In 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.

Invited Lectures.- Algorithmic Randomness, Quantum Physics, and Incompleteness.- On the Complexity of Universal Programs.- Finite Sets of Words and Computing.- Universality and Cellular Automata.- Leaf Language Classes.- Selected Contributions.- Computational Completeness of P Systems with Active Membranes and Two Polarizations.- Computing with a Distributed Reaction-Diffusion Model.- Computational Universality in Symbolic Dynamical Systems.- Real Recursive Functions and Real Extensions of Recursive Functions.- Ordering and Convex Polyominoes.- Subshifts Behavior of Cellular Automata. Topological Properties and Related Languages.- Evolution and Observation: A Non-standard Way to Accept Formal Languages.- The Computational Power of Continuous Dynamic Systems.- Abstract Geometrical Computation for Black Hole Computation.- Is Bosco's Rule Universal?.- Sequential P Systems with Unit Rules and Energy Assigned to Membranes.- Hierarchies of DLOGTIME-Uniform Circuits.- Several New Generalized Linear- and Optimum-Time Synchronization Algorithms for Two-Dimensional Rectangular Arrays.- Register Complexity of LOOP-, WHILE-, and GOTO-Programs.- Classification and Universality of Reversible Logic Elements with One-Bit Memory.- Universal Families of Reversible P Systems.- Solving 3CNF-SAT and HPP in Linear Time Using WWW.- Completing a Code in a Regular Submonoid of the Free Monoid.- On Computational Universality in Language Equations.- Attacking the Common Algorithmic Problem by Recognizer P Systems.- On the Minimal Automaton of the Shuffle of Words and Araucarias.