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Weak Growing ContextSensitive Grammars
, 1995
"... Well investigated are growing contextsensitive languages (GCSL), i. e. languages defined by grammars that have only growing rules, where the left side of a growing rule is shorter than its right side. GCSL is characterized by quasi growing contextsensitive grammars (QGCSG), i. e. the rules therein ..."
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Well investigated are growing contextsensitive languages (GCSL), i. e. languages defined by grammars that have only growing rules, where the left side of a growing rule is shorter than its right side. GCSL is characterized by quasi growing contextsensitive grammars (QGCSG), i. e. the rules therein are growing only with respect to a valuation of all the strings by a homomorphism to natural numbers with addition. In this paper we introduce weak growing contextsensitive grammars (WGCSG), i. e. grammars that are growing with a weighted valuation of all strings, where the weights are the values of a position valuation. Here we evaluate a string by summing up every product of a symbol value with its position value. For every position valuation which does not agree with the beginning of any exponential function, the corresponding class of WGCSGs characterizes CSL, shown by a somehow tricky proof. Such a valuation function is called unsteady. On the other hand all WGCSG related to steady ...
The Emergent Computational Potential of Evolving Artificial Living Systems
, 2002
"... The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such org ..."
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The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such organisms. We describe a scenario in which an artificial living (AL) system is involved in a potentially infinite, unpredictable interaction with an active or passive environment, to which it can react by learning and adjusting its behaviour. By making use of sequences of cognitive transducers one can also model the evolution of AL systems caused by `architectural' changes. Among the examples are `communities of agents', i.e. by communities of mobile, interactive cognitive transducers.
Code Problems on Traces
 Szalas (Eds.), Proc. 21st Internat. Sympos. on Mathematical Foundations of Computer Science (MFCS'96), Lecture Notes in Comput. Sci
, 1996
"... . The topic of codes in the framework of trace monoids leads to interesting and challenging decision problems of combinatorial flavour. We give an overview of the current state of some basic questions in this field. Among these, we consider the existence problem for strong codings, cliquepreserving ..."
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. The topic of codes in the framework of trace monoids leads to interesting and challenging decision problems of combinatorial flavour. We give an overview of the current state of some basic questions in this field. Among these, we consider the existence problem for strong codings, cliquepreserving morphisms and the unique decipherability problem (code problem). 1 Introduction Free partially commutative monoids [7] offer a mathematically sound framework for modelling and analyzing concurrent systems. This was made popular by the work of Mazurkiewicz. He investigated originally the behaviour of safe 1labelled Petri nets [17] and the computer science community quickly recognized the importance of this work. The basic concept is to consider a system as a finite set of actions \Sigma , together with a fixed symmetric independence relation I ` \Sigma \Theta \Sigma , denoting pairs of actions which can be scheduled in parallel. In the setting defined by a pair (\Sigma ; I) we identify seq...
The Emergent Computational Potential of Evolving Artificial Living Systems ∗
"... The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such org ..."
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The computational potential of artificial living systems can be studied without knowing the algorithms that govern their behavior. Modeling single organisms by means of socalled cognitive transducers, we will estimate the computational power of AL systems by viewing them as conglomerates of such organisms. We describe a scenario in which an artificial living (AL) system is involved in a potentially infinite, unpredictable interaction with an active or passive environment, to which it can react by learning and adjusting its behaviour. By making use of sequences of cognitive transducers one can also model the evolution of AL systems caused by ‘architectural ’ changes. Among the examples are ‘communities of agents’, i.e. by communities of mobile, interactive cognitive transducers. Most AL systems show the emergence of a computational power that is not present at the level of the individual organisms. Indeed, in all but trivial cases the resulting systems possess a superTuring computing power. This means that the systems cannot be simulated by traditional computational models like Turing machines and may in principle solve noncomputable tasks. The results are derived using nonuniform complexity theory. “What we can do is understand some of the general principles of how living things work, and why they exist at all.” From: R. Dawkins, The Blind Watchmaker, 1986. 1