Victor Mitrana

Networks of evolutionary processors

Abstract. In this paper we consider networks of evolutionary processors as language generating and computational devices. When the filters are regular languages one gets the computational power of Turing machines with networks of size at most six, depending on the underlying graph. When the filters are defined by random context conditions, we obtain an incomparability result with the families of regular and context-free languages. Despite their simplicity, we show how the latter networks might be used for solving an NP-complete problem, namely the “3-colorability problem”, in linear time and linear resources (nodes, symbols, rules).

Solving NP-Complete Problems With Networks of Evolutionary Processors

We propose a computational device based on evolutionary rules and communication within a network, similar to that introduced in [4], called network of evolutionary processors. An NP-complete problem is solved by networks of evolutionary processors of linear size in linear time. Some furher directions of research are finally discussed.

Hybrid networks of evolutionary processors

A hybrid network of evolutionary processors consists of several processors which are placed in nodes of a virtual graph and can perform one simple operation only on the words existing in that node in accordance with some strategies. Then the words which can pass the output filter of each node navigate simultaneously through the network and enter those nodes whose input filter was passed. We prove that these networks with filters defined by simple random-context conditions, used as language generating devices, are able to generate all linear languages in a very efficient way, as well as non-context-free languages. Then, when using them as computing devices, we present two linear solutions of the Common Algorithmic Problem.

Evolutionary systems : a language generating device inspired by evolving communities of cells

Abstract. We introduce a language generating device based on string operations suggested by the evolution of cell populations, called evolutionary system. Cells are represented by strings which describe their DNA sequences. The cell community evolves according to gene mutations and cell divison defined by operations on strings. The paper deals with the generative power of these mechanisms (a characterization of the class of recursively enumerable languages is presented) and the dynamics of the string population. A connection between the growth function of D0L systems and the population growth relation of evolutionary systems is also given.

Where Mathematics, Computer Science, Linguistics and Biology Meet

There are not many interdisciplinary scientific fields as formal language theory. In this volume, it is presented as the very intersection point between Mathematics, Computer Science, Linguistics and Biology. The book is a collection of papers going deep into classical topics in computer science inspired formal languages, as well as other ones showing new concepts and problems motivated in linguistics and biology. The papers are organized in four sections: Grammars and Grammar Systems, Automata, Languages and Combinatorics, and Models of Molecular Computing. They clearly prove the power, wealth and vitality of the theory nowadays and sketch some trends for its future development. The volume is intended for an audience of computer scientists, computational linguists, theoretical biologists and any other people interested in dealing with the problems and challenges of interdisciplinarity.

Hybrid networks of evolutionary processors are computationally complete

Abstract.A hybrid network of evolutionary processors (an HNEP) consists of several language processors which are located in the nodes of a virtual graph and able to perform only one type of point mutations (insertion, deletion, substitution) on the words found in that node, according to some predefined rules. Each node is associated with an input and an output filter, defined by some random-context conditions. After applying in parallel a point mutation to all the words existing in every node, the new words which are able to pass the output filter of the respective node navigate simultaneously through the network and enter those nodes whose input filter they are able to pass. We show that even the so-called elementary HNEPs are computationally complete. In this case every node is able to perform only one instance of the specified operation: either an insertion, or a deletion, or a substitution of a certain symbol. We also prove that in the case of non-elementary networks, any recursively enumerable language over a common alphabet can be obtained with an HNEP whose underlying structure is a fixed graph depending on the common alphabet only.

Accepting hybrid networks of evolutionary processors

We consider time complexity classes defined on accepting hybrid networks of evolutionary processors (AHNEP) similarly to the classical time complexity classes defined on the standard computing model of Turing machine. By definition, AHNEPs are deterministic. We prove that the classical complexity class NP equals the set of languages accepted by AHNEPs in polynomial time.

Recent advances in formal languages and applications

Basic Notation and Terminology.- Janusz Brzozowski.- Maxime Crochemore, Thierry Lecroq.- Jozef Gruska.- Tom Head, Dennis Pixton.- Lucian Ilie.- Jarkko Kari.- Satoshi Kobayashi.- Hans-Jorg Kreowski, Renate Klempien-Hinrichs, Sabine Kuske.- Mitsunori Ogihara.- Friedrich Otto.- Holger Petersen.- Shuly Wintner.- Hsu-Chun Yen.

PARALLEL FINITE AUTOMATA SYSTEMS COMMUNICATING BY STATES

An accepting device based on the communication between finite automata working in parallel is introduced. It consists of several finite automata working independently but communicating states to each other by request. Several variants of parallel communicating finite automata systems are investigated from their computational power point of view. We prove that all of them are at most as powerful as multi-head finite automata. Homomorphical characterizations of recursively enumerable languages are obtained starting from languages recognized by all variants of parallel communicating finite automata systems having at most three components. We present a brief comparison with the parallel communicating grammar systems. Some remarks suggesting that these devices might be mildly context-sensitive ones as well as a few open problems and directions for further research are also discussed.

Two complementary operations inspired by the DNA hairpin formation: Completion and reduction

We consider two complementary operations: Hairpin completion introduced in [D. Cheptea, C. Martin-Vide, V. Mitrana, A new operation on words suggested by DNA biochemistry: Hairpin completion, in: Proc. Transgressive Computing, 2006, pp. 216-228] with motivations coming from DNA biochemistry and hairpin reduction as the inverse operation of the hairpin completion. Both operations are viewed here as formal operations on words and languages. We settle the closure properties of the classes of regular and linear context-free languages under hairpin completion in comparison with hairpin reduction. While the class of linear context-free languages is exactly the weak-code image of the class of the hairpin completion of regular languages, rather surprisingly, the weak-code image of the class of the hairpin completion of linear context-free languages is a class of mildly context-sensitive languages. The closure properties with respect to the hairpin reduction of some time and space complexity classes are also studied. We show that the factors found in the general cases are not necessary for regular and context-free languages. This part of the paper completes the results given in the earlier paper, where a similar investigation was made for hairpin completion. Finally, we briefly discuss the iterated variants of these operations.