoomzkjngvhm

Synchronized E0L forms

H.A. Maurer, A. Salomaa, D. Wood
1980 Theoretical Computer Science  
Turning to the syntax analysis of synchro-EOL form families, we are lead into the study of ambiguity in EOL systems.  ...  These results are also in contrast with EOL forms, where even short {S, c})-forms have only a restricted characterization with respect to completeness.  ...  Similarly we can defined the notion of interpretation for two grammars G1 and G2, the family of grammars defined by 6, V?(G) and the family of languages defined by G, s(G). 138 HA. Maurer, A.  ... 
doi:10.1016/0304-3975(80)90026-2 fatcat:kr2j2tugtfahtml5zt5ccpq2p4

On the synchronized derivation depth of context-free grammars

Franziska Biegler, Kai Salomaa
2009 Theoretical Computer Science  
This measure differs from the earlier considered synchronization depth in that it counts the depth of the entire derivation tree.  ...  We consider (non-)existence of trade-offs when using synchronized grammars as opposed to non-synchronized grammars and establish lower bounds for certain classes of linear context-free languages.  ...  Now we define which derivation trees of the underlying context-free grammar are considered valid derivations of an SCF grammar.  ... 
doi:10.1016/j.tcs.2009.03.031 fatcat:c2f3p34kgfeahdacqqk5jjpp5a
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