The Determinacy of Context-Free Games

We prove that the determinacy of Gale-Stewart games whose winning sets are accepted by real-time 1-counter B\"uchi automata is equivalent to the determinacy of (effective) analytic Gale-Stewart games which is known to be a large cardinal assumption. We show also that the determinacy of Wadge games between two players in charge of omega-languages accepted by 1-counter B\"uchi automata is equivalent to the (effective) analytic Wadge determinacy. Using some results of set theory we prove that one can effectively construct a 1-counter B\"uchi automaton A and a B\"uchi automaton B such that: (1) There exists a model of ZFC in which Player 2 has a winning strategy in the Wadge game W(L(A), L(B)); (2) There exists a model of ZFC in which the Wadge game W(L(A), L(B)) is not determined. Moreover these are the only two possibilities, i.e. there are no models of ZFC in which Player 1 has a winning strategy in the Wadge game W(L(A), L(B)).Comment: To appear in the Proceedings of the 29 th International Symposium on Theoretical Aspects of Computer Science, STACS 201

Decision Problems For Turing Machines

We answer two questions posed by Castro and Cucker, giving the exact complexities of two decision problems about cardinalities of omega-languages of Turing machines. Firstly, it is $D_2(\Sigma_1^1)$-complete to determine whether the omega-language of a given Turing machine is countably infinite, where $D_2(\Sigma_1^1)$ is the class of 2-differences of $\Sigma_1^1$-sets. Secondly, it is $\Sigma_1^1$-complete to determine whether the omega-language of a given Turing machine is uncountable.Comment: To appear in Information Processing Letter

Reverse Evolution: Driving Forces Behind the Loss of Acquired Photosynthetic Traits

BACKGROUND:The loss of photosynthesis has occurred often in eukaryotic evolution, even more than its acquisition, which occurred at least nine times independently and which generated the evolution of the supergroups Archaeplastida, Rhizaria, Chromalveolata and Excavata. This secondary loss of autotrophic capability is essential to explain the evolution of eukaryotes and the high diversity of protists, which has been severely underestimated until recently. However, the ecological and evolutionary scenarios behind this evolutionary "step back" are still largely unknown. METHODOLOGY/PRINCIPAL FINDINGS:Using a dynamic model of heterotrophic and mixotrophic flagellates and two types of prey, large bacteria and ultramicrobacteria, we examine the influence of DOC concentration, mixotroph's photosynthetic growth rate, and external limitations of photosynthesis on the coexistence of both types of flagellates. Our key premises are: large bacteria grow faster than small ones at high DOC concentrations, and vice versa; and heterotrophic flagellates are more efficient than the mixotrophs grazing small bacteria (both empirically supported). We show that differential efficiency in bacteria grazing, which strongly depends on cell size, is a key factor to explain the loss of photosynthesis in mixotrophs (which combine photosynthesis and bacterivory) leading to purely heterotrophic lineages. Further, we show in what conditions an heterotroph mutant can coexist, or even out-compete, its mixotrophic ancestor, suggesting that bacterivory and cell size reduction may have been major triggers for the diversification of eukaryotes. CONCLUSIONS/SIGNIFICANCE:Our results suggest that, provided the mixotroph's photosynthetic advantage is not too large, the (small) heterotroph will also dominate in nutrient-poor environments and will readily invade a community of mixotrophs and bacteria, due to its higher efficiency exploiting the ultramicrobacteria. As carbon-limited conditions were presumably widespread throughout Earth history, such a scenario may explain the numerous transitions from phototrophy to mixotrophy and further to heterotrophy within virtually all major algal lineages. We challenge prevailing concepts that affiliated the evolution of phagotrophy with eutrophic or strongly light-limited environments only

Approaching the Coverability Problem Continuously

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.Comment: 18 pages, 4 figure

La crisis del Narcisismo en la teoría educativa. Hacia un nuevo realismo pedagógico

