Showing papers by "Alfonso Rodríguez-Patón published in 2000"

Computing with membranes: P systems with worm-objects

Abstract: We consider a combination of P systems with objects described by symbols with P systems with objects described by strings. Namely, we work with multisets of strings and consider as the result of a computation the number of strings in a given output membrane. The strings (also called worms) are processed by replication, splitting, mutation, and recombination; no priority among rules and no other ingredient is used. In these circumstances, it is proved that: (1) P systems of this type can generate all recursively enumerable sets of numbers; and moreover, (2) the Hamiltonian Path Problem in a directed graph can be solved in quadratic time, while the SAT problem can be solved in linear time. The interest of the latter result comes from the fact that it is the first time that a polynomial solution to an NP-complete problem has been obtained in the P system framework without making use of the (non-realistic) operation of membrane division.

Conditional Concatenation

Abstract: Inspired from biochemistry and DNA computing, we introduce several variants of controlled concatenation of strings and languages: a finite set of pairs of strings is given and two arbitrary strings are concatenated only when among their substrings (scattered substrings, of various forms) we can find a pair in this control set. Five types of non-iterated and iterated (like Kleene closure) conditional concatenations are considered. The closure properties of abstract families of languages (hence also of families in the Chomsky hierarchy) are settled. They are similar to the closure properties under usual concatenation and Kleene closure. A representation of regular languages in terms of these operations (and a coding) is also given. Then, we use the new concatenation operations as basic operations in Chomsky grammars: rewriting a nonterminal means concatenating a new string with the strings to the left and the right of that nonterminal, hence restricted concatenations can be used. Context-free grammars working in this restricted manner can generate non-context-free languages; in one case, characterizations of recursively enumerable or of context-sensitive languages are obtained, depending on using or not erasing rules. Some topics for further research are also suggested.