## Machines, Computations, and Universality: 4th International Conference, MCU 2004, Saint Petersburg, Russia, September 21-24, 2004, Revised Selected PapersIn this volume, the reader will ?rst?nd the invited talks givenatthe conference. Then, in a second part, he/she will ?nd the contributions which were presented attheconferenceafterselection.Inbothcases, papersaregiveninthealphabetic order of the authors. MCU 2004 was the fourth edition of the conference in theoretical computer science, Machines, Computations and Universality, formerly, Machines etcalculs universels. The ?rst and the second editions, MCU 1995 and MCU 1998, were organized by Maurice Margenstern, respectively in Paris and in Metz (France). The third edition, MCU 2001, was the ?rst one to be organized outside France and it was held in Chi, sin? au (Moldova). Its co-organizers were Maurice Marg- sternandYuriiRogozhin.TheproceedingsofMCU2001werethe?rstto appear in Lecture Notes in Computer Science, see LNCS 2055. From its very beginning, the MCU conference has been an international s- enti?c event. For the fourth edition, Saint Petersburg was chosen to hold the meeting. The success of the meeting con?rmed that the choice was appropriate. MCU 2004 also aimed at high scienti?c standards. We hope that this v- ume will convince the reader that this tradition of the previous conferences was also upheld by this one. Cellular automata and molecular computing are well represented in this volume. And this is the case for quantum computing, formal languages and the theory of automata too. MCU 2004 also did not fail its tra- tion to provide our community with important results on Turing machines. Also a new feature of the Saint Petersburg edition was the contributions on analog models and the presence of unconventional models. |

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### Contents

Algorithmic Randomness Quantum Physics and Incompleteness | 1 |

On the Complexity of Universal Programs | 18 |

Finite Sets of Words and Computing | 36 |

Universality and Cellular Automata | 50 |

Leaf Language Classes | 60 |

Computational Completeness of P Systems with Active Membranes and Two Polarizations | 82 |

Computing with a Distributed ReactionDiffusion Model | 93 |

Computational Universality in Symbolic Dynamical Systems | 104 |

Is Boscos Rule Universal? | 188 |

Sequential P Systems with Unit Rules and Energy Assigned to Membranes | 200 |

Hierarchies of DLOGTIMEUniform Circuits | 211 |

Several New Generalized Linear and OptimumTime Synchronization Algorithms for TwoDimensional Rectangular Arrays | 223 |

Register Complexity of LOOP WHILE and GOTOPrograms | 233 |

Classification and Universality of Reversible Logic Elements with OneBit Memory | 245 |

Universal Families of Reversible P Systems | 257 |

Solving 3CNFSAT and HPP in Linear Time Using WWW | 269 |

Real Recursive Functions and Real Extensions of Recursive Functions | 116 |

Ordering and Convex Polyominoes | 128 |

Subshifts Behavior of Cellular Automata Topological Properties and Related Languages | 140 |

A Nonstandard Way to Accept Formal Languages | 153 |

The Computational Power of Continuous Dynamic Systems | 164 |

Abstract Geometrical Computation for Black Hole Computation | 176 |

Completing a Code in a Regular Submonoid of the Free Monoid | 281 |

On Computational Universality in Language Equations | 292 |

Attacking the Common Algorithmic Problem by Recognizer P Systems | 304 |

On the Minimal Automaton of the Shuffle of Words and Araucarias | 316 |

328 | |

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### Common terms and phrases

AHNEPs alphabet araucaria arithmetic hierarchy automaton block Bosco’s canonical decomposition cell cellular automata clopen sets complexity classes conﬁguration consider construction corresponding deﬁned deﬁnition denoted deterministic diﬀerent dynamical system eﬀective elements encoding energy entity equivalent exists ﬁeld ﬁnal ﬁnite ﬁnite set ﬁrst ﬁxed Fredkin circuit Fredkin gate function f given graph halting hierarchy iﬀ inﬁnite input integer L-convex polyomino language equations leaf language classes Leafp(L Lemma linear mapping Margenstern minimal multisets node objects obtain output P˘aun pair polynomial polyomino position problem proof Proposition PSPACE quantum random real recursive functions regular language resp result reversible reversible computation rules satisﬁability sequence signal simulation solution Springer-Verlag step string submonoid subset subshift symbol systems with active tape Theorem Theoretical Computer Science theory transition Turing machine universal vector word