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**1 - 2**of**2**### The kΩ-Optimization Distributed Meta-Level Control for Cooperation and Competition of Bounded Rational Agents

"... Abstract. The $-calculus process algebra for problem solving applies the cost performance measures to converge to optimal solutions with minimal problem solving costs. The same meta-level kΩ-optimization control can be used to find the best quality solutions (expressed as optimization problems), the ..."

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Abstract. The $-calculus process algebra for problem solving applies the cost performance measures to converge to optimal solutions with minimal problem solving costs. The same meta-level kΩ-optimization control can be used to find the best quality solutions (expressed as optimization problems), the most effective solutions (expressed as search optimization problems), or to find solutions representing the tradeoff between the best quality and least costly solutions (expressed as totally optimization problems). The total optimization is described as an instance of multiobjective optimization. In this paper we demonstrate that cooperation and competition of multiagent systems can be naturally investigated as a multiobjective optimization too.

### Computational Completeness of Interaction Machines and Turing Machines

"... In the paper we prove in a new and simple way that Interaction machines are more powerful than Turing machines. To do that we extend the definition of Interaction machines to multiple interactive components, where each component may perform simple computation. The emerging expressiveness is due to t ..."

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In the paper we prove in a new and simple way that Interaction machines are more powerful than Turing machines. To do that we extend the definition of Interaction machines to multiple interactive components, where each component may perform simple computation. The emerging expressiveness is due to the power of interaction and allows to accept languages not accepted by Turing machines. The main result that Interaction machines can accept arbitrary languages over a given alphabet sheds a new light to the power of interaction. Despite of that we do not claim that Interaction machines are complete. We claim that a complete theory of computer science cannot exist and especially, Turing machines or Interaction machines cannot be a complete model of computation. However complete models of computation may and should be approximated indefinitely and our contribution presents one of such attempts.