Next: Team behaviour in extended
Up: Team behaviour of simple
Previous: Team behaviour of simple
  Contents
Definitions and previous
results in the non-extended case
The first team derivation mode which was studied for simple eco-grammar
systems is the derivation mode
, where
in each step exactly
agents have to work.
Definition 3.1
Consider a simple eco-grammar system
![\ensuremath{\Sigma=(\:V_E,P_E,R_1,\ldots,R_n,
\omega\:)}](img105.gif)
.
We say that
![$ x$](img22.gif)
directly derives
![$ y$](img53.gif)
in
![$ \Sigma$](img110.gif)
in derivation mode
![$ =k$](img12.gif)
(with
![$ x,y\in {V_E}^*$](img112.gif)
and
![$ 1\leq k\leq n$](img152.gif)
, written as
![$ x\ensuremath{\stackrel{=k}{{\Longrightarrow}_{\Sigma}}}y$](img153.gif)
),
if
-
, with
,
,
, and
,
-
, with
,
, and
,
- there exist
different agents in
, namely
, such that
for
, and
-
or
,
where
is the
0L system of the environment.
We denote the transitive and reflexive closure of
by
.
The generated language consists of those words
which can be generated from the axiom in some derivation steps.
Definition 3.2
Consider a simple eco-grammar system
![\ensuremath{\Sigma=(\:V_E,P_E,R_1,\ldots,R_n,
\omega\:)}](img105.gif)
.
The generated language in the derivation mode
![$ =k$](img12.gif)
is the following:
In the following theorem,
we summarise the results
which are presented in [Csuhaj-Varjú and
KelemenováCsuhaj-Varjú and Kelemenová1998] and [CsimaCsima1997], where
relations between
language classes generated by simple eco-grammar systems
with different parameters
and
were examined. (The results
of [Csuhaj-Varjú and
KelemenováCsuhaj-Varjú and Kelemenová1998] are summarised and completed in [CsimaCsima1997].)
Let
denote the
class of languages generated by a simple EG system containing
agents and working in the derivation mode
.
Next: Team behaviour in extended
Up: Team behaviour of simple
Previous: Team behaviour of simple
  Contents
Csima Judit
2002-01-04