NETWORKS OF EVOLUTIONARY PROCESSORS

A Historical Account

Gemma Bel-Enguix, M. Dolores Jim´enez-L´opez and Carlos Mart´ın-Vide

GRLMC, Rovira i Virgili University, Pl. Imperial T`arraco 1, Tarragona, Spain

Keywords:

Networks of Evolutionary Processors, Hybrid NEPs, Accepting and Generating NEPs, Applications, Imple-

mentation.

Abstract:

This paper provides a historical account of Networks of Evolutionary Processors (NEPs), a bioinspired model

of computation based in the behaviour of colonies of cells. NEPs, introduced in (Castellanos et al., 2001),

consist of several processors performing molecular operations, which are placed in an underlying graph. In

the last years, NEPs have demonstrated their generating and accepting power, as well as a good capacity for

solving hard computational problems. Whereas complexity results support the accuracy of the framework,

different variants have been introduced in order to achieve several computational properties. In the future,

NEPs can also be used as a model for research in other ﬁelds.

1 INTRODUCTION

This paper has a historical and genetic purpose. In

the following pages, we attempt to draw a generation

tree for Networks of Evolutionary Processors, high-

lighting the main developments and variants of the

model from the ﬁrst papers up to now. Two surveys

about NEPs have appeared so far in (Mart´ın-Vide and

Mitrana, 2003) and (Mart´ın-Vide and Mitrana, 2005)

with a systematic and uniform exposition of results,

perspectives and challenges of this computational de-

vice. Deﬁnitions and proofs of the main achievements

in the area can be found in such articles. However,

the main goal of this paper is to give a non-formal

explanation of the generation of these cell-inspired

computational mechanisms (Section 2) and to stress

the growing nodes of the tree, the state-of-the-art and

chief branching in every one of the subtypes (Section

3 and 4).

Being a relatively active area in theoretical com-

puter science, networks of evolutionary processors

should be a consistent formal framework for some

other ﬁelds of research. In Section 5 we explore some

attempts in this direction.

We close this general and non-formal overview of

the area portraying some challenges and suggestions

for future development of the topic (Section 6). Fi-

nally, the references of this paper intend to be an al-

most complete collection of papers and publications

on NEPs.

2 NETWORKS OF

EVOLUTIONARY

PROCESSORS: PRECEDENTS

AND INFLUENCES

The ﬁrst paper on Networks of Evolutionary Proces-

sors appeared in 2001, as the conjunction of three

main streams:

a) parallel symbolic processing given by Connection

Machines (Hillis, 1985) and logic ﬂow paradigm

(Errico and Jessope, 1994).

b) networks of parallel language processors (Csuhaj-

Varj´u and Salomaa, 1997), which are mechanisms

inspired in the precedent devices, introducing an

important modiﬁcation: data are strings of lan-

guage.

c) and natural computing motivation, based on the

optimum results obtained by DNA computing

(Adleman, 1994), and membrane and cell com-

puting (P˘aun, 2000).

Connection Machines and logic ﬂow paradigm,

as efﬁcient architectures for parallel and distributed

symbolic processing, have played a key role in the

emergence of the model of networks of evolution-

ary processors. These basic constructs present a

mechanism where several processors are placed in

a node of a complete graph, being each of them

able to handle data. In (Csuhaj-Varj´u and Salomaa,

626

Bel-Enguix G., Jiménez-López M. and Martín-Vide C. (2009).

NETWORKS OF EVOLUTIONARY PROCESSORS - A Historical Account.

In Proceedings of the International Conference on Agents and Artiﬁcial Intelligence, pages 626-631

DOI: 10.5220/0001809406260631

 SciTePress

1997), the formalism was conveniently adapted for

the generation of formal languages, starting from the

idea that data the nodes handle can be strings of

words. By this modiﬁcation the devices described

in (Hillis, 1985) and (Errico and Jessope, 1994),

became language generating contructs (Csuhaj-Varj´u

and Mitrana, 2000; Csuhaj-Varj´u and Salomaa, 2003),

named networks of parallel language processors

(Csuhaj-Varj´u and Salomaa, 1997), closely related to

Grammar Systems (Csuhaj-Varj´u et al., 1994). In the

formal language model, the processors could be any

type of generation device, not excluding molecular

based ones.

