Two collapsing hierarchies of subregularly tree controlled languages

Tree Valence Controlled Grammars

“…We consider a successful derivation ′ in ′ . Any derivation in ′ starts with applying 0 ∶ 0 , then any production from (2) -(3) can be applied with satisfying the production (4). Yet, as soon as production (5) is applied, matrices (2) further cannot be applied.…”

“…Further, they continued to study on the hierarchy of such grammars where they presented several ideas of controlling derivation trees levels of context-free grammar by the regular languages with restricted complexity, by finite union of monoids and by languages accepting deterministic finite automaton (DFA) with mostly prescribed number of states. As a result, they proved that at level 2, the corresponding hierarchy of TC languages already collapsed [4].…”

Structurally and Arithmetically Controlled Grammars

“…The families of all tree The subregularly TC grammars have achieved a good result in generative power as showed in subsequent theorems. The investigation of subregularly TC grammars does not stop there where in the same year in [32] by Dassow and Truthe again continued to study on the hierarchy of subregularly TC languages. In that paper, they presented several ideas of controlling derivation trees levels of context-free grammar by the regular languages with restricted complexity, by finite union of monoids and by languages accepting deterministic finite automata with mostly prescribed number of states.…”

“…Despite their diversity, all of the introduced regulated grammars can be classified into several types depending on their common characteristics like (1) control by prescribed sequences such as matrix grammars [12][13][14][15][16][17], regularly controlled grammars [18], vector grammars [19], different variants of Petri net controlled grammars [20][21][22][23][24][25][26] and Parikh vector controlled grammars [27], (2) control by context conditions such as conditional grammars and ordered grammars [28], random context grammars [29], tree controlled grammars [30][31][32][33][34][35][36][37], semi-conditional grammars [38] and string-regulated graph grammars [39], (3) control by computed sequences such as programmed grammars [40] and valence grammars [41][42][43][44][45][46][47], (4) control by memory such as indexed grammars [48], (5) control by partial parallelism such as scattered context grammars [49], Russian parallel grammars [50], Indian parallel grammars [51] and global indexed grammars [52] and many other regulated grammars ...…”

Conditional Lindenmayer systems with subregular conditions: The non-extended case

“…Investigations on the change of the generative power, if subregular restrictions defined by combinatorial and algebraic properties are done in [4] for regularly controlled grammars, in [8,10] for conditional grammars, in [16] for tree controlled grammars, in [11,25] for networks with evolutionary processors, and in [7,12] for contextual grammars. Results on the effect of subregular restrictions given by bounds on the number of states/nonterminals/productions necessary to accept/generate the regular language can be found in [6] for regularly controlled grammars, in [5] for conditional grammars, in [15] for tree controlled grammars, in [17] for networks with evolutionary processors, and in [12,26] for contextual grammars. In this paper we discuss conditional tabled Lindenmayer systems (conditional T0L systems, for short).…”