Ralf Stiebe

Sequential grammars and automata with valances

We discuss the model of valence grammars, a simple extension of context-free grammars. We show closure properties of context-free valence languages over arbitrary monoids. Chomsky and Greibach normal form theorems and an iteration lemma for context-free valence grammars over the groups Zk are proved. The generative power of different control monoids is investigated. In particular, we show that context-free valence grammars over finite monoids or commutative monoids have the same power as valence grammars over finite groups or commutative groups, respectively.

Extended finite automata over groups

Some results from Dassow and Mitrana (Internat. J. Comput. Algebra (2000)), Griebach (Theoret. Comput. Sci. 7 (1978) 311) and Ibarra et al. (Theoret. Comput. Sci. 2 (1976) 271) are generalized for finite automata over arbitrary groups. The closure properties of these automata are poorer and the accepting power is smaller when abelian groups are considered. We prove that the addition of any abelian group to a finite automaton is less powerful than the addition of the multiplicative group of rational numbers. Thus, each language accepted by a finite automaton over an abelian group is actually a unordered vector language. Characterizations of the context-free and recursively enumerable languages classes are set up in the case of non-abelian groups. We investigate also deterministic finite automata over groups, especially over abelian groups.

The Accepting Power of Finite Automata over Groups

Some results from [2], [5], [6] are generalized for finite automata over arbitrary groups. The accepting power is smaller when abelian groups are considered, in comparison with the non-abelian groups. We prove that this is due to the commutativity. Each language accepted by a finite automaton over an abelian group is actually a unordered vector language. Finally, deterministic finite automata over groups are investigated.

GENERATIVE CAPACITY OF SUBREGULARLY TREE CONTROLLED GRAMMARS

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 belongs to a given regular language. We present some results on the power of such grammars where we restrict the regular languages to some known subclasses of the family of regular languages.

Slender Siromoney matrix languages

A Siromoney matrix grammar is a simple device for the generation of rectangular pictures. In this paper we discuss Siromoney matrix grammars whose picture language are slender, i.e., they contain only a bounded number of pictures for each size. In particular, it is shown that the slenderness decision problem is decidable for Siromoney matrix grammars with context-free rules. Moreover, some closure and decidability questions for slender Siromoney matrix languages are discussed.

Valuated and Valence Grammars: An Algebraic View

Valence grammars were introduced by Gh. P?un in [8] as a grammatical model of chemical processes. Here, we focus on discussing a simpler variant which we call valuated grammars.We give some algebraic characterizations of the corresponding language classes. Similarly, we obtain an algebraic characterization of the linear languages. We also give some Nivat-like representations of valence transductions.

Capacity Bounded Grammars and Petri Nets

A capacity bounded grammar is a grammar whose derivations are restricted by assigning a bound to the number of every nonterminal symbol in the sentential forms. In the paper the generative power and closure properties of capacity bounded grammars and their Petri net controlled counterparts are investigated.

Grammars controlled by Petri Nets

Formal language theory, introduced by Noam Chomsky in the 1950s as a tool for a description of natural languages [8–10], has also been widely involved in modeling and investigating phenomena appearing in computer science, artificial intelligence and other related fields because the symbolic representation of a modeled system in the form of strings makes its processes by information processing tools very easy: coding theory, cryptography, computation theory, computational linguistics, natural computing, and many other fields directly use sets of strings for the description and analysis of modeled systems. In formal language theory a model for a phenomenon is usually constructed by representing it as a set of words, i.e., a language over a certain alphabet, and defining a generative mechanism, i.e., a grammar which identifies exactly the words of this set. With respect to the forms of their rules, grammars and their languages are divided into four classes of Chomsky hierarchy: recursively enumerable, context-sensitive, context-free and regular.

Two collapsing hierarchies of subregularly tree controlled languages

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 belongs to a given regular language. In this paper, we consider first as control sets such regular languages which can be represented by finite unions of monoids. We show that the corresponding hierarchy of tree controlled languages collapses already at the second level. Second, we restrict the number of states allowed in the accepting automaton of the regular control language. We prove that the associated hierarchy has at most five levels.

On Grammars Controlled by Parikh Vectors

We suggest a concept of grammars with controlled derivations where the Parikh vectors of all intermediate sentential forms have to be from a given restricting set. For several classes of restricting sets, we investigate set-theoretic and closure properties of the corresponding language families.