(Castellanos et al., 2001) ﬁnally introduced Net-

works of Evolutionary Processors as a natural deriva-

tion of the studies on natural and cell computing

within symbolic networks paradigm. These for-

malisms were conceived as a type of networks of

language generating systems with the particularity of

having in each node a very simple evolutionary pro-

cessor, able to perform only operations directly in-

spired in point mutations (DNA in vivo evolutionary

processes): substitution, deletion and insertion of a

base pair. The ﬁrst deﬁnition of such devices was ori-

ented to the resolution of NP problems, but later, in

several papers, NEPs were developed as a powerful

and efﬁcient system of computation.

3 GENERATING NEPs AND

HNEPs

The ﬁrst contributions on NEPs theory (Castellanos

et al., 2001; Castellanos et al., 2003) describe these

generating constructions in a general way, allowing

the processors to perform any of the molecular op-

erations: substitution, deletion, insertion. But early

in the literature, a variant is launched that introduces

constraints in the processors: Hybrid NEPs (HNEPs)

(Mart´ın-Vide et al., 203). In HNEPs, only one type of

operation is allowed in every node.

The differentiation between NEPs and HNEPs

produces two large families in the general picture of

NEPs genealogy. Although HNEPs are strictly a type

of NEPs, these two variants are the starting point of

the two main branches in the generation tree.

Several more NEPs variants have appeared from

the ﬁrst scission between NEPs/HNEPs. A num-

ber of subfamilies have been introduced in the last

years: Pictorial NEPs (PNEPs) (Mitrana et al., 2003;

Desanambika et al., 2004; Dersanambika et al.,

2005), Massive Parallel NEPs (MPNEPs) (G´omez-

Blas et al., 2008a), NEPs with ﬁltered connec-

tions (NEPFCs) (de Mingo-L´opez et al., 2005), Ex-

tended NEPs (ENEPs) (de Mingo et al., 2008), NEPs

with nodes of two types NEPs (Dassow and Truthe,

2007a; Dassow and Truthe, 2007b; Alhazov et al.,

2008) and NEPs with splicing rules (NSP) (Choud-

hary and Krithivasan, 2005a), which has other two

variants depending on the types of contexts permit-

ting/forbidding (Choudhary and Krithivasan, 2005c;

Choudhary and Krithivasan, 2005b).

The subclasses of NEPs listed above modify the

data inside the processors (PNEPs), the synchroniza-

tion of the evolution and communication steps (MP-

NEPs), the ﬁltering process (NEPFCs), the extension

of the elements than can be communicated (ENEPs),

the types of nodes (allowing only insertion-deletion,

insertion-substitution, deletion-substitution) and the

nature of rules (NSP).

Pictorial NEPs are variants of Networks of Evo-

lutionary Processors that handle data which is not a

string but a two dimensional construct.

Massive Parallel NEPs are devices in which evo-

lution and communication are performed in parallel.

These types of networks can solve NP-problems in

linear time such as NEPs.

The main idea of NEPs with Filtered Connections

is to move the ﬁlters from the processors to the con-

nections, in order to decrease the complexity of the

nodes of the graph. It has been demonstrated that

NEPFC have the same power for solving problems

than regular NEPs.

Extended NEPs aim to communicate not only the

symbolic information placed inside the nodes, but

also the evolution rules, in a way that the whole con-

ﬁguration of the system is evolving during the com-

putation. This property provides a more realistic

behaviour since operations are conceived as an ex-

changeable object as well.

NEPs with two types of nodes are formally re-

stricted deﬁnitions of NEPs due to nodes with one

of the three main operations are discarded. (Dassow

and Truthe, 2007b) proved that nodes NEPs without

insertion nodes produce only ﬁnite languages, NEPs

without deletion nodes produce only context-sensitive

languages and nodes without substitution nodes pro-

duce recursively enumerable languages.

NEPs with Splicing Rules are a variant of net-

works using splicing instead of point mutations.

Splicing is also based in the behaviour of recombi-

nant DNA, therefore the bio-inspired feature of NEPs

remains. Two subtypes of NEPs consider the exis-

tence of permitting and forbidding contexts, simulat-

ing the switching on/off of the genes in vivo for the

recombination to start.

In what refers to Generation HNEPs, a new sub-

class has been just introduced: OHNEPs (Alhazov

NETWORKS OF EVOLUTIONARY PROCESSORS - A Historical Account

627

et al., 2009), devices with a directed underlying

graph, in which strings are discarded in every node

where no operation can be performed.

