Cellular automata on regular rooted trees

We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts

Parallel Restructuring and Evaluation of Expressions

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-84-C-0149National Science Foundation / CCR-87-0380

Propositional Dynamic Logic with Converse and Repeat for Message-Passing Systems

The model checking problem for propositional dynamic logic (PDL) over message sequence charts (MSCs) and communicating finite state machines (CFMs) asks, given a channel bound $B$, a PDL formula $\varphi$ and a CFM $\mathcal{C}$, whether every existentially $B$-bounded MSC $M$ accepted by $\mathcal{C}$ satisfies $\varphi$. Recently, it was shown that this problem is PSPACE-complete. In the present work, we consider CRPDL over MSCs which is PDL equipped with the operators converse and repeat. The former enables one to walk back and forth within an MSC using a single path expression whereas the latter allows to express that a path expression can be repeated infinitely often. To solve the model checking problem for this logic, we define message sequence chart automata (MSCAs) which are multi-way alternating parity automata walking on MSCs. By exploiting a new concept called concatenation states, we are able to inductively construct, for every CRPDL formula $\varphi$, an MSCA precisely accepting the set of models of $\varphi$. As a result, we obtain that the model checking problem for CRPDL and CFMs is still in PSPACE

Reduction of Depth of Boolean Networks with a Fan-In Constraint

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / DAAB-07-72-C-025

Linearly bounded infinite graphs

Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural class of infinite automata representing their observable computational behavior, called linearly bounded graphs. These automata naturally accept the same languages as the linearly bounded machines defining them. We present some of their structural properties as well as alternative characterizations in terms of rewriting systems and context-sensitive transductions. Finally, we compare these graphs to rational graphs, which are another class of automata accepting the context-sensitive languages, and prove that in the bounded-degree case, rational graphs are a strict sub-class of linearly bounded graphs

Can a supernova be located by its neutrinos?

A future core-collapse supernova in our Galaxy will be detected by several neutrino detectors around the world. The neutrinos escape from the supernova core over several seconds from the time of collapse, unlike the electromagnetic radiation, emitted from the envelope, which is delayed by a time of order hours. In addition, the electromagnetic radiation can be obscured by dust in the intervening interstellar space. The question therefore arises whether a supernova can be located by its neutrinos alone. The early warning of a supernova and its location might allow greatly improved astronomical observations. The theme of the present work is a careful and realistic assessment of this question, taking into account the statistical significance of the various neutrino signals. Not surprisingly, neutrino-electron forward scattering leads to a good determination of the supernova direction, even in the presence of the large and nearly isotropic background from other reactions. Even with the most pessimistic background assumptions, SuperKamiokande (SK) and the Sudbury Neutrino Observatory (SNO) can restrict the supernova direction to be within circles of radius $5^\circ$ and $20^\circ$, respectively. Other reactions with more events but weaker angular dependence are much less useful for locating the supernova. Finally, there is the oft-discussed possibility of triangulation, i.e., determination of the supernova direction based on an arrival time delay between different detectors. Given the expected statistics we show that, contrary to previous estimates, this technique does not allow a good determination of the supernova direction.Comment: 11 pages including 2 figures. Revised version corrects typos, adds some brief comment