A principios de los años 60, las disciplinas relacionadas con la educación cobraron una importancia hasta entonces desconocida. Además de adquirir un status de respetabilidad académica, se les reconoció importancia en el campo de la planificación económica-social. Los nuevos aires provenían de una nueva ideología, encarnada en la Alianza para el Progreso patrocinada por la Administración Kennedy, cuyo punto de partida era la convicción de que el atraso y la miseria eran superables dentro del marco capitalista. En tanto las reformas debían plantearse de forma planificada y gradual, la educación se presentaba como un instrumento clave en el diseño y puesta en práctica del proyecto. El clima internacional, expresado en la "coexistencia pacífica" ofrecía un marco adecuado para imaginar un mundo donde la beligerancia estaba controlada y las sociedades nacionales se pensaban como comunidades homogéneas. La planificación permitía en este contexto prevenir los conflictos potenciales y también asegurar en un futuro el bienestar individual y social. Como es lógico, la ciencia social prevalente en estos años no parecía preocupada demasiado por las tensiones sociales; en última instancia el análisis de la conflictividad sólo distorsionaría la óptica de asepsia y objetividad que se requiere para los expertos en planificación. No es de extrañar entonces que la comunidad científica, al menos en los países centrales compartiera extensamente el paradigma neo-positivista. En este mundo encantado, la Sociología y la Economía de la Educación invadieron la escena académica como disciplinas serias, que sustituían con un ethos modernizante a las especulaciones de los filósofos y pedagogos de viejo cuño. En España este ethos llegó tardíamente, casi con una década de retraso de la mano del Opus Dei y en una peculiar combinación de espiritualismo y materialismo tecnocrático que poco tenía que ver con las críticas que el proyecto desarrollista suscitaba ya para entonces. La nueva ideología presentaba a la educación de forma omnipotente. Para decirlo de forma gráfica y apelando a la metáfora psicoanalítica, imperaba entre los teóricos de la educación una imagen narcisista de su propia práctica, por otra parte, desentendida de los contextos históricos reales donde se aplicaba. La eficacia de la educación estaba garantizada de antemano, eficacia tanto para socializar en la perpetuación del orden social, como para seleccionar a los más aptos para desempeñar los distintos roles que la sociedad adjudicaba en virtud de las necesi dades del desarrollo económico. Así, el funcionalismo sociológico se unía a la Economía Marginalista de la educación en un matrimonio muy bien avenido, comple mentario en la división de tareas: mientras el primero informaba teóricamente de las bondades y posibilidades de la educación, la segunda se ocupaba de las cuestiones prácticas que llevarían a la planificación de los recursos humanos

Bounded Determinization of Timed Automata with Silent Transitions

Deterministic timed automata are strictly less expressive than their non-deterministic counterparts, which are again less expressive than those with silent transitions. As a consequence, timed automata are in general non-determinizable. This is unfortunate since deterministic automata play a major role in model-based testing, observability and implementability. However, by bounding the length of the traces in the automaton, effective determinization becomes possible. We propose a novel procedure for bounded determinization of timed automata. The procedure unfolds the automata to bounded trees, removes all silent transitions and determinizes via disjunction of guards. The proposed algorithms are optimized to the bounded setting and thus are more efficient and can handle a larger class of timed automata than the general algorithms. The approach is implemented in a prototype tool and evaluated on several examples. To our best knowledge, this is the first implementation of this type of procedure for timed automata.Comment: 25 page

On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems

We prove a general finite convergence theorem for "upward-guarded" fixpoint expressions over a well-quasi-ordered set. This has immediate applications in regular model checking of well-structured systems, where a main issue is the eventual convergence of fixpoint computations. In particular, we are able to directly obtain several new decidability results on lossy channel systems.Comment: 16 page

Interaction via reduction and nonlinear superconformal symmetry

We show that the reduction of a planar free spin-1/2 particle system by the constraint fixing its total angular momentum produces the one-dimensional Akulov-Pashnev-Fubini-Rabinovici superconformal mechanics model with the nontrivially coupled boson and fermion degrees of freedom. The modification of the constraint by including the particle's spin with the relative weight $n\in \N$, $n>1$, and subsequent application of the Dirac reduction procedure (`first quantize and then reduce') give rise to the anomaly free quantum system with the order $n$ nonlinear superconformal symmetry constructed recently in hep-th/0304257. We establish the origin of the quantum corrections to the integrals of motion generating the nonlinear superconformal algebra, and fix completely its form.Comment: 12 pages; typos correcte