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Defining families of trees with E0L grammars

1991
*
Discrete Applied Mathematics
*

Wood,

doi:10.1016/0166-218x(91)90100-b
fatcat:fml7quvum5h4vpprscin5ieqle
*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. ...##
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How to get rid of pseudoterminals

1980
*
Information and Control
*

We investigate the role

doi:10.1016/s0019-9958(80)90515-x
fatcat:6lmrqwtlnfht5jibshbf62lhu4
*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) . ...##
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Two collapsing hierarchies of subregularly tree controlled languages

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. ...

##
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Membrane Systems Using Noncooperative Rules with Unconditional Halting
[chapter]

2009
*
Lecture Notes in Computer Science
*

consisting

doi:10.1007/978-3-540-95885-7_10
fatcat:qf7iva3vtjhndndhgcwghieray
*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] . ...##
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Complexity of E0L structural equivalence

1995
*
RAIRO - Theoretical Informatics and Applications
*

The set

doi:10.1051/ita/1995290604711
fatcat:srktc66sznel7k73r674kxevhy
*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. ...##
###
Decidability of structural equivalence of E0L grammars

1991
*
Theoretical Computer Science
*

The set

doi:10.1016/0304-3975(91)90176-3
fatcat:dw75hztgxzdhjguf62dp2kv3ru
*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*. ...##
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Parallel Hyperedge Replacement Grammars
[article]

2021
*
arXiv
*
pre-print

generated by various

arXiv:2101.02310v1
fatcat:qivtxhs2eje5vclhhnq2iohfji
*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. ...##
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Applications of scheduling theory to formal language theory

1985
*
Theoretical Computer Science
*

We approach the study

doi:10.1016/0304-3975(85)90092-1
fatcat:3r2kay6gkvetnm6iqrorxazyku
*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*. ...##
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On ambiguity in E0L systems

1980
*
Theoretical Computer Science
*

It is demonstrated that the degree

doi:10.1016/0304-3975(80)90025-0
fatcat:kdns7ocztzaofjy7uedi7bo7dq
*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. ...##
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Structured OL-systems
[chapter]

1974
*
Lecture Notes in Computer Science
*

The systems, also called developmental systems, were introduced in connection

doi:10.1007/3-540-06867-8_17
fatcat:mgdfyaseqnhtpnai4ei3auapji
*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. ...##
###
Beginnings
[chapter]

1980
*
Lecture Notes in Computer Science
*

A number

doi:10.1007/3-540-10233-7_1
fatcat:m57ng67jsjez3prkivij34zaaq
*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. ...##
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Nonterminal complexity of tree controlled grammars

2011
*
Theoretical Computer Science
*

It is proved that the number

doi:10.1016/j.tcs.2011.06.033
fatcat:7zhugq7fmngmzdz6ufkhmza4vq
*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. ...##
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Complexity of EOL structural equivalence
[chapter]

1994
*
Lecture Notes in Computer Science
*

The set

doi:10.1007/3-540-58338-6_105
fatcat:dmgvqskxynao7hpoomzkjngvhm
*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. ...##
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Synchronized E0L forms

1980
*
Theoretical Computer Science
*

Turning to the syntax analysis

doi:10.1016/0304-3975(80)90026-2
fatcat:kr2j2tugtfahtml5zt5ccpq2p4
*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. ...##
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On the synchronized derivation depth of context-free grammars

2009
*
Theoretical Computer Science
*

This measure differs from the earlier considered synchronization depth in that it counts the depth

doi:10.1016/j.tcs.2009.03.031
fatcat:c2f3p34kgfeahdacqqk5jjpp5a
*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*. ...
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