Simple chain grammars and languages

A subclass of the LR(0)-grammars, the class of simple chain grammars is introduced. Although there exist simple chain grammars which are not LL(k) for any k>0, this new class of grammars is very closely related to the LL(1) and simple LL(1) grammars. In fact it can be shown that every simple chain grammar has an equivalent simple LL(1) grammar. Cover properties for simple chain grammars are investigated and a deterministic pushdown transducer which acts as a right parser for simple chain grammars is presented

Tightening the Complexity of Equivalence Problems for Commutative Grammars

We show that the language equivalence problem for regular and context-free commutative grammars is coNEXP-complete. In addition, our lower bound immediately yields further coNEXP-completeness results for equivalence problems for communication-free Petri nets and reversal-bounded counter automata. Moreover, we improve both lower and upper bounds for language equivalence for exponent-sensitive commutative grammars.Comment: 21 page

Invisible pushdown languages

Context free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on words. However, it is possible to restore some of these properties by making the structure of the tree visible, such as is done by visibly pushdown languages, or finite automata on trees. In this paper, we show that the structure given by such approaches remains invisible when it is read by a finite automaton (on word). In particular, we show that separability with a regular language is undecidable for visibly pushdown languages, just as it is undecidable for general context free languages

Extended macro grammars and stack controlled machines

K-extended basic macro grammars are introduced, where K is any class of languages. The class B(K) of languages generated by such grammars is investigated, together with the class LB(K) of languages generated by the corresponding linear basic grammars. For any full semi-AFL K, B(K) is a full AFL closed under iterated LB(K)-substitution, but not necessarily under substitution. For any machine type D, the stack controlled machine type corresponding to D is introduced, denoted S(D), and the checking-stack controlled machine type CS(D). The data structure of this machine is a stack which controls a pushdown of data structures from D. If D accepts K, then S(D) accepts B(K) and CS(D) accepts LB(K). Thus the classes B(K) are characterized by stack controlled machines and the classes LB(K), i.e., the full hyper-AFLs, by checking-stack controlled machines. A full basic-AFL is a full AFL K such that B(K)C K. Every full basic-AFL is a full hyper-AFL, but not vice versa. The class of OI macro languages (i.e., indexed languages, i.e., nested stack automaton languages) is a full basic-AFL, properly containing the smallest full basic-AFL. The latter is generated by the ultrabasic macro grammars and accepted by the nested stack automata with bounded depth of nesting (and properly contains the stack languages, the ETOL languages, i.e., the smallest full hyper-AFL, and the basic macro languages). The full basic-AFLs are characterized by bounded nested stack controlled machines

One-Membrane P Systems with Activation and Blocking of Rules

We introduce new possibilities to control the application of rules based on the preceding applications, which can be de ned in a general way for (hierarchical) P systems and the main known derivation modes. Computational completeness can be obtained even for one-membrane P systems with non-cooperative rules and using both activation and blocking of rules, especially for the set modes of derivation. When we allow the application of rules to in uence the application of rules in previous derivation steps, applying a non-conservative semantics for what we consider to be a derivation step, we can even \go beyond Turing"