Acta Cybernetica 14 (2000) 455-459. A Note on Decidability of Reachability for Conditional Petri Nets Ferucio Laurentiiu TIPLEA * Cristina BADARAU * Abstract The aim of this note is to prove that the reachability problem for Petri nets controlled by finite automata, in the sense of [5], is decidable. 1 Introduction and preliminaries In [5] a new restriction on the transition rule of Petri nets has been introduced by associating to each transition t a language Lt from a family £ of languages. Petri nets obtained in this way have been called C-conditional Petri Nets (C-cPN, for short). In an C-cPN 7, a sequence w of transitions is a transition sequence of 7 if it is a transition sequence in the classical sense and additionally w\ G Lt for any decomposition w = witw2- In other words, the transition t is conditioned by the transition sequence previously applied. It has been proved in [6] that the reachability problem for C-cPN in the case that C contains the Dyck language and is closed under inverse homomorphisms and letter-disjoint shuffle product, is undecidable. The families of context-free, context-sensitive, recursive, recursively enumerable languages, and all the families of L-type Petri net languages satisfy the conditions above, but this is not the case of the family of regular languages; the reachability problem for C3-cPN, where £3 is the family of regular languages, remained open. In this paper we give a positive answer to this problem. The set of non-negative integers is denoted by N. For an alphabet V (that is, a nonempty finite set), V* denotes the free monoid generated by V under the operation of concatenation and A denotes the unity of V*. The elements of V* are called words over V. A language over V is any subset of V*. Given a word w G V*, |ui| denotes the length of w. A finite deterministic automaton is a 5-tuple A = (Q,V,S,qo,Qf), where Q is the set of states, V is the set of input symbols, qo G Q is the initial state, Qj C Q is the set of final states and 6 is a function from Q x V into Q. The language accepted by A is defined by L(A) = {w G V*\S(q0,w) G Qf} (the extension of <5 to 'Faculty of Computer Science,"Al. I. Cuza" University of Ia§i, 6600 Ia^i, Romania, e-mail: fItipleaQinfoiasi.ro 455