Extended finite automata over groups

We consider a simple and natural extension of a finite automaton, namely an element of a given group is associated with each configuration. An input string is accepted if and only if the neutral element of the group is associated to a final configuration reached by the automaton. 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. We get a new characterization of the context-free languages as soon as the considered group is the binary free group. The result cannot be carried out in the deterministic case. Some remarks about other groups are also presented

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

Regulation by Valences

Valences are a very simple and yet powerful method of regulated rewriting. In this paper we give an overview on different aspects of this subject. We discuss closure properties of valence languages. It is shown that matrix grammars can be simulated by valence grammars over finite monoids. A Chomsky normal form theorem is proved for multiplicative valence grammars, thereby solving the open question of the existence of normal forms for unordered vector grammars. This also gives an alternative proof of the inclusion of context-free unordered vector languages in LOG(CFL). Moreover, we investigate valences in parallel systems, thereby solving part of open problems posted in [5, p. 267]. Remark: A short version of this paper appeared in the proceedings of the 22nd MFCS conference 1997, see [6]. Regulation by Valences 1 1 Introduction Valences were introduced in 1980 by Paun [15] as a mechanism of regulated rewriting. The original idea was to assign to a context-free core rule an integer, ..

Some Remarks on Codes Defined by Petri Nets 1 Masami Ito

Abstract: With any Petri net we associated its CPN language which consists of all sequences of transitions which reach a marking with an empty place whereas all proper prefixes of the sequence lead to positive markings. We prove that any CPN language can be accepted by a partially blind multicounter machine, and that any partially blind multicounter language is the morphic image of some CPN language. As a corollary we obtain the decidability of membership, emptiness and finiteness problem for CPN languages. We characterize the very strictly bounded regular languages, which are CPN languages, and give a condition for a Petri net, which ensures that its generated language is regular. We give a dense CPN language and prove that no dense regular language is a CPN language