4 ACCEPTING NEPs AND HNEPs

Both, NEPs and HNEPs were initially designed as

generating devices. But after the introduction of

HNEPs many papers started focusing in their Ac-

cepting power. However, after the ﬁrst type of Ac-

cepting HNEPs (Margenstern et al., 2004) was intro-

duced, many articles focused in the recognition power

of HNEPs.

Some papers tackle the capacity of AHNEPs for

solving NP-problems (Manea and Mitrana, 2007). In

(Manea, 2004; Manea, 2007), AHNEPs are used to

recognize CF languages. Moreover, a number of pa-

pers have been devoted to study the complexity and

demonstrate the universality of such devices. Exam-

ples of this line of research can be found in (Manea

et al., 2006b; Manea et al., 2007b).

One variant of AHNEPs has been introduced so

far, Timed AHNEPs (Manea, 2005), that provides the

AHNEP of a clock for regulating the number of steps

and the stopping points of the system.

In what refers to NEPs, only several subclasses of

the model have been applied to recognition, or have

been created specially for it. The ﬁrst attempts were

focused in the use of Networks with splicing pro-

cessors (Manea et al., 2005). This variant has been

proved to have the same potential for solving NP-

problems than regular NEPs (Manea et al., 2006a).

On the other hand, complexity results have been stud-

ied for the model in (Manea et al., 2007a), and also in

(Loos et al., 2008), where it is shown that accepting

networks of splicing processors (ANSPs) of size 2 are

computationally complete.

Besides, a version of Accepting NEPs with ﬁl-

tered networks has been also deﬁned (Dr˘agoi et al.,

2007), and approached with from the complexity is-

sues (Dr˘agoi and Manea, 2008).

Finally, a version combining ANSP and ANEPFC

has also been introduced, Accepting Networks

of Splicing Processors with Filtered Connections

(ANSPFC) (Castellanos et al., 2007), that attempts

simplifying Accepting Networks of Splicing Proces-

sors by moving the ﬁlters from the nodes to the edges.

A new device, accepting networks of non-

inserting evolutionary processors (ANNIEPs), has

been formalized and studied in (Dassow and Mi-

trana, 2008) with several variants. These networks

are somehow similar to the NEPs with nodes of two

types, since insertion does not exist in the nodes.

Figure 1: Generating and Accepting classes of NEPs.

5 APPLICATIONS AND

IMPLEMENTATIONS

NEPs have been developed up to the point of be-

ing able to become a model for several other ﬁelds.

Two differentapplications have been developedso far,

one of them considering the suitability of NEPs to be

used as Decision Systems (G´omez-Blas et al., 2008b;

G´omez-Blas, 2008) and Symbolic information and

rule-based behaviour make Networks of Evolutionary

Processors an efﬁcient tool to obtain decisions based

on objects present in the network.

Another idea has been to apply the accepting

power of HNEPs to the parsing of natural languages

(Bel-Enguix and Jim´enez-L´opez, 2005). This is a

challenging and promising topic, but its main issues,

like the optimization and the complexity for every

ICAART 2009 - International Conference on Agents and Artificial Intelligence

628

type of sentences, remain to be studied yet.

There is still a lack of computational implementa-

tions of the theoretical constructions. An implemen-

tation of Massive Parallel NEPs has been already pre-

sented (D´ıaz et al., 2007). There exist also at least

two Java implementations (D´ıaz et al., 2008; Ortega,

2009), as well as several ongoing works dealing with

the same objective: to achieve computational applica-

tions able to operate with data as the theoretical con-

structs of NEPs do.

6 FINAL REMARKS

From the introduction of the ﬁrst models of NEPs,

such devices have shown their efﬁciency and optimal-

ity in both, generation and recognition of languages,

as well as their capacity to solve hard computational

problems. Some important computational properties

have been proved, and the issues of optimization and

complexity have been tackled in a number of pa-

pers. Several variants have been introduced for im-

proving the generating and accepting power of NEPs,

performing modiﬁcations in different elements of the

systems (nodes, underlying graph, rules, input data,

ﬁlters), demonstrating again their ﬂexibility.

The main open ﬁeld of research for the future is

to build models of computation based on NEPs that

can work as a framework in other areas, such as game

theory, linguistics or engineering. From the modular

theories of mind to automatic learning or hardware

implementation, a wide area of applications should

be explored for optimizing and spreading this bio-

inspired cooperative model of computing.

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