## Unconventional Models of Computation, UMC’2K: Proceedings of the Second International Conference on Unconventional Models of Computation, (UMC’2K)I. Antoniou, C.S. Calude, M.J. Dinneen The Second International Conference on Unconventional Models of Compu UMC'2K, organized by the Centre for Discrete Mathematics and The tation, oretical Computer Science, the International Solvay Institutes for Physics and Chemistry and the Vrije Universiteit Brussel Theoretical Physics Division was held at Solvay Institutes from 13 to 16 December, 2000. The computers as we know them today, based on silicon chips, are get ting better and better, cheaper and cheaper, and are doing more and more for us. Nonetheless, they still give rise to frustrations because they are unable to cope with many tasks of practical interest: Too many problems are effectively intractable. A simple example: cyber movie networks face the near impossible task of building a brand in a computing and communication almost vacuum. Fortunately, for billions of years nature itself has been "computing" with molecules and cells. These natural processes form the main motivation for the construction of radically new models of computation, the core interest of our conference. The ten invited speakers at the conference were: 1. Accardi (Rome, Italy), S. Bozapalidis (Thessaloniki, Greece), K. Gustafson (Boulder, USA), T. Head (Binghamton, USA), T. Hida (Nagoya, Japan), v. Ivanov (Dubna, Russia), G. Piiun (Bucharest, Romania), G. Rozenberg (Lei den, the Netherlands). H. Siegelmann (Haifa, Israel), and E. Winfree (Caltech, USA). The Programme Committee consisting ofM. Amos (Liverpool, UK), I. An toniou (Co-chair, Brussels, Belgium), S. Bozapalidis (Thessaloniki, Greece), G. |

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### Contents

On the OhyaMasuda Quantum SAT Algorithm | 1 |

Computational Methods and Tools for Modeling and Analysis of Complex Processes | 10 |

Quantum Recognizable Tree Functions | 25 |

An Unconventional Computational Linear Algebra | 48 |

Splicing Systems Aqueous Computing and Beyond | 68 |

Some Methods of Computation in White Noise Calculus | 85 |

Attacking NPComplete Problems | 94 |

DNA Processing in Ciliates The Wonders of DNA Computing in vivo | 116 |

Upper and Lower Bounds on ContinuousTime Computation | 135 |

P Systems with Valuations | 154 |

The Quantum Domain As a Triadic Relay | 167 |

On P Systems with Active Membranes | 187 |

Spatial Computing on SelfTimed Cellular Automata | 202 |

Inaccessibility in Decision Procedures | 215 |

On the Power of Nonlinear Mappings in Switching Map Systems | 234 |

The New Frontier | 248 |

Macroscopic Molecular Computation with Gene Networks | 119 |

In Vitro Transcriptional Circuits | 121 |

Parallelizing with Limited Number of Ancillae | 123 |

Quantum Computation Relative to Oracles | 273 |

Solving NPComplete Problems Using P Systems with Active Membranes | 289 |

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### Common terms and phrases

active membranes algebra algorithms ancillae applied automaton Boolean boundary dimension bounded box-counting dimension cell Cellular Automata classical clauses CN gates complex computational power Computer Science consisting of CN corresponding decision procedure defined denote DNA Computing dynamical systems eigenvalues elementary evolution rules finite graph halting set Hamiltonian Path Problem Henon map Hermitian Hilbert space initial input integration iteration Lemma linear matrix maximum independent set membrane membrane division membrane structure molecules multisets node nonlinear NP-complete NP-complete problems objects operator trigonometry oracle output P-systems parallel Paun physical polarity polynomial Proof Proposition PSPACE quantum circuit consisting quantum computation qubit random real number realized recognizable recursive functions result Rozenberg rules of type self-timed signal simulate skin membrane solve step string switching map systems Theorem theory tion transformation tree Turing machines unitary operator variables vectors